FIELD

[0001] Aspects of embodiments of the present disclosure relate to the field of sensors systems and methods for six-degree of freedom pose estimation of objects in a scene, including deformable objects located in the scene.

BACKGROUND

[0002] In many areas of automation, such as robotics, sensors are used to determine the physical relationship of objects in the real world. For example, robotic systems often use sensing systems to measure the locations of various physical objects in order to, for example, grasp an object that may arrive at a variety of orientations, reorient the object into a desired position, and connect the object to another object. The position and orientation of an object with respect to a reference coordinate system may be referred to as a “pose” and, in a three-dimensional coordinate system, generally includes six degrees of freedom — rotation around three axes and translation along the three axes.

SUMMARY

[0003] Aspects of embodiments of the present disclosure relate to the field of sensors, in particular systems and methods for performing measurements of the poses of objects in a scene.

[0004] According to one embodiment of the present disclosure, a method for estimating a pose of a deformable object includes: receiving, by a processor, a plurality of images depicting the deformable object from multiple viewpoints; computing, by the processor, one or more object-level correspondences and a class of the deformable object depicted in the images; loading, by the processor, a 3-D model corresponding to the class of the deformable object; aligning, by the processor, the 3-D model to the deformable object depicted in the plurality of images to compute a six-degree of freedom (6-DoF) pose of the object; and outputting, by the processor, the 3-D model and the 6-DoF pose of the object.

[0005] The loading the 3-D model may include loading the 3-D model from a library including 3-D models of a plurality of different classes of objects.

[0006] The 3-D model may include a surface texture, and the aligning the 3-D model may include: computing, by the processor, a plurality of uv correspondence maps between the surface texture of the 3-D model and corresponding ones of the plurality of images; matching, by the processor, correspondences between the images and locations in 3-D coordinate space to compute an initial deformation and pose of the 3-D model; and updating, by the processor, a plurality of locations of a plurality of vertices of the 3-D model to deform the 3-D model to match the images of the object.

[0007] The computing the uv correspondence maps may include supplying the images to a trained neural network.

[0008] The computing the uv correspondence maps may include supplying the images to a keypoint detector and detecting corresponding locations of keypoints in the images and in the surface texture of the 3-D model.

[0009] The updating the locations of the vertices may be subject to physical constraints on the vertices, the physical constraints being specified in the 3-D model. [0010] The loading the 3-D model may include: loading the 3-D model from a library of 3-D models including a collection of 3-D models corresponding to the class of the deformable object, the 3-D models of the collection representing different physical configurations of an object of the class; and selecting the 3-D model based on a closest matching model from the collection of 3-D models of corresponding to the class.

[0011] The aligning the 3-D model may include: refining a deformation of the 3-D model selected from the collection of 3-D models by updating a plurality of vertex positions of a plurality of vertices to match appearances of the object in the images captured from the multiple viewpoints.

[0012] The collection of 3-D models may include a plurality of synthesized 3-D modes generated from an initial 3-D model corresponding to the class of the deformable object in one configuration by: generating a first scene including the initial 3-D model deformed into a first deformed 3-D model in accordance with a physics simulation engine under a plurality of simulation conditions; perturbing the simulation conditions to produce a plurality of perturbed simulation conditions; and rendering a second scene including the initial 3-D model deformed into a second deformed 3-D model in accordance with the physics simulation engine under the perturbed simulation conditions.

[0013] The collection of 3-D models may include a plurality of captured 3-D models of a physical object of the class of the deformable object, the captured 3-D models corresponding to captures of the physical object deformed into a plurality of configurations.

[0014] The aligning the 3-D model may include refining a plurality of vertex positions of a plurality of vertices of the 3-D model to match appearances of the object in the images captured from the multiple viewpoints. [0015] The refining the plurality of vertex positions may be performed based on minimizing a loss function E including the sum of a first component E _x and a second component E ₂ , wherein E _x represents pixel-level differences between an appearance of the object in the images and an appearance of the object in renderings of the 3-D model in a current pose from viewpoints corresponding to the images, and wherein E ₂ represents a degree of alignment of a silhouette of the object in the images and a silhouette of the 3-D model in the renderings of the 3-D model from the viewpoints corresponding to the images.

[0016] The renderings may be generated from the 3-D model by a pipeline including a differentiable Tenderer, and the plurality of vertex positions may be updated by backpropagating errors computed by the loss function E through the pipeline including the differentiable Tenderer.

[0017] The refining the plurality of positions of the vertices may be performed by a transformation neural network trained to compute a deformed 3-D model based on an input canonical 3-D model and the images of the object, the transformation neural network including: a feature extraction network trained to extract multiscale features from the images; and a graph convolutional neural network trained to generate the deformed 3-D model from the multiscale features and the input canonical 3-D model. [0018] The transformation neural network may be trained based on training data including a plurality of training samples, each of the training samples including a 3-D model deformed in accordance with a generated scene and multi-view renderings of the 3-D model corresponding to images rendered from different virtual viewpoints. [0019] The aligning the 3-D model may include updating a current pose to minimize a loss function E including the sum of a first component E _x and a second component E ₂ , wherein E _x represents pixel-level differences between an appearance of the object in the images and an appearance of the object in renderings of the 3-D model in the current pose from viewpoints corresponding to the images, and wherein E ₂ represents a degree of alignment of a silhouette of the object in the images and a silhouette of the 3-D model in the renderings of the 3-D model from the viewpoints corresponding to the images.

[0020] The first component E _x of the loss function E may be where I _n is an image from viewpoint n among N viewpoints, R _n (M ) is a rendering of the 3-D model M from viewpoint n, and the 3-D model M is a function of translation and rotation parameters of the current pose. [0021] The first component E _t of the loss function E may include differences between rendered surface normals of the 3-D model and images corresponding to surface normals maps of surfaces.

[0022] The surface normals maps may be computed from polarization raw frames.

[0023] The second component E ₂ of the loss function E may be: wherein S _pn is the silhouette of the 3-D model as it appears in a rendering from an n- th viewpoint R _n (M) and S _n is the silhouette of the object as it appears in the image I _n from the n-th viewpoint, wherein the 0 operator is a pixel-wise product operator, and wherein the 0 operator is a pixel-wise addition operator.

[0024] The images may include polarization raw frames.

[0025] According to one embodiment of the present disclosure, a system for estimating a pose of a deformable object includes: a camera system configured to capture images of a scene from multiple viewpoints; a processor configured to receive the images of the scene from the camera system; and memory storing instructions that, when executed by the processor, cause the processor to: receive a plurality of images depicting the deformable object from multiple viewpoints; compute one or more object-level correspondences and a class of the deformable object depicted in the images; load a 3-D model corresponding to the class of the deformable object; align the 3-D model to the deformable object depicted in the plurality of images to compute a six-degree of freedom (6-D0F) pose of the object; and output the 3-D model and the 6-D0F pose of the object.

[0026] The instructions to load the 3-D model include instructions that, when executed by the processor, cause the processor to load the 3-D model from a library including 3-D models of a plurality of different classes of objects.

[0027] The 3-D model may include a surface texture, and the instructions to align the 3-D model may include instructions that, when executed by the processor, cause the processor to: compute a plurality of uv correspondence maps between the surface texture of the 3-D model and corresponding ones of the plurality of images; match correspondences between the images and locations in 3-D coordinate space to compute an initial deformation and pose of the 3-D model; and update a plurality of locations of a plurality of vertices of the 3-D model to deform the 3-D model to match the images of the object.

[0028] The instructions to compute the uv correspondence maps may include instructions that, when executed by the processor, cause the processor to supply the images to a trained neural network. [0029] The instructions to compute the uv correspondence maps may include instructions that, when executed by the processor, cause the processor to: supply the images to a keypoint detector and to detecting corresponding locations of keypoints in the images and in the surface texture of the 3-D model.

[0030] The instructions to update the locations of the vertices may include instructions that, when executed by the processor, cause the processor subject the update to physical constraints on the vertices, the physical constraints being specified in the 3-D model.

[0031] The instructions to load the 3-D model may include instructions that, when executed by the processor, cause the processor to: load the 3-D model from a library of 3-D models including a collection of 3-D models corresponding to the class of the deformable object, the 3-D models of the collection representing different physical configurations of an object of the class; and select the 3-D model based on a closest matching model from the collection of 3-D models of corresponding to the class. [0032] The instructions to align the 3-D model may include instructions that, when executed by the processor, cause the processor to: refine a deformation of the 3-D model selected from the collection of 3-D models by updating a plurality of vertex positions of a plurality of vertices to match appearances of the object in the images captured from the multiple viewpoints.

[0033] The collection of 3-D models includes a plurality of synthesized 3-D modes generated from an initial 3-D model corresponding to the class of the deformable object in one configuration by: generating a first scene including the initial 3-D model deformed into a first deformed 3-D model in accordance with a physics simulation engine under a plurality of simulation conditions; perturbing the simulation conditions to produce a plurality of perturbed simulation conditions; and rendering a second scene including the initial 3-D model deformed into a second deformed 3-D model in accordance with the physics simulation engine under the perturbed simulation conditions.

[0034] The collection of 3-D models may include a plurality of captured 3-D models of a physical object of the class of the deformable object, the captured 3-D models corresponding to captures of the physical object deformed into a plurality of configurations.

[0035] The instructions to align the 3-D model may include instructions that, when executed by the processor, cause the processor to refine a plurality of vertex positions of a plurality of vertices of the 3-D model to match appearances of the object in the images captured from the multiple viewpoints.

[0036] The instructions to refine the plurality of vertex positions may include instructions to perform the refinement based on minimizing a loss function E including the sum of a first component E _t and a second component E ₂ , wherein E _t represents pixel-level differences between an appearance of the object in the images and an appearance of the object in renderings of the 3-D model in a current pose from viewpoints corresponding to the images, and wherein E ₂ represents a degree of alignment of a silhouette of the object in the images and a silhouette of the 3-D model in the renderings of the 3-D model from the viewpoints corresponding to the images.

[0037] The renderings may be generated from the 3-D model by a pipeline including a differentiable Tenderer, and the plurality of vertex positions may be updated by backpropagating errors computed by the loss function E through the pipeline including the differentiable Tenderer.

[0038] The instructions to refine the plurality of positions of the vertices may include instructions that, when executed by the processor, cause the processor perform the refinement by a transformation neural network trained to compute a deformed 3-D model based on an input canonical 3-D model and the images of the object, the transformation neural network including: a feature extraction network trained to extract multiscale features from the images; and a graph convolutional neural network trained to generate the deformed 3-D model from the multiscale features and the input canonical 3-D model.

[0039] The transformation neural network may be trained based on training data including a plurality of training samples, each of the training samples including a 3-D model deformed in accordance with a generated scene and multi-view renderings of the 3-D model corresponding to images rendered from different virtual viewpoints. [0040] The instructions to align the 3-D model may include instructions that, when executed by the processor, cause the processor to update a current pose to minimize a loss function E including the sum of a first component E _x and a second component E ₂ , wherein E _x represents pixel-level differences between an appearance of the object in the images and an appearance of the object in renderings of the 3-D model in the current pose from viewpoints corresponding to the images, and wherein E ₂ represents a degree of alignment of a silhouette of the object in the images and a silhouette of the 3-D model in the renderings of the 3-D model from the viewpoints corresponding to the images.

[0041] The first component E _x of the loss function E may be: where I _n is an image from viewpoint n among N viewpoints, R _n (M ) is a rendering of the 3-D model M from viewpoint n, and the 3-D model M is a function of translation and rotation parameters of the current pose. [0042] The first component E _t of the loss function E may include differences between rendered surface normals of the 3-D model and images corresponding to surface normals maps of surfaces.

[0043] The surface normals maps may be computed from polarization raw frames.

[0044] The second component E ₂ of the loss function E may be: wherein S _pn is the silhouette of the 3-D model as it appears in a rendering from an n- th viewpoint R _n (M) and S _n is the silhouette of the object as it appears in the image I _n from the n-th viewpoint, wherein the 0 operator is a pixel-wise product operator, and wherein the 0 operator is a pixel-wise addition operator.

[0045] The images may include polarization raw frames.

BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, together with the specification, illustrate exemplary embodiments of the present invention, and, together with the description, serve to explain the principles of the present invention.

[0047] FIG. 1A is a schematic diagram depicting a pose estimation system according to one embodiment of the present disclosure.

[0048] FIG. 1 B is a high-level depiction of the interaction of light with transparent objects and non-transparent (e.g., diffuse and/or reflective) objects.

[0049] FIG. 2A is a perspective view of a camera array according to one embodiment of the present disclosure.

[0050] FIG. 2B is a cross sectional view of a portion of a camera array according to one embodiment of the present disclosure.

[0051] FIG. 2C is a perspective view of a stereo camera array system according to one embodiment of the present disclosure.

[0052] FIG. 3 is a flowchart depicting a general pipeline for computing six-degree- of-freedom (6-D0F) poses of objects, including deformable objects, according to some embodiments of the present disclosure.

[0053] FIG. 4A is a flow diagram of a process for object level correspondence according to one embodiment.

[0054] FIG. 4B is a block diagram of an architecture for instance segmentation and mask generation of step according to one embodiment.

[0055] FIG. 4C is a more detailed flow diagram of a matching algorithm employed at step 404 (FIG. 4A) for identifying object-level correspondence for a particular object instance in a first segmentation mask according to one embodiment. [0056] FIG. 5 is a flowchart depicting a method for computing 6-DoF poses of objects based on the appearance of object surface texture using multiple viewpoints reconstruction according to some embodiments of the present disclosure.

