In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning frameworks. Standard explicit shape representations (voxels, point clouds, or meshes) are often easily rendered, but can suffer from limited geometric fidelity, among other issues. On the other hand, implicit representations (occupancy, distance, or radiance fields) preserve greater fidelity, but suffer from complex or inefficient rendering processes, limiting scalability. In this work, we devise Directed Distance Fields (DDFs), a novel neural shape representation that builds upon classical distance fields. The fundamental operation in a DDF maps an oriented point (position and direction) to surface visibility and depth. This enables efficient differentiable rendering, obtaining depth with a single forward pass per pixel, as well as differential geometric quantity extraction (e.g., surface normals), with only additional backward passes. Using probabilistic DDFs (PDDFs), we show how to model inherent discontinuities in the underlying field. We then apply DDFs to several applications, including single-shape fitting, generative modelling, and single-image 3D reconstruction, showcasing strong performance with simple architectural components via the versatility of our representation. Finally, since the dimensionality of DDFs permits view-dependent geometric artifacts, we conduct a theoretical investigation of the constraints necessary for view consistency. We find a small set of field properties that are sufficient to guarantee a DDF is consistent, without knowing, for instance, which shape the field is expressing.

Multi-finger grasping relies on high quality training data, which is hard to obtain: human data is hard to transfer and synthetic data relies on simplifying assumptions that reduce grasp quality. By making grasp simulation differentiable, and contact dynamics amenable to gradient-based optimization, we accelerate the search for high-quality grasps with fewer limiting assumptions. We present Grasp'D-1M: a large-scale dataset for multi-finger robotic grasping, synthesized with Fast- Grasp'D, a novel differentiable grasping simulator. Grasp'D- 1M contains one million training examples for three robotic hands (three, four and five-fingered), each with multimodal visual inputs (RGB+depth+segmentation, available in mono and stereo). Grasp synthesis with Fast-Grasp'D is 10x faster than GraspIt! and 20x faster than the prior Grasp'D differentiable simulator. Generated grasps are more stable and contact-rich than GraspIt! grasps, regardless of the distance threshold used for contact generation. We validate the usefulness of our dataset by retraining an existing vision-based grasping pipeline on Grasp'D-1M, and showing a dramatic increase in model performance, predicting grasps with 30% more contact, a 33% higher epsilon metric, and 35% lower simulated displacement. Additional details at https://dexgrasp.github.io.

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior generative model of geometric disentanglement for 3D shapes, wherein the space of object geometry is factorized into rigid orientation, non-rigid pose, and intrinsic shape. The resulting model can be trained from raw 3D shapes, without correspondences, labels, or even rigid alignment, using a combination of classical spectral geometry and probabilistic disentanglement of a structured latent representation space. Our improvements include more sophisticated handling of rotational invariance and the use of a diffeomorphic flow network to bridge latent and spectral space. The geometric structuring of the latent space imparts an interpretable characterization of the deformation space of an object. Furthermore, it enables tasks like pose transfer and pose-aware retrieval without requiring supervision. We evaluate our model on its generative modelling, representation learning, and disentanglement performance, showing improved rotation invariance and intrinsic-extrinsic factorization quality over the prior model.