Reconstructing a dynamic scene from image inputs is a fundamental computer vision task with many downstream applications. Despite recent advancements, existing approaches still struggle to achieve high-quality reconstructions from unseen viewpoints and timestamps. This work introduces the ReMatching framework, designed to improve reconstruction quality by incorporating deformation priors into dynamic reconstruction models. Our approach advocates for velocity-field based priors, for which we suggest a matching procedure that can seamlessly supplement existing dynamic reconstruction pipelines. The framework is highly adaptable and can be applied to various dynamic representations. Moreover, it supports integrating multiple types of model priors and enables combining simpler ones to create more complex classes. Our evaluations on popular benchmarks involving both synthetic and real-world dynamic scenes demonstrate that augmenting current state-of-the-art methods with our approach leads to a clear improvement in reconstruction accuracy.

Integrating a notion of symmetry into point cloud neural networks is a provably effective way to improve their generalization capability. Of particular interest are $E(3)$ equivariant point cloud networks where Euclidean transformations applied to the inputs are preserved in the outputs. Recent efforts aim to extend networks that are equivariant with respect to a single global $E(3)$ transformation, to accommodate inputs made of multiple parts, each of which exhibits local $E(3)$ symmetry. In practical settings, however, the partitioning into individually transforming regions is unknown a priori. Errors in the partition prediction would unavoidably map to errors in respecting the true input symmetry. Past works have proposed different ways to predict the partition, which may exhibit uncontrolled errors in their ability to maintain equivariance to the actual partition. To this end, we introduce APEN: a general framework for constructing approximate piecewise-$E(3)$ equivariant point networks. Our framework offers an adaptable design to guaranteed bounds on the resulting piecewise $E(3)$ equivariance approximation errors. Our primary insight is that functions which are equivariant with respect to a finer partition (compared to the unknown true partition) will also maintain equivariance in relation to the true partition. Leveraging this observation, we propose a compositional design for a partition prediction model. It initiates with a fine partition and incrementally transitions towards a coarser subpartition of the true one, consistently maintaining piecewise equivariance in relation to the current partition. As a result, the equivariance approximation error can be bounded solely in terms of (i) uncertainty quantification of the partition prediction, and (ii) bounds on the probability of failing to suggest a proper subpartition of the ground truth one. We demonstrate the practical effectiveness of APEN using two data types exemplifying part-based symmetry: (i) real-world scans of room scenes containing multiple furniture-type objects; and, (ii) human motions, characterized by articulated parts exhibiting rigid movement. Our empirical results demonstrate the advantage of integrating piecewise $E(3)$ symmetry into network design, showing a distinct improvement in generalization accuracy compared to prior works for both classification and segmentation tasks

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.

We present a novel method for reconstructing a 3D implicit surface from a large-scale, sparse, and noisy point cloud. Our approach builds upon the recently introduced Neural Kernel Fields (NKF) [58] representation. It enjoys similar generalization capabilities to NKF, while simultaneously addressing its main limitations: (a) We can scale to large scenes through compactly supported kernel functions, which enable the use of memory-efficient sparse linear solvers. (b) We are robust to noise, through a gradient fitting solve. (c) We minimize training requirements, enabling us to learn from any dataset of dense oriented points, and even mix training data consisting of objects and scenes at different scales. Our method is capable of reconstructing millions of points in a few seconds, and handling very large scenes in an out-of-core fashion. We achieve state-of-the-art results on reconstruction benchmarks consisting of single objects (ShapeNet [5], ABC [33]), indoor scenes (ScanNet [11], Matterport3D [4]), and outdoor scenes (CARLA [16], Waymo [49]).