[0057] FIG. 6 is a flowchart depicting a method for computing 6-DoF poses of objects based on a library of models of objects according to some embodiments of the present disclosure.

[0058] FIG. 7 is a flowchart depicting a method for computing 6-DoF poses of objects based on shape morphing according to some embodiments of the present disclosure.

[0059] FIG. 8 is a depiction of a neural network architecture configured to transform an input 3-D model to a deformed 3-D model matching or consistent with the images captured of an object according to one embodiment of the present disclosure.

[0060] FIG. 9 is a flowchart depicting a method for computing 6-DoF poses of objects based on a library of models of objects and shape morphing according to some embodiments of the present disclosure.

[0061] FIG. 10 is a flowchart depicting a method for selecting a technique for estimating a pose of an object based on whether surface texture is visible in the surfaces of the object as depicted in the input images / of the object according to one embodiment of the present disclosure.

[0062] FIG. 11 is a flowchart depicting a method for generating a collection of 3-D models of a type or class of object for a library of 3-D models of objects according to one embodiment of the present disclosure.

DETAILED DESCRIPTION

[0063] In the following detailed description, only certain exemplary embodiments of the present invention are shown and described, by way of illustration. As those skilled in the art would recognize, the invention may be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein.

[0064] Pose estimation generally refers to a technique for estimating or predicting the location and orientation of objects. Some forms of pose estimation refer to detecting the physical pose of a human figure, such as the position and orientation of a person’s head, arms, legs, and joints. Pose estimation may also refer more generally to the position and orientation of various animate or inanimate physical objects in a scene. For example, autonomously navigating robots may maintain information regarding the physical poses of objects around them (e.g., humans, vehicles, equipment, other robots, barriers, doors, and the like) in order to avoid collisions and to predict trajectories of other moving objects. As another example, in the case of robotics for use in manufacturing, pose estimation may be used to detect the position and orientation of components and workpieces such that a robotic arm can approach the components and workpieces from the correct angle to obtain a proper grip on the part for assembly with other components of a manufactured product (e.g., gripping the head of a screw and threading the screw into a hole, whereas gripping a screw by the tip would make it difficult to insert into a hole, or gripping a flexible printed circuit, flexible circuit, or flex circuit and attaching the ends of the connector to different components of the manufactured product, such as connecting a flexible printed circuit to two different rigid circuit boards) and orient and/or reorient components and workpieces for assembly.

[0065] Aspects of embodiments of the present disclosure relate to systems and methods for automated six degree of freedom (6-DoF) estimation of a wide variety of objects in a scene. The six degrees of freedom in three dimensional space include positional coordinates (e.g., x, y, and z translational coordinates in a three- dimensional global coordinate system) and orientation coordinates (e.g., q, f, and y rotational coordinates in the three-dimensional global coordinate system).

[0066] Estimating the 6-DoF poses of deformable objects is useful in the field of robotics, such as in robotic systems that manipulate deformable objects. In particular, robotic systems may use the 6-DoF poses of objects in a scene to determine which of the objects are graspable. (An object may be considered to be graspable if it is not blocked by other objects and having mechanically stable surfaces that can be grasped by the end effector of a robotic arm without damaging the object). The robotic system may then grasp a detected graspable object and manipulate that object in some way (e.g., attach a flexible component to an object of manufacture, pick a deformable item and pack the deformable item into a box for shipping, or maintain control of a deformable object during transport). Robotic systems may also be commonly applied to bin packing or placing deformable items into a bin (such as a rigid box for shipping). Examples of such deformable objects include food packaging (bags of chips, candy, etc.), mechanical springs, folded clothing, and the like.

[0067] Some approaches to estimating the 6-DoF poses of objects involve aligning a given 3-D model of the object with the object as observed in the environment. This enables the robotic system to determine the pose of the physical object based on the virtual pose of the aligned 3-D model. Flowever, in the case of deformable objects, these existing 3-D models may not be representative of the actual 3-D configurations of the objects in the real world. For example, a 3-D model of a rope may depict the rope in a bundled state, but the actual rope may be folded or twisted, such that the 3-D model of the rope is not representative of the physical rope that is presented to the robotic system. Likewise, a 3-D model of a flex circuit may depict the flex circuit in a flat or substantially planar shape, whereas the flex circuit that is present in the environment may be curved or bent at various portions, due to interactions with external forces such as gravity and other objects in contact with the flex circuit. The process of grasping the object may deform the object from its configuration prior to grasping, and the configuration of the object may further change in the course of manipulating the object (e.g., through interaction with gravity and other forces in the environment).

[0068] Some comparative approaches to estimating the poses of deformable objects relate to the special case of garments (or clothing) as viewed on bodies. Some other comparative approaches relate to the special case of estimating the poses of human bodies and other articulated objects that have well-defined constraints within which the poses may vary (e.g., constraints set by the range of motion of human joints).

[0069] Aspects of embodiments of the present disclosure relate to improving the accuracy of the detection of 6-DoF poses of the general case of arbitrary objects, including arbitrary deformable objects. Arbitrary deformable objects include objects have at least some portions that are continuously pliable (e.g., a cloth, a rope or string, wires and cables, flexible tubing, soft rubber parts, a bag or other pliable container containing rigid or soft objects and/or fluids, foam packing materials, flex circuits which may have rigid connectors at their ends, or the like), objects that are pliable and that retain their shapes after being bent into various shapes (e.g., metal wires, metal sheets or foil, and the like), and objects that may have a stable (e.g., low energy) configuration but that can also be deformed into other configurations (e.g., springs, firm rubber parts, and the like). The accurate estimation of the 6-DoF poses of deformable objects enables robotic systems to accurately pick such deformable objects, thereby expanding the scope of robotic automation.

[0070] Some aspects of embodiments of the present disclosure relate to detecting the poses of deformable objects having three-dimensional shapes that can vary continuously through a range of possible configurations. The term “configuration” may be used herein to refer to a physical arrangement of different parts of an object with respect to an object coordinate system (as opposed to a world or global coordinate system). For example, a rigid object may be considered to have a single “configuration,” as the term is used herein, even through its pose within its external environment can be varied (e.g., the rigid object can be rotated and positioned with six degrees of freedom in the external environment). On the other hand, a hinge may have an infinite number of possible configurations because the angle between the components on the opposite sides of the hinge may vary continuously between the extremes of the range of motion. Likewise, a rope may have an infinite number of configurations because every point along the length of the rope may be bent and/or twisted as constrained by the flexibility or pliability of the rope. The configuration of an object may alternatively be referred to herein as a “physical configuration” and/or an “object configuration.”

[0071] Some aspects of embodiments of the present disclosure relate to various techniques for estimating the three-dimensional, six-degree-of-freedom (6DoF) poses of deformable objects, including embodiments in which these techniques are used individually (e.g., only one technique is applied) as well as embodiments in which the techniques are used in combination to produce more accurate results. For example, an output of a first technique may be supplied as input to a second technique, different techniques can be implemented in parallel and used as factors in a joint optimization problem, and/or different techniques are used alternatingly using an iterative approach to compute a pose of a deformable object.

[0072] The six degrees of freedom in three dimensional space include positional coordinates (e.g., x, y, and z translational coordinates in a three-dimensional global coordinate system) and orientation coordinates (e.g., q, f, and y rotational coordinates in the three-dimensional coordinate system). A pose estimation system according to embodiments of the present disclosure, may combine the six dimensional pose of an object within the scene with a 3-D model of the object (e.g., a 3-D mesh model of the object such as a computer aided design or CAD model, where the mesh may include a collection of vertices and edges connecting the vertices, each of the vertices having three-dimensional coordinates (e.g., x, y, z coordinates), and where the three-dimensional coordinates may be represented in an object coordinate system relative to the object itself or a global coordinate system relative to some external environment). In the case of deformable objects, some aspects of embodiments of the present disclosure relate to identifying and/or generating a 3-D model of the object that corresponds to the configuration of the object, as described in more detail below.

[0073] In addition, while aspects of embodiments of the present disclosure are described herein in the context of detecting the six-degree-of-freedom poses of deformable objects, in practice, embodiments of the present disclosure described herein can also be applied to detecting the 6DoF poses of rigid objects (e.g., non- deformable objects), and uses or applications of embodiments of the present disclosure are not limited to the case of deformable objects.

[0074] FIG. 1A is a schematic diagram depicting a pose estimation system 1 according to one embodiment of the present disclosure. As shown in FIG. 1 A, a main camera 10 is arranged such that its field of view 12 captures an arrangement 20 of objects 22 in a scene. In the embodiment shown in FIG. 1A, the main camera 10 is located above the support platform (e.g., spaced apart from the objects 22 along the direction of gravity), but embodiments of the present disclosure are not limited thereto — for example, the main camera 10 can be arranged to have a downward angled view of the objects 22.

[0075] In some embodiments, one or more support cameras 30 are arranged at different poses around the scene containing the arrangement 20 of objects 22. Accordingly, each of the support cameras 30, e.g., first support camera 30a, second support camera 30b, and third support camera 30c, captures a different view of the objects 22 from a different view point (e.g., a first viewpoint, a second viewpoint, and a third viewpoint, respectively). While FIG. 1A shows three support cameras 30, embodiments of the present disclosure are not limited thereto and may include, for example, at least one support camera 30 and may include more than three support cameras 30. In addition, while the mail camera 10 is depicted in FIG. 1A as a stereo camera, embodiments of the present disclosure are not limited thereto, and may be used with, for example, a monocular main camera.

[0076] A pose estimator 100 according to various embodiments of the present disclosure is configured to compute or estimate poses of the objects 22 based on information captured by the main camera 10 and the support cameras 30. According to various embodiments of the present disclosure, the pose estimator 100 is implemented using one or more processing circuits or electronic circuits configured to perform various operations as described in more detail below. Types of electronic circuits may include a central processing unit (CPU), a graphics processing unit (GPU), an artificial intelligence (Al) accelerator (e.g., a vector processor, which may include vector arithmetic logic units configured efficiently perform operations common to neural networks, such dot products and softmax), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a digital signal processor (DSP), or the like. For example, in some circumstances, aspects of embodiments of the present disclosure are implemented in program instructions that are stored in a non-volatile computer readable memory where, when executed by the electronic circuit (e.g., a CPU, a GPU, an Al accelerator, or combinations thereof), perform the operations described herein to compute a processing output 20, such as an instance segmentation map, from input polarization raw frames 18 (the underlying images captured by polarization cameras or cameras with polarization filters in their optical paths). The operations performed by the pose estimator 100 may be performed by a single electronic circuit (e.g., a single CPU, a single GPU, or the like) or may be allocated between multiple electronic circuits (e.g., multiple GPUs or a CPU in conjunction with a GPU). The multiple electronic circuits may be local to one another (e.g., located on a same die, located within a same package, or located within a same embedded device or computer system) and/or may be remote from one other (e.g., in communication over a network such as a local personal area network such as Bluetooth®, over a local area network such as a local wired and/or wireless network, and/or over wide area network such as the internet, such a case where some operations are performed locally and other operations are performed on a server hosted by a cloud computing service). One or more electronic circuits operating to implement the pose estimator 100 may be referred to herein as a computer or a computer system, which may include memory storing instructions that, when executed by the one or more electronic circuits, implement the systems and methods described herein.

[0077] In more detail, the main camera 10 and the support cameras 30 are configured to estimate the poses of objects 22 detected within their fields of view 12 (while FIG. 1 A illustrates a field of view 12 for the main camera 10 using dashed lines, the fields of view of the support cameras 30 are not explicitly shown). In the embodiment shown in FIG. 1A, the objects 22 are depicted abstractly as simple three-dimensional solids such as spheres, rectangular prisms, and cylinders. Flowever, embodiments of the present disclosure are not limited thereto and characterization of pose estimators may be performed using any arbitrary object for which a pose with respect to a camera can be clearly defined, including deformable objects mentioned above, such as flex circuits, bags or other pliable containers containing solids, liquids, and/or fluids, flexible tubing, and the like.

[0078] In particular, a “pose” refers to the position and orientation of an object with respect to a reference coordinate system. For example, a reference coordinate system may be defined with the main camera 10 at the origin, where the direction along the optical axis of the main camera 10 (e.g., a direction through the center of its field of view 12) is defined as the z-axis of the coordinate system, and the x and y axes are defined to be perpendicular to one another and perpendicular to the z-axis. (Embodiments of the present disclosure are not limited to this particular coordinate system, and a person having ordinary skill in the art would understand that poses can be mathematically transformed to equivalent representations in different coordinate systems.)

[0079] Each object 22 may also be associated with a corresponding coordinate system of its own, which is defined with respect to its particular shape. For example, a rectangular prism with sides of different lengths may have a canonical coordinate system defined where the x-axis is parallel to its shortest direction, z-axis is parallel to its longest direction, the y-axis is orthogonal to the x-axis and z-axis, and the origin is located at the centroid of the object 22.

[0080] Generally, in a three-dimensional coordinate system, objects 22 have six degrees of freedom — rotation around three axes (e.g., rotation around x-, y-, and z- axes) and translation along the three axes (e.g., translation along x-, y-, and z-axes). For the sake of clarity, symmetries of the objects 22 will not be discussed in detail herein, but may be addressed, for example, by identifying multiple possible poses with respect to different symmetries (e.g., in the case of selecting the positive versus negative directions of the z-axis of a right rectangular prism), or by ignoring some rotational components of the pose (e.g., a right cylinder is rotationally symmetric around its axis).

