Related papers: Toward bilipshiz geometric models

We present a novel approach to learning a point-wise, meaningful embedding for point-clouds in an unsupervised manner, through the use of neural-networks. The domain of point-cloud processing via neural-networks is rapidly evolving, with…

Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…

We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…

Learning to generate 3D point clouds without 3D supervision is an important but challenging problem. Current solutions leverage various differentiable renderers to project the generated 3D point clouds onto a 2D image plane, and train deep…

Point cloud completion is a fundamental task in 3D vision. A persistent challenge in this field is simultaneously preserving fine-grained details present in the input while ensuring the global structural integrity of the completed shape.…

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…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However,…

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

Learning local descriptors is an important problem in computer vision. While there are many techniques for learning local patch descriptors for 2D images, recently efforts have been made for learning local descriptors for 3D points. The…

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…

Evaluating uncertainty is critical for reliable use of Mobile Laser Scanning (MLS) point clouds in many high-precision applications such as Scan-to-BIM, deformation analysis, and 3D modeling. However, obtaining the ground truth (GT) for…

While neural networks can enjoy an outstanding flexibility and exhibit unprecedented performance, the mechanism behind their behavior is still not well-understood. To tackle this fundamental challenge, researchers have tried to restrict and…

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these…

We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that that the relative geometry of…

The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention,…

Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties,…