The task of shape space learning involves mapping a train set of shapes to and from a latent representation space with good generalization properties. Often, real-world collections of shapes have symmetries, which can be defined as transformations that do not change the essence of the shape. A natural way to incorporate symmetries in shape space learning is to ask that the mapping to the shape space (encoder) and mapping from the shape space (decoder) are equivariant to the relevant symmetries. In this paper, we present a framework for incorporating equivariance in encoders and decoders by introducing two contributions: (i) adapting the recent Frame Averaging (FA) framework for building generic, efficient, and maximally expressive Equivariant autoencoders; and (ii) constructing autoencoders equivariant to piecewise Euclidean motions applied to different parts of the shape. To the best of our knowledge, this is the first fully piecewise Euclidean equivariant autoencoder construction. Training our framework is simple: it uses standard reconstruction losses, and does not require the introduction of new losses. Our architectures are built of standard (backbone) architectures with the appropriate frame averaging to make them equivariant. Testing our framework on both rigid shapes dataset using implicit neural representations, and articulated shape datasets using mesh-based neural networks show state of the art generalization to unseen test shapes, improving relevant baselines by a large margin. In particular, our method demonstrates significant improvement in generalizing to unseen articulated poses.

Recently, neural networks have been used as implicit representations for surface reconstruction, modelling, learning, and generation. So far, training neural networks to be implicit representations of surfaces required training data sampled from a ground-truth signed implicit functions such as signed distance or occupancy functions, which are notoriously hard to compute. In this paper we introduce Sign Agnostic Learning (SAL), a deep learning approach for learning implicit shape representations directly from raw, unsigned geometric data, such as point clouds and triangle soups. We have tested SAL on the challenging problem of surface reconstruction from an un-oriented point cloud, as well as end-to-end human shape space learning directly from raw scans dataset, and achieved state of the art reconstructions compared to current approaches. We believe SAL opens the door to many geometric deep learning applications with real-world data, alleviating the usual painstaking, often manual pre-process.

Representing shapes as level-sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level-sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the input point cloud and to have a unit norm gradient, possesses an implicit geometric regularization property that favors smooth and natural zero level-set surfaces, avoiding bad zero-loss solutions. We provide a theoretical analysis of this property for the linear case, and show that, in practice, our method leads to state-of-the-art implicit neural representations with higher level-of-details and fidelity compared to previous methods.

In this work we address the challenging problem of multiview 3D surface reconstruction. We introduce a neural network architecture that simultaneously learns the unknown geometry, camera parameters, and a neural renderer that approximates the light reflected from the surface towards the camera. The geometry is represented as a zero level-set of a neural network, while the neural renderer, derived from the rendering equation, is capable of (implicitly) modeling a wide set of lighting conditions and materials. We trained our network on real world 2D images of objects with different material properties, lighting conditions, and noisy camera initializations from the DTU MVS dataset. We found our model to produce state of the art 3D surface reconstructions with high fidelity, resolution and detail.

The level sets of neural networks represent fundamental properties such as decision boundaries of classifiers and are used to model non-linear manifold data such as curves and surfaces. Thus, methods for controlling the neural level sets could find many applications in machine learning. In this paper we present a simple and scalable approach to directly control level sets of a deep neural network. Our method consists of two parts: (i) sampling of the neural level sets, and (ii) relating the samples' positions to the network parameters. The latter is achieved by a sample network that is constructed by adding a single fixed linear layer to the original network. In turn, the sample network can be used to incorporate the level set samples into a loss function of interest. We have tested our method on three different learning tasks: improving generalization to unseen data, training networks robust to adversarial attacks, and curve and surface reconstruction from point clouds. For surface reconstruction, we produce high fidelity surfaces directly from raw 3D point clouds. When training small to medium networks to be robust to adversarial attacks we obtain robust accuracy comparable to state-of-the-art methods.

This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions to volumetric functions and vise-versa. A point cloud convolution is defined by pull-back of the Euclidean volumetric convolution via an extension-restriction mechanism. The point cloud convolution is computationally efficient, invariant to the order of points in the point cloud, robust to different samplings and varying densities, and translation invariant, that is the same convolution kernel is used at all points. PCNN generalizes image CNNs and allows readily adapting their architectures to the point cloud setting. Evaluation of PCNN on three central point cloud learning benchmarks convincingly outperform competing point cloud learning methods, and the vast majority of methods working with more informative shape representations such as surfaces and/or normals.