[0081] In some embodiments, it is assumed that a three-dimensional (3-D) model or computer aided design (CAD) model representing a canonical or ideal version of each type of object 22 in the arrangement of objects 20 is available. For example, in some embodiments of the present disclosure, the objects 22 are individual instances of manufactured components that have a substantially uniform appearance from one component to the next. Examples of such manufactured components include screws, bolts, nuts, connectors, and springs, as well as specialty parts such electronic circuit components (e.g., packaged integrated circuits, light emitting diodes, switches, resistors, and the like), laboratory supplies (e.g. test tubes, PCR tubes, bottles, caps, lids, pipette tips, sample plates, and the like), and manufactured parts (e.g., handles, switch caps, light bulbs, and the like). Accordingly, in these circumstances, a CAD model defining the ideal or canonical shape of any particular object 22 in the arrangement 20 may be used to define a coordinate system for the object (e.g., the coordinate system used in the representation of the CAD model).

[0082] As noted above, some aspects of embodiments of the present disclosure relate to computing (e.g., identifying and/or generating) a 3-D model of the object whose pose is being estimated, where the 3-D model has a configuration matching that of the object (e.g., a 3-D model of a flex circuit that is curved and/or twisted in substantially the same way as the flex circuit seen among the objects 22).

[0083] Based on a reference coordinate system (or camera space, e.g., defined with respect to the pose estimation system) and an object coordinate system (or object space, e.g., defined with respect to one of the objects), the pose of the object may be considered to be a rigid transform (rotation and translation) from object space to camera space. The pose of object 1 in camera space 1 may be denoted as P _c , and the transform from object 1 space to camera space may be represented by the matrix: where the rotation submatrix R

Rii Rl2 P13

R = P21 ^22 23

-P31 R32 R33- represents rotations along the three axes from object space to camera space, and the translation submatrix T: represents translations along the three axes from object space to camera space. [0084] If two objects — Object A and Object B — are in the same camera C coordinate frame, then the notation P _CA is used to indicate the pose of Object A with respect to camera C and P _CB is used to indicate the pose of Object B with respect to camera C. For the sake of convenience, it is assumed herein that the poses of objects are represented based on the reference coordinate system, so the poses of objects A and B with respect to camera space C may be denoted P _A and P _B , respectively.

[0085] If Object A and Object B are actually the same object, but performed during different pose estimation measurements, and a residual pose P _err or P _AB ( P _AB = P _err ) is used to indicate a transform from pose P _A to pose P _B , then the following relationship should hold:

^A^err ⁼ PB (1) and therefore

Perr = ¾¾ (2)

[0086] Ideally, assuming the object has not moved (e.g., translated or rotated) with respect to the main camera 10 between the measurements of pose estimates P _A and P _B , then P _A and P _B should both be the same, and P _err should be the identity matrix (e.g., indicating no error between the poses):

1 0 0 0 0 1 0 0 0 0 1 0 -0 0 0 1

[0087] In a similar manner, the pose of a particular object can be computed with respect to views from two different cameras. For example, images of Object A captured by a main camera C can be used to compute the pose P _CA of Object A with respect to main camera C. Likewise, images of Object A captured by a first support camera can be used to compute the pose P _SiA of object A with respect to the support camera 5 _X. If the relative poses of main camera C and support camera are known, then the pose P _SiA can be transformed to the coordinate system of the main camera C.

[0088] Ideally, assuming that the known relative poses of main camera C and support camera are accurate and the poses calculated based on the data captured by the two cameras is accurate, then P _CA and P _SiA should both be the same, and P _err should be the identity matrix (e.g., indicating no error between the poses): rl 0 0 0-

0 1 0 0 0 0 1 0 -0 0 0 1

[0089] Differences P _err between the actual measured value as computed based on the estimates computed by the pose estimator 100 and the identity matrix may be considered to be errors: where R _err is the rotation error and T _err is the translation error. The function R( ) converts P _err into an axis-angle where the magnitude is the rotation difference, and the function T( ) extracts the translation component of the pose matrix.

[0090] The axis-angle representation from rotation matrix R is given by:

Tr (R) = 1

16> I = arccos where Tr( ) denotes the matrix trace (the sum of the diagonal elements of the matrix), and Q represents the angle of rotation

[0091] Some aspects of embodiments of the present disclosure relate to computing a high accuracy pose estimate of objects 22 in a scene based on a joint estimate of the poses the objects across the main camera 10 and the support cameras 30. Some aspects of embodiments of the present disclosure also relate to providing information to assist in the control of a robotic arm 24 having an end effector 26 that may be used to grasp and manipulate objects 22. The robotic arm 24, including its end effector 26, may be controlled by a robotic arm controller 28, which receives the six-degree-of-freedom poses computed by the pose estimator 100, which may include 3-D models representing various objects 22 in the scene 1, where the 3-D models have configurations that estimate or approximate the configurations of their corresponding real-world objects, noting, for example, that the configuration of portions of the objects 22 that are occluded or otherwise not visible in the fields of view 12 of the main camera 10 and support cameras 30 may be difficult or impossible to estimate with high accuracy.

[0092] Pose estimation hardware

[0093] In the embodiment shown in FIG. 1A, the pose estimation system 1 includes a main camera 10. and one or more support cameras 30. In some embodiments of the present disclosure, the main camera 10 includes a stereo camera. Examples of stereo cameras include camera systems that have at least two monocular cameras spaced apart from each other along a baseline, where the monocular cameras have overlapping fields of view and optical axes that are substantially parallel to one another. While embodiments of the present disclosure will be presented herein in embodiments where the main camera 10 and the support cameras 30 are passive cameras (e.g., that are not connected to a dedicated light projector and that instead use ambient lighting or other light sources), embodiments of the present disclosure are not limited thereto and may also include circumstances where one or more active light projector are included in the camera system, thereby forming an active camera system, where the active light projector may be configured to project structured light or a pattern onto the scene. The support cameras 30 may be stereo cameras, monocular cameras, or combinations thereof (e.g., some stereo support cameras and some monocular support cameras).

[0094] The main camera 10 and the support cameras 30 may use the same imaging modalities or different imaging modalities. Examples of imaging modalities include monochrome, color, infrared, ultraviolet, thermal, polarization, and combinations thereof.

[0095] The interaction between light and transparent objects is rich and complex, but the material of an object determines its transparency under visible light. For many transparent household objects, the majority of visible light passes straight through and a small portion (~4% to ~8%, depending on the refractive index) is reflected. This is because light in the visible portion of the spectrum has insufficient energy to excite atoms in the transparent object. As a result, the texture (e.g., appearance) of objects behind the transparent object (or visible through the transparent object) dominate the appearance of the transparent object. For example, when looking at a transparent glass cup or tumbler on a table, the appearance of the objects on the other side of the tumbler (e.g., the surface of the table) generally dominate what is seen through the cup. This property leads to some difficulties when attempting to detect surface characteristics of transparent objects such as glass windows and glossy, transparent layers of paint, based on intensity images alone: [0096] FIG. 1 B is a high-level depiction of the interaction of light with transparent objects and non-transparent (e.g., diffuse and/or reflective) objects. As shown in FIG. 1 B, a polarization camera 10 captures polarization raw frames of a scene that includes a transparent object 41 in front of an opaque background object 42. A light ray 43 hitting the image sensor 14 of the polarization camera 10 contains polarization information from both the transparent object 41 and the background object 42. The small fraction of reflected light 44 from the transparent object 41 is heavily polarized, and thus has a large impact on the polarization measurement, in contrast to the light 45 reflected off the background object 42 and passing through the transparent object 41.

[0097] Similarly, a light ray hitting the surface of an object may interact with the shape of the surface in various ways. For example, a surface with a glossy paint may behave substantially similarly to a transparent object in front of an opaque object as shown in FIG. 1 B, where interactions between the light ray and a transparent or translucent layer (or clear coat layer) of the glossy paint causes the light reflecting off of the surface to be polarized based on the characteristics of the transparent or translucent layer (e.g., based on the thickness and surface normals of the layer), which are encoded in the light ray hitting the image sensor. Similarly, as discussed in more detail below with respect to shape from polarization (SfP) theory, variations in the shape of the surface (e.g., direction of the surface normals) may cause significant changes in the polarization of light reflected by the surface of the object. For example, smooth surfaces may generally exhibit the same polarization characteristics throughout, but a scratch or a dent in the surface changes the direction of the surface normals in those areas, and light hitting scratches or dents may be polarized, attenuated, or reflected in ways different than in other portions of the surface of the object. Models of the interactions between light and matter generally consider three fundamentals: geometry, lighting, and material. Geometry is based on the shape of the material. Lighting includes the direction and color of the lighting. Material can be parameterized by the refractive index or angular reflection/transmission of light. This angular reflection is known as a bi-directional reflectance distribution function (BRDF), although other functional forms may more accurately represent certain scenarios. For example, the bidirectional subsurface scattering distribution function (BSSRDF) would be more accurate in the context of materials that exhibit subsurface scattering (e.g. marble or wax).

[0098] A light ray 43 hitting the image sensor 14 of a polarization camera 10 has three measurable components: the intensity of light (intensity image//), the percentage or proportion of light that is linearly polarized (degree of linear polarization/DOLP/p), and the direction of that linear polarization (angle of linear polarization/AOLP/0). These properties encode information about the surface curvature and material of the object being imaged, which can be used by the pose estimator 100 to detect transparent objects, as described in more detail below. In some embodiments, by using one or more polarization cameras, the pose estimator 100 can detect other optically challenging objects based on similar polarization properties of light passing through translucent objects and/or light interacting with multipath inducing objects or by non-reflective objects (e.g., matte black objects). [0099] In more detail, the polarization camera 10 may further includes a polarizer or polarizing filter or polarization mask 16 placed in the optical path between the scene 1 and the image sensor 14. According to various embodiments of the present disclosure, the polarizer or polarization mask 16 is configured to enable the polarization camera 10 to capture images of the scene 1 with the polarizer set at various specified angles (e.g., at 45° rotations or at 60° rotations or at non-uniformly spaced rotations).

[00100] As one example, FIG. 1 B depicts an embodiment where the polarization mask 16 is a polarization mosaic aligned with the pixel grid of the image sensor 14 in a manner similar to a red-green-blue (RGB) color filter (e.g., a Bayer filter) of a color camera. In a manner similar to how a color filter mosaic filters incoming light based on wavelength such that each pixel in the image sensor 14 receives light in a particular portion of the spectrum (e.g., red, green, or blue) in accordance with the pattern of color filters of the mosaic, a polarization mask 16 using a polarization mosaic filters light based on linear polarization such that different pixels receive light at different angles of linear polarization (e.g., at 0°, 45°, 90°, and 135°, or at 0°, 60° degrees, and 120°). Accordingly, the polarization camera 10 using a polarization mask 16 such as that shown in FIG. 1 B is capable of concurrently or simultaneously capturing light at four different linear polarizations. One example of a polarization camera is the Blackfly® S Polarization Camera produced by FLIR® Systems, Inc. of Wilsonville, Oregon.

[00101] While the above description relates to some possible implementations of a polarization camera using a polarization mosaic, embodiments of the present disclosure are not limited thereto and encompass other types of polarization cameras that are capable of capturing images at multiple different polarizations. For example, the polarization mask 16 may have fewer than four polarizations or more than four different polarizations, or may have polarizations at different angles than those stated above (e.g., at angles of polarization of: 0°, 60°, and 120° or at angles of polarization of 0°, 30°, 60°, 90°, 120°, and 150°). As another example, the polarization mask 16 may be implemented using an electronically controlled polarization mask, such as an electro-optic modulator (e.g., may include a liquid crystal layer), where the polarization angles of the individual pixels of the mask may be independently controlled, such that different portions of the image sensor 14 receive light having different polarizations. As another example, the electro-optic modulator may be configured to transmit light of different linear polarizations when capturing different frames, e.g., so that the camera captures images with the entirety of the polarization mask set to, sequentially, to different linear polarizer angles (e.g., sequentially set to: 0 degrees; 45 degrees; 90 degrees; or 135 degrees). As another example, the polarization mask 16 may include a polarizing filter that rotates mechanically, such that different polarization raw frames are captured by the polarization camera 10 with the polarizing filter mechanically rotated with respect to the lens 12 to transmit light at different angles of polarization to image sensor 14. Furthermore, while the above examples relate to the use of a linear polarizing filter, embodiments of the present disclosure are not limited thereto and also include the use of polarization cameras that include circular polarizing filters (e.g., linear polarizing filters with a quarter wave plate). Accordingly, in various embodiments of the present disclosure, a polarization camera uses a polarizing filter to capture multiple polarization raw frames at different polarizations of light, such as different linear polarization angles and different circular polarizations (e.g., handedness). [00102] As a result, the polarization camera 10 captures multiple input images (or polarization raw frames) of the scene including the surfaces of the objects 22. In some embodiments, each of the polarization raw frames corresponds to an image taken behind a polarization filter or polarizer at a different angle of polarization f _roί (e.g., 0 degrees, 45 degrees, 90 degrees, or 135 degrees). Each of the polarization raw frames is captured from substantially the same pose with respect to the scene 1 (e.g., the images captured with the polarization filter at 0 degrees, 45 degrees, 90 degrees, or 135 degrees are all captured by a same polarization camera 10 located at a same location and orientation), as opposed to capturing the polarization raw frames from disparate locations and orientations with respect to the scene. The polarization camera 10 may be configured to detect light in a variety of different portions of the electromagnetic spectrum, such as the human-visible portion of the electromagnetic spectrum, red, green, and blue portions of the human-visible spectrum, as well as invisible portions of the electromagnetic spectrum such as infrared and ultraviolet.

