Or Litany

We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a functional map, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an image diffusion model directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as guidance during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace‐Beltrami operator. We show that our approach is competitive with state‐of‐the‐art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.

We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a functional map, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an image diffusion model directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as guidance during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.

3D instance segmentation is fundamental to geometric understanding of the world around us. Existing methods for instance segmentation of 3D scenes rely on supervision from expensive, manual 3D annotations. We propose UnScene3D, the first fully unsupervised 3D learning approach for class-agnostic 3D instance segmentation of in-door scans. UnScene3D first generates pseudo masks by leveraging self-supervised color and geometry features to find potential object regions. We operate on a basis of ge-ometric oversegmentation, enabling efficient representation and learning on high-resolution 3D data. The coarse proposals are then refined through self-training our model on its predictions. Our approach improves over clustering-based alternatives to unsupervised 3D instance segmentation methods by more than 300% Average Precision score, demonstrating effective instance segmentation even in challenging, cluttered 3D scenes.

Recent advances in machine learning have led to increased interest in solving visual computing problems using methods that employ coordinate‐based neural networks. These methods, which we callneural fields, parameterize physical properties of scenes or objects across space and time. They have seen widespread success in problems such as 3D shape and image synthesis, animation of human bodies, 3D reconstruction, and pose estimation. Rapid progress has led to numerous papers, but a consolidation of the discovered knowledge has not yet emerged. We provide context, mathematical grounding, and a review of over 250 papers in the literature on neural fields. InPart I, we focus on neural field techniques by identifying common components of neural field methods, including different conditioning, representation, forward map, architecture, and manipulation methods. InPart II, we focus on applications of neural fields to different problems in visual computing, and beyond (e.g., robotics, audio). Our review shows the breadth of topics already covered in visual computing, both historically and in current incarnations, and highlights the improved quality, flexibility, and capability brought by neural field methods. Finally, we present a companion website that acts as a living database that can be continually updated by the community.

Recent advances in machine learning have created increasing interest in solving visual computing problems using a class of coordinate-based neural networks that parametrize physical properties of scenes or objects across space and time. These methods, which we call neural fields, have seen successful application in the synthesis of 3D shapes and image, animation of human bodies, 3D reconstruction, and pose estimation. However, due to rapid progress in a short time, many papers exist but a comprehensive review and formulation of the problem has not yet emerged. In this report, we address this limitation by providing context, mathematical grounding, and an extensive review of literature on neural fields. This report covers research along two dimensions. In Part I, we focus on techniques in neural fields by identifying common components of neural field methods, including different representations, architectures, forward mapping, and generalization methods. In Part II, we focus on applications of neural fields to different problems in visual computing, and beyond (e.g., robotics, audio). Our review shows the breadth of topics already covered in visual computing, both historically and in current incarnations, demonstrating the improved quality, flexibility, and capability brought by neural fields methods. Finally, we present a companion website that contributes a living version of this review that can be continually updated by the community.