[00103] FIG. 2A is a perspective view of a camera array 10' according to one embodiment of the present disclosure. FIG. 2B is a cross sectional view of a portion of a camera array 10' according to one embodiment of the present disclosure. Some aspects of embodiments of the present disclosure relate to a camera array in which multiple cameras (e.g., cameras having different imaging modalities and/or sensitivity to different spectra) are arranged adjacent to one another and in an array and may be controlled to capture images in a group (e.g., a single trigger may be used to control all of the cameras in the system to capture images concurrently or substantially simultaneously). In some embodiments, the individual cameras are arranged such that parallax shift between cameras is substantially negligible based on the designed operating distance of the camera system to objects 2 and 3 in the scene 1 , where larger spacings between the cameras may be tolerated when the designed operating distance is large.

[00104] FIG. 2B shows a cross sectional view of two of the cameras 10A' and 10B' of the camera array 10' shown in FIG. 2A. As seen in FIG. 2B, each camera or camera module (10A' and 10B') includes a corresponding lens, a corresponding image sensor, and may include one or more corresponding filters. For example, in some embodiments, camera 10A' is a visible light color camera that includes lens 12A', image sensor 14A', and color filter 16A' (e.g., a Bayer filter). In the embodiment shown in FIG. 2B, the filter 16 is located behind the lens 12 (e.g., between the lens 12 and the image sensor 14), but embodiments of the present disclosure are not limited thereto. In some embodiments, the filter 16 is located in front of the lens 12, and in some embodiments, the filter 16 may include multiple separate components, where some components are located in front of the lens and other components are located behind the lens (e.g., a polarizing filter in front of the lens 12 and a color filter behind the lens 12). In some embodiments, camera 10B' is a polarization camera that includes lens 12B', image sensor 14B', and polarizing filter 16B' (a polarization camera may also include a visible light color filter or other filter for passing a particular portion of the electromagnetic spectrum, such as an infrared filter, ultraviolet filter, and the like). In some embodiments of the present disclosure, the image sensors four cameras 10A', 10B', 10C', and 10D' are monolithically formed on a same semiconductor die, and the four cameras are located in a same housing with separate apertures for the lenses 12 corresponding to the different image sensors. Similarly, the filters 16 may correspond to different portions of a single physical layer that has different optical filter functions (e.g., different linear polarizing angles or circular polarizers, color filters with corresponding spectral response functions, and the like) in different regions of the layer (corresponding to the different cameras). In some embodiments, a filter 16 of a polarization camera includes a polarization mask 16 similar to the Sony® IMX250MZR sensor, which includes a polarization mosaic aligned with the pixel grid of the image sensor 14 in a manner similar to a red-green- blue (RGB) color filter (e.g., a Bayer filter) of a color camera. In a manner similar to how a color filter mosaic filters incoming light based on wavelength such that each pixel in the image sensor 14 receives light in a particular portion of the spectrum (e.g., red, green, or blue) in accordance with the pattern of color filters of the mosaic, a polarization mask 16 using a polarization mosaic filters light based on linear polarization such that different pixels receive light at different angles of linear polarization (e.g., at 0°, 45°, 90°, and 135°, or at 0°, 60° degrees, and 120°). Accordingly, a camera of the camera array 10' may use a polarization mask 16 to concurrently or simultaneously capture light at four different linear polarizations. [00105] In some embodiments, a demosaicing process is used to compute separate red, green, and blue channels from the raw data. In some embodiments of the present disclosure, each polarization camera may be used without a color filter or with filters used to transmit or selectively transmit various other portions of the electromagnetic spectrum, such as infrared light.

[00106] As noted above, embodiments of the present disclosure relate to multi modal and/or multi-spectral camera arrays. Accordingly, in various embodiments of the present disclosure, the cameras within a particular camera array include cameras configured to perform imaging in a plurality of different modalities and/or to capture information in a plurality of different spectra.

[00107] As one example, in some embodiments, the first camera 10A' is a visible light camera that is configured to capture color images in a visible portion of the electromagnetic spectrum, such as by including a Bayer color filter 16A' (and, in some cases, a filter to block infrared light), and the second camera 10B', third camera 10C', and fourth camera 10D' are polarization cameras having different polarization filters, such filters having linear polarization angles of 0°, 60°, and 120°, respectively. The polarizing filters in the optical paths of each of the cameras in the array cause differently polarized light to reach the image sensors of the cameras.

The individual polarization cameras in the camera array have optical axes that are substantially perpendicular to one another, are placed adjacent to one another, and have substantially the same field of view, such that the cameras in the camera array capture substantially the same view of a scene as the visible light camera 10A', but with different polarizations. While the embodiment shown in FIG. 2A includes a 2x2 array of four cameras, three of which are polarization cameras, embodiments of the present disclosure are not limited thereto, and the camera array may more than three polarization cameras, each having a polarizing filter with a different polarization state (e.g., a camera array may have four polarization cameras along with the visible light color camera 10A', where the polarization cameras may have polarization filters with angles of linear polarization, such as 0°, 45°, 90°, and 135°). In some embodiments, one or more of the cameras may include a circular polarizer.

[00108] As another example, one or more of the cameras in the camera array 10' may operate in other imaging modalities and/or other imaging spectra, such as polarization, near infrared, far infrared, shortwave infrared (SWIR), longwave infrared (LWIR) or thermal, ultraviolet, and the like, by including appropriate filters 16 (e.g., filters that pass light having particular polarizations, near-infrared light, SWIR light, LWIR light, ultraviolet light, and the like) and/or image sensors 14 (e.g., image sensors optimized for particular wavelengths of electromagnetic radiation) for the particular modality and/or portion of the electromagnetic spectrum.

[00109] For example, in the embodiment of the camera array 10' shown in FIG. 2A, four cameras 10A', 10B', 10C', and 10D' are arranged in a 2x2 grid to form a camera array, referred to herein as a camera array, where the four cameras have substantially parallel optical axes. The four cameras may be controlled together such that they capture images substantially simultaneously. In some embodiments, the four cameras are configured to capture images using the same exposure settings (e.g., same aperture, length of exposure, and gain or “ISO” settings). In some embodiments, the exposure settings for the different cameras can be controlled independently from one another (e.g., different settings for each camera), where the processing circuit 100 jointly or holistically sets the exposure settings for the cameras based on the current conditions of the scene 1 and the characteristics of the imaging modalities and spectral responses of the cameras 10A', 10B', 10C', and 10D' of the camera array 10'.

[00110] In some embodiments, the various individual cameras of the camera array are registered with one another by determining their relative poses (or relative positions and orientations) by capturing multiple images of a calibration target, such as a checkerboard pattern, an ArUco target (see, e.g., Garrido-Jurado, Sergio, et al. "Automatic generation and detection of highly reliable fiducial markers under occlusion." Pattern Recognition 47.6 (2014): 390-402.) or a ChArUco target (see, e.g., An, Gwon Flwan, et al. "Charuco board-based omnidirectional camera calibration method." Electronics 7.12 (2018): 421.). In particular, the process of calibrating the targets may include computing intrinsic matrices characterizing the internal parameters of each camera (e.g., matrices characterizing the focal length, image sensor format, and principal point of the camera) and extrinsic matrices characterizing the pose of each camera with respect to world coordinates (e.g., matrices for performing transformations between camera coordinate space and world or scene coordinate space). Different cameras within a camera array may have image sensors with different sensor formats (e.g., aspect ratios) and/or different resolutions without limitation, and the computed intrinsic and extrinsic parameters of the individual cameras enable the processing circuit 100 to map different portions of the different images to a same coordinate space (where possible, such as where the fields of view overlap).

[00111] FIG. 2C is a perspective view of a stereo camera array system 10 according to one embodiment of the present disclosure. For some applications, stereo vision techniques are used to capture multiple images of scene from different perspectives. As noted above, in some embodiments of the present disclosure, individual cameras (or camera modules) within a camera array 10' are placed adjacent to one another such that parallax shifts between the cameras are small or substantially negligible based on the designed operating distance of the camera system to the subjects being imaged (e.g., where the parallax shifts between cameras of a same array are less than a pixel for objects at the operating distance). In addition, as noted above, in some embodiments, differences in the poses of the individual cameras within a camera array 10' are corrected through image registration based on the calibrations (e.g., computed intrinsic and extrinsic parameters) of the cameras such that the images are aligned to a same coordinate system for the viewpoint of the camera array.

[00112] In stereo camera array systems according to some embodiments, the camera arrays are spaced apart from one another such that parallax shifts between the viewpoints corresponding to the camera arrays are detectable for objects in the designed operating distance of the camera system. This enables the distances to various surfaces in a scene (the “depth”) to be detected in accordance with a disparity measure or a magnitude of a parallax shift (e.g., larger parallax shifts in the locations of corresponding portions of the images indicate that those corresponding portions are on surfaces that are closer to the camera system and smaller parallax shifts indicate that the corresponding portions are on surfaces that are farther away from the camera system). These techniques for computing depth based on parallax shifts are sometimes referred to as Depth from Stereo

[00113] Accordingly, FIG. 2C depicts a stereo camera array system 10 having a first camera array 10-T and a second camera array 10-2' having substantially parallel optical axes and spaced apart along a baseline 10-B. In the embodiments shown in FIG. 2C, the first camera array 10-T includes cameras 10A', 10B', 10C', and 10D' arranged in a 2x2 array similar to that shown in FIG. 2A and FIG. 2B. Likewise, the second camera array 10-2' includes cameras 10E', 10F', 10G', and 10FT arranged in a 2x2 array, and the overall stereo camera array system 10 includes eight individual cameras (e.g., eight separate image sensors behind eight separate lenses). In some embodiments of the present disclosure, corresponding cameras of the camera arrays 10-1 ' and 10-2' are of the same type or, in other words, configured to capture raw frames or images using substantially the same imaging modalities or in substantially the same spectra. In the specific embodiment shown in FIG. 2C, cameras 10A' and 10E' may be of a same first type, cameras 10B' and 10F' may be of a same second type, cameras 10C' and 10G' may be of a same third type, and cameras 10D' and 10H' may be of a same fourth type. For example, cameras 10A' and 10E' may both have linear polarizing filters at a same angle of 0°, cameras 10B' and 10F' may both have linear polarizing filters at a same angle of 45°, cameras 10C' and 10G' may both be viewpoint-independent cameras having no polarization filter (NF), such as near-infrared cameras, and cameras 10D' and 10H' may both have linear polarizing filters at a same angle of 90°. As another example, cameras 10A' and 10E' may both be viewpoint-independent cameras such as visible light cameras without polarization filters, cameras 10B' and 10F' may both be thermal cameras, cameras 10C' and 10G' may both have polarization masks with a mosaic pattern polarization filters at different angles of polarization (e.g., a repeating pattern with polarization angles of 0°, 45°, 90°, and 135°), and cameras 10D' and 10H' may both be thermal (LWIR) cameras.

[00114] While some embodiments are described above wherein each array includes cameras of different types in a same arrangement, embodiments of the present disclosure are not limited thereto. For example, in some embodiments, the arrangements of cameras within a camera array are mirrored along an axis perpendicular to the baseline 10-B. For example, cameras 10A' and 10F' may be of a same first type, cameras 10B' and 10E' may be of a same second type, cameras 10C' and 10H' may be of a same third type, and cameras 10D' and 10G' may be of a same fourth type.

[00115] In a manner similar to that described for calibrating or registering cameras within a camera array, the various polarization camera arrays of a stereo camera array system may also be registered with one another by capturing multiple images of calibration targets and computing intrinsic and extrinsic parameters for the various camera arrays. The camera arrays of a stereo camera array system 10 may be rigidly attached to a common rigid support structure 10-S in order to keep their relative poses substantially fixed (e.g., to reduce the need for recalibration to recompute their extrinsic parameters). The baseline 10-B between camera arrays is configurable in the sense that the distance between the camera arrays may be tailored based on a desired or expected operating distance to objects in a scene — when the operating distance is large, the baseline 10-B or spacing between the camera arrays may be longer, whereas the baseline 10-B or spacing between the camera arrays may be shorter (thereby allowing a more compact stereo camera array system) when the operating distance is smaller.

[00116] As noted above with respect to FIG. 1 B, a light ray 43 hitting the image sensor 14 of a polarization camera 10 has three measurable components: the intensity of light (intensity image//), the percentage or proportion of light that is linearly polarized (degree of linear polarization/DOLP/p), and the direction of that linear polarization (angle of linear polarization/AOLP/0). [00117] Measuring intensity /, DOLP p, and AOLP f at each pixel requires 3 or more polarization raw frames of a scene taken behind polarizing filters (or polarizers) at different angles, f _roί (e.g., because there are three unknown values to be determined: intensity /, DOLP p, and AOLP f. For example, a polarization camera such as those described above with respect to FIGS. 1 B, 1C, 1 D, and 1 E captures polarization raw frames with four different polarization angles f _roί , e.g., 0 degrees,

45 degrees, 90 degrees, or 135 degrees, thereby producing four polarization raw frames 1 _fron denoted herein as I ₀ , l ₄₅ , I ₉₀ , and l _135.

[00118] The relationship between I _fro1 and intensity I, DOLP p, and AOLP f at each pixel can be expressed as:

[00119] Accordingly, with four different polarization raw frames I _fro1 (/ ₀ , I ₄₅ , I _g0 , and I ₁₃₅ ), a system of four equations can be used to solve for the intensity /, DOLP p, and AOLP f.

[00120] Shape from Polarization (SfP) theory (see, e.g., Gary A Atkinson and Edwin R Hancock. Recovery of surface orientation from diffuse polarization. IEEE transactions on image processing, 15(6): 1653-1664, 2006.) states that the relationship between the refractive index (n), azimuth angle (q _a ) and zenith angle (q _z ) of the surface normal of an object and the f and p components of the light ray coming from that object follow the following characteristics when diffuse reflection is dominant: and when the specular reflection is dominant: p

F = q _a (11 ) 2

[00121] Note that in both cases p increases exponentially as q _z increases and if the refractive index is the same, specular reflection is much more polarized than diffuse reflection.

[00122] Accordingly, some aspects of embodiments of the present disclosure relate to applying SfP theory to detect or measure the gradients of surfaces (e.g., the orientation of surfaces or their surface normals or directions perpendicular to the surfaces) based on the raw polarization frames of the objects, as captured by the polarization cameras among the main camera 10 and the support cameras 30. Computing these gradients produces a gradient map (or slope map or surface normals map) identifying the slope of the surface depicted at each pixel in the gradient map. These gradient maps can then be used when estimating the pose of the object by aligning a pre-existing 3-D model (e.g., CAD model) of the object with the measured surface normals (gradients or slopes) of the object in based on the slopes of the surfaces of the 3-D model, as described in more detail below.

[00123] Estimating six-degree-of-freedom poses of objects in a scene [00124] Estimating the six-degree-of-freedom (6-DoF) poses of objects in a scene is a useful task in various applications such as robotics, where understanding the three-dimensional (3-D) shapes and locations of objects in a scene provides more information to a robot controller regarding an environment, thereby improving situational awareness and enabling the robot controller to interact appropriately with the environment, in accordance the particular tasks assigned to the robot. As noted above, autonomously navigating robots or vehicles may maintain information about the poses of objects in a scene in order to assist with navigation around those objects in order to predict trajectories and to avoid collisions with those objects. As another example, in the case of manufacturing, pose estimation may be used by robotic systems to manipulate the workpieces and place and/or attach components to those workpieces.

[00125] Some aspects of systems and methods for estimating the six-degree-of- freedom poses of objects are described in International Patent Application No. PCT/US21/15926, titled “SYSTEMS AND METHODS FOR POSE DETECTION AND MEASUREMENT,” filed in the United States Patent and Trademark Office on January 29, 2021, the entire disclosure of which is incorporated by reference herein. Generally, the approach described in the above-referenced international patent application relate to computing a 6-DoF pose of an object in a scene by determining a class or type of the object (e.g., a known or expected object) and aligning a corresponding 3-D model of the object (e.g., a canonical or ideal version of the object based on known design specifications of the object and/or based on the combination of a collection of samples of the object) with the various views of the object, as captured from different viewpoints around the object.

[00126] In some environments, the poses of a scene containing a plurality of rigid objects can be determined based on a single 3-D model for each type of object in the scene. For example, the scene may include a single type or class of object (such as a single type of rigid metal bracket) or a combination of different types or classes of rigid objects (e.g., a first class of rigid metal brackets and a second class of metal screws, where the metal screws may be threaded through corresponding screw holes in the metal bracket). Each type of object (e.g., the metal bracket and the metal screws) may be represented by a corresponding canonical 3-D model. Because all such rigid objects are expected or assumed to have substantially the same shape (e.g., manufacturing quality control procedures have removed most or all malformed or damaged components), and therefore these canonical 3-D models are expected to match the configuration of the objects observed in the scene with high accuracy. However, in the case of objects that are deformable (e.g., non-rigid), the objects of a particular type or class may be observed in of a wide range of different configurations. Therefore, a single rigid 3-D model may be insufficient to accurately represent the pose and configuration of object in the scene. For example, a flex circuit (or flexible printed circuit board) may have any of a wide range of potential configurations, where the circuit may be flat, curved, twisted, tangled with other flex circuits, and/or the like. A single rigid 3-D model of the flex circuit may depict that component in only a single configuration (e.g., flat), which makes it difficult or impossible to accurately align the pose of the 3-D model to the observed pose of the flex circuit in the scene which may have a physical configuration other than a flat configuration, due to twists and bends in the flexible portion. In addition, the configuration or shape of the deformable object may change dynamically over time as the deformable object interacts with other objects in the scene. For example, lifting a flexible printed circuit board by one connector, can cause the other parts of the flex circuit to bend and/or twist under the influence of gravity. Furthermore, a robotic system may need to manipulate the flex circuit to remove (or create) twists before connecting the flex circuit to a workpiece.

[00127] Therefore, aspects of embodiments of the present disclosure relate to additional techniques for computing the 6-DoF poses of deformable objects. For the sake of convenience, aspects of embodiments of the present disclosure will be described in the context of detecting the 6-DoF poses of flex circuits (or flexible printed circuit boards), but embodiments of the present disclosure are not limited thereto, and may be applied to any of a wide range of deformable objects such as objects that include one or more continuously pivotable joints and objects (e.g., a hinge or other object including multiple rigid components with pliable connections therebetween), objects that have at least some portions that are continuously pliable (e.g., a cloth, a rope or string, wires and cables, flexible tubing, soft rubber parts, a bag or other pliable container containing rigid or soft objects and/or fluids, foam packing materials, or the like) and objects that are pliable and that retain their shapes after being bent into various shapes (e.g., metal wires, metal sheets or foil). [00128] FIG. 3 is a flowchart depicting a method for computing six-degree-of- freedom (6-DoF) poses of objects, including deformable objects, according to some embodiments of the present disclosure.

[00129] In operation 310, the pose estimator 100 controls a plurality of cameras, such as the master camera 10 and the support cameras 30, to capture images of the scene from multiple viewpoints. In some embodiments, the cameras are configured to capture images concurrently or substantially simultaneously. Each camera is arranged at a different pose with respect to the scene 1 , such that each camera captures scene from its corresponding different viewpoint. Accordingly, the collection of images captured by the cameras represent a collection of multi-viewpoint images of the scene 1. (In some embodiments, the images are captured from multiple viewpoints using one or more cameras, such as by moving the one or more cameras between different viewpoints while keeping the scene fixed, and/or rigidly transforming the scene between captures by the one or more cameras.)

[00130] In some circumstances, one or more of the “cameras” are multi-modal cameras that capture multiple images from the same viewpoint, but having in different modalities, such as different portions of the electromagnetic spectrum (e.g., red, green and blue portions of the visible light spectrum, near infrared light, far infrared light, ultraviolet light, etc.), different optical filters (e.g., linear polarization filters at different angles and/or circular polarization filters), and combinations thereof. Accordingly, a collection of multi-viewpoint images of a scene does not require that all images be captured from different viewpoints, but only that there are at least two images captured from different viewpoints. Such a collection of multi viewpoint images therefore may include at least some images that are captured from the same viewpoint.

[00131] In operation 330, the pose estimator 100 computes object-level correspondences on the multi-viewpoint images of the scene. More specifically, instances of one or more types of objects are identified in the multi-viewpoint images of the scene, and corresponding instances of objects are identified between the multi-viewpoint images. For example, a scene 1 may include two cubes and three spheres, and various of the multi-viewpoint images may depict some or all of these five objects. A process of instance segmentation identifies the pixels in each of the images that depict the five objects, in addition to labeling them separately based on the type or class of object (e.g., a classification as a “sphere” or a “cube”) as well as instance labels (e.g., assigning a unique label to each of the objects, such as numerical labels “1,” “2,” “3,” “4,” and ”5”). Computing object-level correspondences between the multi-viewpoint images further relates to computing consistent labels between the different viewpoints (for example, such that the same cube is labeled “1” from each of the viewpoint).

[00132] Systems and methods for computing object-level correspondences are described in International Patent Application No. PCT/US21/15926, titled “SYSTEMS AND METHODS FOR POSE DETECTION AND MEASUREMENT,” filed in the United States Patent and Trademark Office on January 29, 2021 , which, as noted above, is incorporated by reference herein in its entirety. For the sake of clarity, some techniques for computing object-level correspondences on images are described herein with reference to FIGS. 4A, 4B, and 4C.

[00133] In general terms, embodiments of the present disclosure are directed to reducing a search space for conducting image processing tasks such as, for example, pixel-level correspondence. In one embodiment, instance segmentation is performed to identify different instances of objects in images portraying a scene as viewed from different viewpoints, and instance segmentation maps/masks may be generated in response to the instance segmentation operation. The instance segmentation masks may then be employed for computing object level correspondences.

[00134] In one embodiment, object level correspondence allows the matching of a first instance of an object appearing in a first image that depicts a view of a scene from a first viewpoint, to a second instance of the same object appearing in a second image that depicts a view of a scene from a second viewpoint. Once object level correspondence is performed, the search space for performing, for example, pixel- level correspondence, may be limited to the regions of the image that correspond to the same object. Reducing the search space in this manner may result in faster processing of pixel-level correspondence and other similar tasks.

[00135] FIG. 4A is a flow diagram of a process for object level correspondence according to one embodiment. The process may be implemented by one or more processing circuits or electronic circuits that are components of the pose estimator 100. It should be understood that the sequence of steps of the process is not fixed, but can be modified, changed in order, performed differently, performed sequentially, concurrently, or simultaneously, or altered into any desired sequence, as recognized by a person of skill in the art. The process described with respect to FIG. 4A may be used, in some embodiments of the present disclosure, to compute object level correspondences in operation 330 of FIG. 3, but embodiments of the present disclosure are not limited thereto.

[00136] The process starts, and at block 400, the pose estimator 100 receives multi-view images from the main and support cameras 10, 30. A first image captured by one of the cameras may depict one or more objects in a scene from a first viewpoint, and a second image captured by a second camera may depict the one or more objects in the scene from a second viewpoint different from the first viewpoint. The images captured by the cameras may be, for example, polarized images and/or images that have not undergone any polarization filtering.

[00137] At block 402 the pose estimator 100 performs instance segmentation and mask generation based on the captured images. In this regard, the pose estimator 100 classifies various regions (e.g. pixels) of an image captured by a particular camera 10, 30 as belonging to particular classes of objects. Each of the different instances of the objects in the image may also be identified, and unique labels be applied to each of the different instances of objects, such as by separately labeling each object in the image with a different identifier.

[00138] In one embodiment, segmentation masks delineating the various object instances are also be generated. Each segmentation mask may be a 2-D image having the same dimensions as the input image, where the value of each pixel may correspond to a label (e.g. a particular instance of the object depicted by the pixel). A different segmentation mask may be generated for different images depicting different viewpoints of the objects of interest. For example, a first segmentation mask may be generated to depict object instances in a first image captured by a first camera, and a second segmentation mask may be generated to depict object instances in a second image captured by a second camera. As convolutional neural network such as, for example, Mask R-CNN, may be employed for generating the segmentation masks.

[00139] At block 404, the pose estimator 100 engages in object-level correspondence of the objects identified in the segmentation masks. In this regard, the pose estimator may invoke a matching algorithm to identify a segmented instance of a particular object in one image as corresponding (or matching) a segmented instance of the same object in another image. The matching algorithm may be constrained to search for matching object instances along an epipolar line through an object instance in one image to find a corresponding object instance in a different image. In one embodiment, the matching algorithm compares different features of the regions corresponding to the segmented object instances to estimate the object correspondence. The matching of object instances from one image to another may narrow a search space for other image processing tasks such as, for example, performing pixel level correspondence or keypoint correspondence. The search space may be narrowed to the identified regions of the images that are identified as corresponding to the same object.

[00140] At block 406, the pose estimator 100 generates an output based on the object-level correspondence. The output may be, for example, a measure of disparity or an estimated depth (e.g., distance from the cameras 10, 30) of the object based on the disparity between corresponding instances as depicted in the various images. In one embodiment, the output is a three-dimensional reconstruction of the configuration of the object and a 6-DoF pose of the object, as described in more detail below with respect to FIG. 3.

[00141] FIG. 4B is a block diagram of an architecture for instance segmentation and mask generation of step 402 according to one embodiment. Input images 410 captured by the various cameras 10, 30 are provided to a deep learning network 412 such as, for example, a CNN backbone. In the embodiments where the images include polarized images, the deep learning network may be implemented as a Polarized CNN backbone as described in PCT Patent Application No. PCT/US2020/048604, also filed as U.S. Pat. App. No. 17/266046, the content of which is incorporated herein by reference.

[00142] In one embodiment, the deep learning network 412 is configured to generate feature maps based on the input images 410, and employ a region proposal network (RPN) to propose regions of interest from the generated feature maps. The proposals by the CNN backbone may be provided to a box head 414 for performing classification and bounding box regression. In one embodiment, the classification outputs a class label 416 for each of the object instances in the input images 410, and the bounding box regression predicts bounding boxes 418 for the classified objects. In one embodiment, a different class label 416 is provided to each instance of an object.

[00143] The proposals by the CNN backbone may also be provided to a mask head 420 for generating instance segmentation masks. The mask head 416 may be implemented as a fully convolutional network (FCN). In one embodiment, the mask head 420 is configured to encode a binary mask for each of the object instances in the input images 410.

[00144] FIG. 4C is a more detailed flow diagram of a matching algorithm employed at step 404 (FIG. 4A) for identifying object-level correspondence for a particular object instance in a first segmentation mask according to one embodiment. The process may repeat for all object instance identified in the first segmentation mask. The sequence of steps of the process of FIG. 4C is not fixed, but can be modified, changed in order, performed differently, performed sequentially, concurrently, or simultaneously, or altered into any desired sequence, as recognized by a person of skill in the art.

[00145] At block 430, the matching algorithm identifies features of a first object instance in a first segmentation mask. The identified features for the first object instance may include a shape of the region of the object instance, a feature vector in the region, and/or keypoint predictions in the region. The shape of the region for the first object instance may be represented via a set of points sampled along the contours of the region. Where a feature vector in the region is used as the feature descriptor, the feature vector may be an average deep learning feature vector extracted via a convolutional neural network.

[00146] At block 432, the matching algorithm identifies an epipolar line through the first object instance in the first segmentation mask.

[00147] At block 434, the matching algorithm identifies one or more second object instances in a second segmentation mask that may correspond to the first object instance. A search for the second object instances may be constrained to the epipolar line between the first segmentation map and the second segmentation map that runs through the first object instance. In one embodiment, the matching algorithm searches approximately along the identified epiploar line to identify object instances in the second segmentation mask having a same class identifier as the first object instance. For example, if the first object instance belongs to a “dog” class, the matching algorithm evaluates object instances in the second segmentation mask that also belong to the “dog” class, and ignores objects that belong to a different class (e.g., a “cat” class).

[00148] At block 436, the matching algorithm identifies the features of the second object instances that belong the same class. As with the first object instance, the features of a particular second object instance may include a shape of the region of the second object instance, a feature vector representing the region, and/or keypoint predictions in the region.

[00149] At block 438, the matching algorithm compares the features of the first object instance to the features of second object instances for determining a match. In one embodiment, the matching algorithm identifies a fit between the features of the first object instance and features of the second object instances for selecting a best fit. In one embodiment, the best fit may be identified via a matching function such as the Hungarian matching function. In one embodiment, the features of the object instances are represented as probability distributions, and the matching function attempts to find a match of the probability distributions that minimizes a Kullback- Leibler (KL) divergence.

[00150] At block 440, a determination is made as to whether a match has been found. If the answer is YES, an output is generated at block 442. The output may include, for example, information (e.g. object ID) of the second object instance that matched the first object instance.

[00151] If the answer is NO, an output may be generate indicating a match failure at block 444. [00152] Accordingly, object level correspondences can be computed from the multi-viewpoint images. These object level correspondences may be used to extract corresponding crops or patches from the multi-viewpoint images, where each of these crops or patches depicts a single instance of an object, and collections of corresponding crops or patches depict the same instance of an object from multiple viewpoints.

[00153] In operation 350, the pose estimator 100 loads a 3-D model of the object based on the detected object type one or more object detected in the scene (e.g., for each detected instance of a type of object). For example, in a circumstance where the collection of objects 22 includes a mixture of different types of flexible printed circuit boards, the process of computing object-level correspondences assigns both an instance identifier and a type (or classification) to each detected instance of a flexible printed circuit board (e.g., which of the different types of printed circuit boards). Therefore, a 3-D model of the object may then be loaded from a library based on the detected object type.

[00154] In operation 370, the pose estimator 100 aligns the corresponding 3-D model to the appearances of the object to be consistent with the appearance of the object as seen from the different multiple viewpoints. The alignment process in operation 370 may also include deforming the 3-D model to match the estimated configuration of the actual object in the scene. This alignment of the 3-D model provides the 6-DoF pose of the object in a global coordinate system (e.g., a coordinate system based on the main camera 10 or based on the robot controller 28).

[00155] Various techniques for loading an appropriate model from a library in accordance with operation 350 and aligning the loaded model in accordance with operation 370 will be described in more detail below. In embodiments of the present disclosure, the various techniques described below may be used independently or in combination, such as by supplying a 3-D mesh model output from one technique as an input 3-D mesh model of another technique. In addition, some aspects of embodiments of the present disclosure relate to selecting between different techniques based on detected characteristics of objects in the scene and applying the selected techniques to computing a 6-DoF pose of an object.

[00156] Generally, the methods described herein will make use of a 3-D model or computer-aided-design (CAD) model C of the object (e.g., as loaded in operation 350) and two-dimensional (2-D) image data / of the object (e.g., as captured by the cameras in operation 310 and with object-level corresponding patches of the images extracted therefrom in operation 330). In some embodiments, the output of the 6- DoF pose estimation technique (computed by the pose estimator 100) includes a mesh M and its 6-DoF pose a global coordinate system (e.g., 3 dimensional translational and rotational coordinates in the coordinate system used by the controller 28 of a robotic arm 24 or a coordinate system oriented with respect to a master camera 10) for each of the detected objects in the scene.

[00157] FIG. 5 is a flowchart depicting a method 500 for computing 6-DoF poses of objects based on the appearance of object surface texture using multiple viewpoints reconstruction according to some embodiments of the present disclosure. In some circumstances, the pose estimator 100 estimates the poses of deformable objects 22 having distinct surface textures (textures in the sense of color and other aspects controlling the appearance of a surface, as opposed to being limited to three- dimensional surface roughness or indentations, which may also affect the visual appearance of the surface). For example, a flexible printed circuit board may have visible texture in the form of screen-printed markings and labels (e.g., labeling pins and numbers for various components) and may also have visible electrical traces that connect various electronic components that are mounted on the flexible printed circuit board (e.g., wires that electrically connect different connectors on the flexible printed circuit board). As another example, a commercial product may be wrapped in standardized printed packaging, more concretely, a particular type of candy may be wrapped in a particular type of plastic film, where the film has a printed color texture (e.g., logos for the candy and the brand, pictures of the product, nutrition information, ingredients list, and the like). The shapes of these packaged food products may be inconsistent from one instance to the next, or even as a single instance is manipulated and moved, because the packaging may not tightly conform to the shape of the product contained therein, because of variation in the shape of the product, and/or because the product may be loose within the packaging (e.g., in the case of a bag of loose candy such as jelly beans or a bag of peanuts), thereby resulting in the configuration of the object, and the shape of its outer surface, to change as the object is moved around. Similar issues may occur with other packaged goods, such as refill packages for liquid soaps and detergents and shrink wrapped packages of paper products.

[00158] Accordingly, some aspects of embodiments of the present disclosure relate to using the known or expected visible surface texture associated with a particular type or class of object to estimate the deformation of the instance of the object observed in the scene 1.

[00159] In more detail, in operation 350, a 3-D model associated with the type of object is loaded from a library of models. For example, when the object instance is classified as a particular type of printed circuit board, a 3-D model of the printed circuit board is loaded from the library of models. As another example, when the object instance is a classified as a particular size and variety of candy bar, a 3-D model of that type of candy bar is loaded from the library of models. In various embodiments of the present disclosure, the library of 3-D models stores at least one 3-D model (e.g., 3-D mesh model) for each type of object, where the 3-D model also includes a surface texture (e.g., a 2-D image) mapped onto the surface of the 3-D model in a uv coordinate space.

[00160] In operation 510, for each of the n images I _n of the same object instance from different viewpoints, the pose estimator 100 computes or predicts a uv correspondence map. Each uv correspondence map is a dense correspondence between pixels of the image and points on the surface of the CAD model C. In some embodiments, the correspondence map is computed using a trained neural network, such as a neural network trained specifically for a particular type of object having a particular surface texture (e.g., a particular piece of packaging having a particular printed design). In particular, in some embodiments, the input to such a trained neural network is an image of the object from one viewpoint, and the output of the network is the uv correspondence map for that viewpoint, where the correspondence map identifies locations or coordinates in the surface texture in uv coordinate space (e.g., a coordinate space with respect to the surface texture or the surface of the 3-D model C). In some embodiments, the correspondences are detected based on detecting keypoints on the surface of the object and identifying the corresponding locations of keypoints in the surface texture of the 3-D model in uv coordinate space. [00161] In operation 530, the pose estimator 100 matches the dense correspondences from the uv correspondence map and the position of the points in 3-D space. In particular, for each of the images, the camera pose in a global coordinate system is known. Accordingly, the pose estimator 100 triangulates the 3- D locations of corresponding points seen in multiple images based on the known poses of the cameras that captured the images and based on, for example, projective reconstruction through epipolar geometry. These computed 3-D locations of corresponding points that appear in the different images generates a point cloud that partly defines the surface shape of resulting mesh M where it is visible to the cameras. In addition, the corresponding points of the surface texture of the 3-D model can be mapped to the point cloud to generate a partial 3-D model, where the pose of the partial 3-D model may be updated to minimize a difference (e.g., as represented by a loss function) between the current estimated pose of the 3-D model and the images.

[00162] In operation 550, the pose estimator 100 updates the locations or positions of vertices of the 3-D model to reconstruct the remainder of the model. For example, in some embodiments, the pose estimator 100 performs a physical simulation with additional specific constraints based on the object class. As one example of a constraint, when predicting or estimating the pose of a sealed bag (e.g., containing a liquid or granular product), the sealed bags may have a known, consistent fill volume, and therefore the fixed volume of the bag acts as a constraint that limits the possible shapes (e.g., positions of the vertices) of portions of the object that are not depicted in the images (e.g., portions that are not visible or invisible to the cameras due to, for example, occlusion). Performing such a simulation subject to constraints reduces the search space for minimizing or optimizing a loss function to update the locations of the vertices of the 3-D model to match the images / of the object.

[00163] In some embodiments, a loss function E is defined as follows: where I _n is an image from viewpoint n among N viewpoints, R _n (M ) is a (2-D) render of mesh (or 3-D model) M from viewpoint n, the mesh M is a function of translation (t) and rotation (r) parameters accordingly, and ||-|| ₂ indicates an L ₂ -norm. (In some embodiments, the mesh M is also a function of the positions of the vertices of the mesh model M.) S _pn and S _n are silhouettes of the object as they appear in the render R _n (M) and the real image I _n accordingly, and these silhouettes may be interpreted as binary images (e.g., having a value of 1 at pixel locations belonging to the object and having a value of 0 at pixel locations that do not belong to the object). The ® operator is a pixel-wise (or element-wise) product operator, the ® operator is a pixel- wise (or element-wise) addition operator, and || || indicates an L- _L -norm. The E _x component in Equation (13) of the loss function E in Equation (12) may be interpreted as a pixel level differences between the appearance of the object in the renderings, in accordance with the current mesh position, versus the real images captured by the cameras. The E ₂ component in Equation (14) of the loss function E in Equation (12) may be interpreted as an intersection-over-union (IOU) loss, measuring the alignment of the silhouette of model M with the silhouette of the object as it appears in the images /.

[00164] In some embodiments of the present disclosure, one or more of the cameras (e.g., the master camera 10 and/or the support cameras 30) may include polarization cameras configured to capture polarization raw frames of objects. In some embodiments, the pose estimator 100 is configured to compute the surface normals of surfaces in a scene based on shape from polarization (SfP) techniques, as described above. Accordingly, in some embodiments of the present disclosure, the loss function E further accounts for differences in the surface normals in a rendering of a 3-D model versus surface normals as computed based on the polarization raw frames using SfP. For example, in some embodiments, Equation (12) is modified to further include a term E ₃ relating to differences in surface normals. In some embodiments of the present disclosure, the images / include surface normals maps, where each pixel corresponds to the slope of the surface depicted at that pixel (as computed based on the polarization raw frames and SfP), and a corresponding rendering R(M ) is a normals map identifying a computed the slope of the surface of the 3-D model of the object at each pixel, as viewed from the pose of the n-th camera and as the 3-D model is posed in accordance with its parameters (e.g., rotation r and translation t).

[00165] Accordingly, computing the locations or positions of the vertices of the 3-D model to match the images / of the object based on identifying correspondences between the images and with the surface texture of the 3-D model generates an updated deformation and pose of a 3-D model M in a global coordinate space, which is output by the pose estimator 100 as the detected pose of the object.

[00166] While embodiments of the present disclosure are described above in the context of textures as observable in images captured by color (e.g., visible light) cameras, embodiments of the present disclosure are not limited thereto, and the techniques described with respect to FIG. 5 may also be applied to images captured by cameras in other modalities, such as polarization cameras (e.g., a camera with a polarization filter), infrared cameras, and the like, where surface texture is observable in those other imaging modalities. For example, polarization imaging may enable the detection of reflective surfaces that produce glare, as well as the detection of transparent surfaces (e.g., a completely transparent bag or a bag having a transparent portions to show the contents of the bag).

[00167] Some aspects of embodiments of the present disclosure relate to detecting the 6-DoF poses of deformable objects in general, including the case where some or all of the surface of the deformable objects have little or no distinctive surface texture (e.g., textureless or uniform surface textures or that contain confusing textures such as repeating patterns).

[00168] FIG. 6 is a flowchart depicting a method 600 for computing 6-DoF poses of objects based on a library of 3-D models of objects according to some embodiments of the present disclosure. Inputs to the technique 600 shown in FIG. 6 include images / of the object, as extracted by the pose estimator based on identifying object-level correspondences in operation 330 and a type or class of the object depicted in the images, as determined through instance segmentation performed in operation 330. [00169] In operation 610, the pose estimator 100 identifies a collection of 3-D models within the library of 3-D models of objects, where the identified collection of 3-D models includes different 3-D models corresponding to different possible deformations of the same object or same class or type of object. For example, a collection of models for a particular flexible printed circuit board (e.g., representing a class of flexible printed circuit boards that are substantially the same) may correspond to various possible deformations or physical conditions of the flex circuit, such as with various portions of the flex circuit curved and/or twisted in different ways. As another example, a collection of models for a bag of hard candies may correspond to different ways in which the hard candies may be distributed within the bag, as well as various ways in which the bag may be folded, compressed, wrinkled, and the like, subject to physical constraints (e.g., standard fill levels of the bag with respect to both product and air and topological constraints, such as excluding unlikely configurations such as a bag tied into a knot). Details on embodiments for generating collections of models of a type or class of object in various configurations will be described in more detail below. In some embodiments, a collection of 3-D models for a given class or type of object may include on the order of thousands of different 3-D models of the object in different configurations that cover the space of configurations that are most likely to be observed in a scene 1.

[00170] In operation 630, the pose estimator 100 searches the collection of 3-D models of the object type for a deformed mesh M _t that most closely matches the shape of the object in the scene as depicted in the images / of the object. In some embodiments, the quality of the match is quantified based on the loss function E defined above with respect to Equation (12).

[00171] In some embodiments of the present disclosure, the search is performed using a brute-force search among all of the 3-D models or mesh models in the collection of 3-D models (e.g., computing the loss function for all 3-D models and for some set of rotations r of the model, such as 36 possible rotations along each axis of rotation).

[00172] In some embodiments of the present disclosure, a cluster-based search is performed, where the pose estimator 100 evaluates the quality of the match between the images / of the object and several different candidate 3-D models from the collection having very different configurations from one another. After identifying a most similar 3-D model from the candidate 3-D models, a cluster of 3-D models that are similar to the identified, most similar 3-D model is selected (and less similar to any of the other representative 3-D models). The process may then continue by selecting candidate models that are different from one another within the current cluster of 3-D models, and comparing the images / of the object to the candidate 3-D models of the cluster, and iteratively identifying smaller clusters of models (e.g., clusters of more similar models) until a stopping condition is met, such as when only a single 3-D model remains in a cluster, such as when an iteration limit is reached, or such as where all of the candidate models have the same match quality with respect to the images / of the object (in which case one of the candidate models may be selected randomly).

[00173] In some embodiments of the present disclosure, the input images / of the object include one or more depth maps computed from the cameras 10, 30. For example, any of the master camera 10 and/or support cameras 30 may include a stereo camera system that captures stereo pairs of images, where the stereo pairs are used to compute the one or more depth maps (or depth scans) of the object from one or more viewpoints. In some embodiments, these one or more depth maps or depth scans are converted into 3-D point clouds representing the shape of the object. (In some embodiments, 3-D point clouds captured from different viewpoints are merged using, for example, an iterative closest point algorithm, or directly merged by transforming the locations of the points of the point cloud to a common coordinate system based on the known relative poses of the cameras at the different viewpoints.) In some embodiments, the resulting point cloud is used to select a small group of 3-D models (e.g., three to five different 3-D models) from the collection of 3- D models of the object type or class. This selection of 3-D models that match the one or more depth maps may be made using an iterative closest point algorithm to find a best alignment between the point cloud and the various 3-D models of the collection, and to evaluate the quality of the alignment based on a loss function (e.g., a distance from each of the points of the point cloud to the surface of the 3-D model). In some embodiments, the group of 3-D models that match the one or more depth maps is used to perform a further cluster-based search as described above. In some embodiments, the group of 3-D models that match the one or more depth maps are used as candidates updating the poses of each (e.g., iteratively updating the rotation and translation of the 3-D models) to be consistent with all of the images / of the object (e.g., the depth maps as well as other images, such as color images), and a model having a lowest error (e.g., as computed in accordance with the loss function E), is output as the 3-D model M.

[00174] According to some embodiments of the present disclosure, the pose estimator 100 selects the 3-D model from the collection of 3-D models and its estimated 6-DoF pose through joint optimization over multiple variables. In some embodiments, these variables include a selection index (selecting a particular 3-D model) and pose. In some embodiments, these variables include differentiable functional variation and pose. [00175] In some embodiments of the present disclosure, a machine learning model such as a neural network, is trained to classify objects as depicted in the images / of the object to identify meshes that are most similar to the meshes in the collection to select a set of the most probable (e.g., most similar) meshes to try. Such a machine learning model may be referred to herein as a trained deformation classifier. For example, the output of the trained deformation classifier may be a vector having a length equal to the number of different 3-D models in the collection of 3-D models of different configurations of the object, where the values of the vector represent a confidence or likelihood that a corresponding 3-D model of the collection matches the configuration of the object depicted in the images /. The identified most probable models may all be posed with six degrees of freedom to align with the object depicted in the input images / to find a model minimizing an error or loss function. In some embodiments, the pose estimator 100 generates an average 3-D mesh model based on the average (e.g., mean) of the identified template models (mean shape) and performs a rigid 6-DoF pose estimation of the average 3-D mesh model based on the images / of the object.

[00176] In some embodiments of the present disclosure, the pose estimator 100 identifies a 3-D model from the 3-D models of the collection of models in accordance with a probabilistic approach. In more detail, each of the 3-D models in the collection of models may be associated with one or more probabilities, each of the one or more probabilities representing the likelihood of observing the object in the particular configuration associated with the 3-D model, where different probabilities associated with a particular condition may correspond to different contexts of the object (e.g., whether the object is free versus attached to some other component, whether the object is at the top of a pile versus underneath or pressed against other objects, and/or other environmental conditions such as the ambient temperature and/or air pressure). For example, a sealed bag of candies may be observed with a variety of total volumes that follow a Normal distribution around a mean typical (e.g., intended) fill volume, and where the total volume of the bag may vary based on ambient air pressure. The shape of the bag may be more constrained when the fill volume is higher and may be more varied when the fill volume is lower. A lower bound of volume may correspond to approximately the volume of the candies (corresponding to a case where the bag has been punctured), and volumes between this lower bound and a lower end of a typical fill volume may be unlikely to be observed (e.g., because a bag may be unlikely to hold air after it is punctured). For any particular volume of the bag, the possible configurations of the bag may be non-uniform ly distributed, where more extreme bending or folding of the bag may be less likely than more median (e.g., flatter) configurations of the bag. Accordingly, in some embodiments of the present disclosure, the pose estimator 100 identifies a 3-D model from the collection based on consistency with the images / of the object, where the consistency is weighted by the probability of observing the particular configuration of the object represented by the 3-D model. Methods for estimating the probability of observing an object in a particular configuration will be described in more detail below with respect to methods for generating collections of 3-D models of objects for a library.

[00177] FIG. 7 is a flowchart depicting a method for computing 6-DoF poses of objects based on shape morphing according to some embodiments of the present disclosure.

[00178] In operation 710, the pose estimator 100 estimates the 6-DoF pose of the input 3-D model C to align the 3-D model to the input images /, such as by minimizing a loss function E as described above. In some embodiments, the 3-D model C is a model as identified from a collection of 3-D models of a type of object stored in a library of models in accordance with techniques described above with respect to FIG. 6.

[00179] In operation 730, the pose estimator 100 refines the positions of the vertices of the 3-D model (or 3-D mesh model) to morph the 3-D model to more closely match the appearance of the object in the images / (such as by further reducing or minimizing an error metric or loss function E). In some embodiments of the present disclosure, this is performed using a differentiable renderer-based refinement step with the deformation of the 3-D model being optimized to minimize error metric E. In more detail, the use of a differential Tenderer enables errors computed by the loss function E to be back-propagated through the differentiable 3- D Tenderer to identify transformations to the underlying 3-D model (e.g., updates to the positions of the vertices of the 3-D model) that would reduce the error, such as by applying gradient descent (see, e.g., Liu, Shichen, et al. "Soft rasterizer: A differentiable Tenderer for image-based 3d reasoning." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2019.).

[00180] As noted above, in some embodiments of the present disclosure, the loss function includes components accounting for the error or difference between the surface normals of the object as measured from polarization raw frames captured of the object in the scene by polarization cameras and the rendered surface normals of the 3-D model in its state of deformation and pose. Accordingly, the use of polarization to measure the surface normals of objects in a scene can further improve the accuracy of the 6-DoF pose computed by the pose estimator 100. [00181] FIG. 8 is a depiction of an architecture of a transformation network 800 configured to transform an input 3-D model (or canonical or representative 3-D model of the object) to a deformed 3-D model matching or consistent with the images captured of an object according to one embodiment of the present disclosure. The deformed 3-D model may differ from the input canonical 3-D model in that the positions of some of the vertices are transformed (e.g., translated within the object coordinate space) such that the configuration or shape of the deformed 3- D mesh model is more consistent with the appearance of the object than the input canonical 3-D mesh model.

[00182] As shown in FIG. 8, the pose estimator 100 supplies input images 810 to a feature extraction network 811 to generate a plurality of feature maps. The input images 810 may include images captured by the cameras 10, 30 and/or images generated from those images, such as depth maps (e.g., computed from stereo pairs of images), tenors in polarization representation space such as AOLP and DOLP maps (e.g., computed from polarization raw frames), surface normals maps, and the like.

[00183] In the embodiment shown in FIG. 8, the feature extraction network 811 includes a convolutional neural network (CNN) backbone 812, which computes feature maps from the input images 810 and supplies the feature maps to a feature pyramid network (FPN) 814. The CNN backbone 812 may have an architecture such as the CNN backbones used in Mask R-CNN (Fie, Kaiming, et al. "Mask R-CNN." Proceedings of the IEEE International Conference on Computer Vision. 2017.), AlexNet (see, e.g., Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Flinton. "ImageNet classification with deep convolutional neural networks." Advances in neural information processing systems. 2012.), VGG (see, e.g., Simonyan, Karen, and Andrew Zisserman. "Very deep convolutional networks for large-scale image recognition." arXiv preprint arXiv: 1409.1556 (2014).), ResNet-101 (see, e.g., Kaiming Fie, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 770-778, 2016.), MobileNet (see, e.g., Howard, Andrew G., et al. "Mobilenets: Efficient convolutional neural networks for mobile vision applications." arXiv preprint arXiv: 1704.04861 (2017).), MobileNetV2 (see, e.g., Sandler, Mark, et al. "MobileNetV2: Inverted residuals and linear bottlenecks." Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2018.), and MobileNetV3 (see, e.g., Howard, Andrew, et al. "Searching for MobileNetV3." Proceedings of the IEEE International Conference on Computer Vision. 2019.), although embodiments of the present disclosure are not limited thereto. The feature pyramid network (FPN) 814 (see, e.g., Lin, Tsung-Yi, et al. "Feature pyramid networks for object detection." Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2017.) enables the capture of multiscale features in the images (e.g., distinctive features of objects appearing at different sizes within the image), although embodiments of the present disclosure are not limited thereto, and other networks for capturing multiscale features may be used, such as a U-Net (see, e.g., Ronneberger, Olaf, Philipp Fischer, and Thomas Brox. "U-Net: Convolutional networks for biomedical image segmentation." International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, Cham, 2015.).

[00184] The image features computed by the feature extraction network 811 are combined (e.g., concatenated) with a representation of the canonical 3-D mesh model at a concatenation node 816, and the model, and the combined image features and the canonical 3-D mesh model are supplied as input to a CAD model to CAD deformed model (CAD2CADD) network 818, such as a graph convolutional neural network, to generate a deformed 3-D mesh model. In some embodiments, the CAD2CADD network 818 includes multiscale skip connections to preserve detail at different spatial frequencies.

[00185] Some aspects of embodiments of the present disclosure relate to performing end-to-end training of the transformation network 800 for transforming a canonical 3-D mesh model to a deformed 3-D mesh model, where the deformed 3-D mesh model matches or is consistent with the shape of the object depicted in the input images 810. In some embodiments, a separate transformation network 800 is trained for each type of object expected to be observed by the pose estimator 100 (e.g., separate networks for each different type of flexible printed circuit board, other components, and workpieces in a pose estimator 100 configured in an electronics manufacturing context, or separate networks for each different type of bag of candy and for each different type of box that the bags of candies will be packed into, in the case of a pose estimator 100 supporting a food packing robotic system).

[00186] The transformation network 800 may be trained based on labeled training data, where the training data includes a particular input 3-D mesh model and sets of input images along with their corresponding ground truth deformed 3-D mesh model. The training set may include a large number of different deformed 3-D mesh models representing different configurations of the object, along with input images depicting an object in the particular configuration. Systems and methods for generating training data will be described in more detail below.

[00187] To perform end-to-end training, sets of training images and training initial or canonical 3-D mesh models are supplied to the transformation network 800 to compute output deformed 3-D mesh models. The output deformed 3-D mesh models are then compared against the ground truth training deformed 3-D mesh models to compute an error in accordance with a loss function. The errors are used to update the parameters of the transformation network 800 (e.g., the weights of connections within the various neural networks, such as the feature extraction network 811 , which may include a CNN backbone 812 and a feature pyramid network 814, and the CAD2CADD network 818) in accordance with a backpropagation algorithm.

[00188] In some embodiments, the loss function used to compute the error uses a chamfer distance (see, e.g., Kurenkov, Andrey, et al. "Deformnet: Free-form Deformation Network for 3D Shape Reconstruction from a Single Image." 2018 IEEE Winter Conference on Applications of Computer Vision (WACV). IEEE, 2018., the entire disclosure of which is incorporated by reference herein). In addition, in some embodiments, regularization is applied to the activations and/or outputs of the transformation network 800, including regularization of the surface normals, requiring smoothness on the output deformed 3-D mesh model (e.g., disfavoring or smoothing out irregular or extreme deformations in the output model), and functional smoothness (e.g., ensuring that the CAD2CADD network 818 applies equal motion). [00189] In some embodiments, the process of training the transformation network 800 includes the retraining of the feature extraction network 811 to output features that are more closely linked to vertices/edges. For example, a pre-trained CNN backbone 812 and pre-trained feature pyramid network 814 may be used at the start of the training process, and, after performing training of the entire transformation network 800, the feature extraction network 811 computes image features relate more closely to detecting features related to the vertices and edges of objects depicted in the input images 810. In some embodiments, the feature extraction network 811 is trained to detect these features that are more closely related to vertices and edges in a process that is separate from (e.g., performed before) the end-to-end training of the transformation network 800 as a whole. For example, the feature extraction network 811 may be trained using training data that includes input images and desired output feature maps in which the vertices and edges of the object are labeled.

[00190] FIG. 9 is a flowchart depicting a method for computing 6-DoF poses of objects based on a library of models of objects and shape morphing according to some embodiments of the present disclosure. The method 900 shown in FIG. 9 may be used to perform operations 350 and 370 of method 300 as shown in FIG. 3. As shown in FIG. 9, in operation 910 the pose estimator 100 may use images / of an object and the object type or class to identify a closest or most similar 3-D model from a library of models and a 6-DoF pose of the identified 3-D model that maximizes or optimizes a consistency between the posed identified 3-D model and the object depicted in the images. Operation 910 may be performed using techniques corresponding to those described above with respect to method 600 and depicted in FIG. 6. In operation 930, the pose estimator 100 refines the shape of the 3-D model identified in operation 910, such as by further deforming the mesh (e.g., modifying the positions of the vertices of the mesh) to more closely match the appearance of the object in the input images /. Operation 930 may be performed using techniques corresponding to those described above with respect to method 700 and depicted in FIG. 7.

[00191] In some circumstances, some parts of an object may have sufficient texture for determining a shape based on uv correspondence mapping (e.g. in accordance with FIG. 5), while other portions of the same object lack sufficient texture for doing so. Accordingly, some aspects of embodiments of the present disclosure relate to applying different techniques for computing or estimating the shapes of different parts of the same object.

[00192] FIG. 10 is a flowchart depicting a method 1000 for selecting a technique for estimating a pose of an object based on whether surface texture is visible in the surfaces of the object as depicted in the input images / of the object according to one embodiment of the present disclosure. The method 1000 shown in FIG. 10 may be used to perform operations 350 and 370 of method 300 as shown in FIG. 3. In operation 1010, the pose estimator 100 detects surface texture in the surfaces of the object depicted in the images / of the object. This may include identifying the regions of the images that include texture (e.g., by detecting the presence of edges, gradients, or keypoints within the regions of the images / identified through instance segmentation in operation 330 as belonging to the object). In operation 1030, the pose estimator 100 determines if surface textures were detected in the surfaces of the object (e.g., whether substantially all of the surfaces of the object depicted in the images / have surface texture). If not, then the pose estimator 100 proceeds, in operation 1050, with estimating the pose of the object based on identifying a most similar 3-D model from the library and/or performing shape deformation, as described above with respect to, for example, method 600 of FIG. 6, method 700 of FIG. 7, and method 900 of FIG. 9. If surface texture is detected, then the pose estimator 100 proceeds, in operation 1070, with estimating the pose of the object based on uv correspondence mapping of surface textures with respect to, for example, method 500 of FIG. 5.

[00193] Generating a library of 3-D models of objects

[00194] In some embodiments of the present disclosure, a library of 3-D models of objects includes representations of all types of objects expected to be encountered by the pose estimator 100 in its operation. For example, a pose estimator 100 providing 6-DoF poses of objects to the controller 28 of a robotic arm 24 may store or otherwise have access to a library of 3-D models of objects that will be encountered by the robotic arm 24 in its operating environment (e.g., the workpieces and components encountered by a robotic arm used in a particular manufacturing context).

[00195] In some embodiments, a library includes one or more models for each of the types or classes of object for which the pose estimator 100 is configured to estimate 6-DoF poses. For example, in the case of a particular flexible printed circuit board, the library may include a collection of 3-D models of the flexible printed circuit board in various configurations (e.g., various degrees of bending and/or twisting of the shape of the flexible printed circuit board). As another example, in the case of a bag of candies, the collection of 3-D models may include different configurations of the bag due to the distributions of candies within the bag and/or different folding, wrinkling, and/or puckering of surfaces of the bag. For the sake of generality, in some embodiments, the same pose estimator 100 is used to estimate the poses both of deformable objects and rigid objects. Accordingly, in some embodiments, a single 3-D model may be sufficient to represent a rigid object. In addition, as discussed above, in some embodiments of the present disclosure, a single deformable mesh model (or 3-D model) is used to represent a type or class of object, and the deformable mesh model is deformed to match the appearance of the instance of the object depicted in the images /. Furthermore, in some embodiments, the 3-D models in the library may be associated with surface textures (e.g., 2-D images) that are mapped onto the surfaces of the 3-D model, and these surface textures are used to estimate the shape and/or pose of the objects depicted in the images /, based on detecting the locations of correspondences (e.g., keypoints) in the images /. In some embodiments, these different techniques may be combined, such as where a type or class of object is associated with multiple 3-D models and a corresponding surface texture for those multiple models, and where those multiple models may be deformable 3-D mesh models.

[00196] FIG. 11 is a flowchart depicting a method for generating a collection of 3-D models of a type or class of object for a library of 3-D models of objects according to one embodiment of the present disclosure. In some embodiments of the present disclosure, a synthetic data generator is used to generate collections of 3-D models representing a deformable object in different physical configurations. The synthetic data generator may include a processor and a memory storing instructions that, when executed by the processor, cause the processor to perform operations for generating the collection of 3-D models. Generated collections of models may be stored in a library, and some or all of the 3-D models stored in the library may be provided or otherwise made accessible to the pose estimator 100, such as being stored in a mass storage device or other memory of the pose estimator 100 or stored remotely from the pose estimator and accessed over a network connection.

[00197] In the embodiment shown in FIG. 11 , the synthetic data generator receives an initial 3-D model of the object type (e.g., a particular bag of candies or a particular flexible printed circuit). The 3-D model may be a 3-D mesh model, which includes a plurality of vertices (e.g., 3-D points in object-level or model-level coordinate space) and edges defining surfaces of the 3-D model. The vertices and edges may be associated with various material properties, such as whether vertices are deformably connected (e.g., in the case of two vertices corresponding to flexible portions of a flexible printed circuit board) or rigidly connected (e.g., in the case of two vertices corresponding to a part of a rigid connector mounted on the flexible printed circuit board). The 3-D model may also store information regarding the physical properties of various portions of the 3-D model, such as spring constants of spring-like portions of objects, tensile strength, elasticity, and the like.

[00198] In operation 1110 of method 1100, the synthetic data generator generates a scene including the supplied initial 3-D model using a physics simulation engine, such as a physics engine incorporated into a 3-D computer graphics rendering system. For example, the Blender® 3-D rendering software includes a physics system that simulates various physical real-world phenomena such as the movement, collision, and potential deformation of rigid bodies, cloth, soft bodies, fluids, and the like, as affected by gravity or other forces. Accordingly, a rigid body simulation may be used for simulating the dropping of rigid components (e.g., screws, bolts, relatively stiff springs) into a rigid virtual bin, and a soft body simulation may be used for elastic or deformable components (e.g., string, wire, plastic sheeting, etc.). The synthetic data generator applies randomization or perturbation to the scene, in which the conditions of scene are modified in order to generate different scenes where the 3-D model of the object type may be perturbed into different configurations when generating multiple scenes.

[00199] The virtual scene may include other objects that may be used to simulate the conditions under which the objects may typically be observed in an operating environment of the pose estimator system 100. For example, if the object is typically be observed supported on a flat surface (e.g., a work bench or a conveyor belt), then different the 3-D model of the object may be rotated to random orientations and dropped onto a flat surface in the physics simulator many times (e.g., thousands of times) to generate a library of possible 3-D deformations of the object. As another example, if the object is typically jumbled in a bin with other objects (of the same type or of different types), then synthetic data generator may be configured to construct a scene including a virtual bin and to jumble the 3-D model of the object with other objects to generate scenes with the object deformed due to physical interactions with the other objects and/or sides of the bin. As a third example, some objects may be connected to other objects (e.g., workpieces in various states of assembly in a manufacturing facility), and therefore the synthetic data generator may be configured to simulate the shape of the deformable object by connecting the 3-D model of the object type to physical models of the workpieces and simulating the interactions between the deformable object and its environment.

[00200] Generating a large number of potential deformations of the 3-D model representing the object type thereby generates a collection of 3-D models of different configurations of the same object type, where the possible configurations are constrained based on the modeled physical characteristics of the object, as simulated by the physics simulator. These generated 3-D models can then be added to the library in association with the object type and retrieved for estimating the 6- DoF poses of objects.

[00201] In some embodiments, in operation 1130 the synthetic data generator also renders images of the randomly generated scene from multiple viewpoints (e.g., through ray tracing or rasterization). In some embodiments, only the object of interest is rendered, excluding other objects in the scene. In some embodiments, all of the objects in the scene visible to the virtual camera are rendered, and in some embodiments the field of view of the rendering is narrowed to depict only a patch corresponding to the object of interest. This process of rendering images may include placing a virtual camera at one or more poses with respect to the scene and rendering a 2-D image of the scene from those virtual viewpoints. In addition to rendering visible light images (e.g., color images), a synthetic data generator may also render images in other imaging spectra such as infrared and ultraviolet light, and using other imaging modalities such as polarization. Systems and methods for synthetic data generation are described in more detail in International Patent Application No. PCT/US21/12073 “SYSTEMS AND METHODS FOR SYNTHESIZING DATA FOR TRAINING STATISTICAL MODELS ON DIFFERENT IMAGING MODALITIES INCLUDING POLARIZED IMAGES,” filed in the United States Patent and Trademark Office on January 4, 2021 , the entire disclosure of which is incorporated by reference herein. The renderings of the scene may be used as part of the training data for training machine learning models, such as for training the transformation network 800 described above with respect to FIG. 8. In more detail, the deformed 3-D model of the object of the current generated scene is paired with the collection of renderings of the current generated scene to produce a training sample. [00202] In operation 1150, the synthetic data generator determines whether to generate more scenes, such as based on whether a designated number of 3-D model configurations has been generated or based on a distribution of observed models across a theoretical range of possible models. If more scenes are to be generated, then the synthetic data generator proceeds with perturbing the conditions of the simulation in operation 1170, such as by jumbling a virtual bin containing the object, dropping the object onto a surface, shaking an object, or the like, and returning to operation 1110 to generate a new scene based on the modified conditions. In the new scene, the 3-D model may be deformed in a different manner than in the previously generated scene or scenes, and the corresponding renderings, if any, may also appear different, thereby generating another training sample. Repeating the process generates a plurality of training samples, which may be used to train machine learning models.

[00203] In some embodiments, training data is generated by performing physical manipulations of real-world instances of objects. In particular, a physical object may be placed into a physical scene and imaged by a collection of cameras (e.g., similar to the master camera 10 and support cameras 30). In addition, a 3-D scanning system may be used to capture a 3-D model of the object within the scene (e.g., a plurality of stereo depth camera systems, time of flight depth camera systems, and/or the like). Perturbations of these scenes may be performed using, for example, a physical agitator to agitate a bin or other container of objects or by using a robot arm to mix or otherwise deform the object or objects in the scene into new configurations. In some embodiments, a robot is trained to perform manipulations of the object to explore the space of possible configurations (e.g., to perturb the object into configurations that the robot has not yet observed). See, e.g., Nair, Ashvin, et al. "Combining self-supervised learning and imitation for vision-based rope manipulation." 2017 IEEE international conference on robotics and automation (ICRA). IEEE, 2017. As a result, the 3-D scanning of real physical objects deformed in a variety of different ways produces a collection of captured 3-D models of the object in a plurality of different configurations.

[00204] While the above techniques for generating synthetic data relate to generating high resolution 3-D mesh models, embodiments of the present disclosure are not limited thereto. In some embodiments, the process of generating data for a library and/or for training data for training machine learning models involves generating imaging approximations (e.g. sparse stereo / geometry) instead of generating high resolution or full resolution 3-D mesh models.

[00205] In some circumstances, the randomly generated 3-D physical configurations of the object (whether generated by the synthetic data generator or by the physical manipulation of real-life objects) are binned or clustered in accordance with similarity (e.g., based on how close the corresponding vertices are to one another between 3-D models representing different configurations), and a representative 3-D model is selected or computed (e.g., through computing a mean 3-D model) from the clustered set of 3-D models. In some circumstances, the 3-D models will be distributed non-uniformly between the different clusters, and therefore a probability distribution may be estimated based on the populations of the cluster. These probabilities may also be stored with the 3-D model and may be used when identifying a most likely matching model in the process of pose estimation.

[00206] Accordingly, aspects of embodiments of the present disclosure relate to systems and methods for performing six degree of freedom pose estimation for deformable objects, including computing an estimated configuration of the deformable object, as represented by a 3-D model of the object, and a pose of the 3- D model of the object that represents the estimated pose of the object observed in a scene by a plurality of cameras at different viewpoints. Some aspects of embodiments of the present disclosure also relate to systems and methods for generating training data for training machine learning models that operate as part of a processing pipeline for computing the estimates of the 6-DoF poses of deformable objects.

[00207] While the present invention has been described in connection with certain exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims, and equivalents thereof.