Related papers: 1-Lipschitz Neural Distance Fields

We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{ \pm 1\}$ only. A basic case of our results states that for…

Neural implicit surface representation methods have recently shown impressive 3D reconstruction results. However, existing solutions struggle to reconstruct driving scenes due to their large size, highly complex nature and their limited…

Reconstructing open surfaces from multi-view images is vital in digitalizing complex objects in daily life. A widely used strategy is to learn unsigned distance functions (UDFs) by checking if their appearance conforms to the image…

Recovery of an underlying scene geometry from multiview images stands as a long-time challenge in computer vision research. The recent promise leverages neural implicit surface learning and differentiable volume rendering, and achieves both…

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…

Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss…

In this paper, we study the generalization capabilities of geometric graph neural networks (GNNs). We consider GNNs over a geometric graph constructed from a finite set of randomly sampled points over an embedded manifold with topological…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the…

This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on…

Neural implicit functions have recently shown promising results on surface reconstructions from multiple views. However, current methods still suffer from excessive time complexity and poor robustness when reconstructing unbounded or…

Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…

Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…

Many robotic tasks involving some form of 3D visual perception greatly benefit from a complete knowledge of the working environment. However, robots often have to tackle unstructured environments and their onboard visual sensors can only…

Deep implicit functions have shown remarkable shape modeling ability in various 3D computer vision tasks. One drawback is that it is hard for them to represent a 3D shape as multiple parts. Current solutions learn various primitives and…

Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…

Scene Completion is the task of completing missing geometry from a partial scan of a scene. Most previous methods compute an implicit representation from range data using a Truncated Signed Distance Function (T-SDF) computed on a 3D grid as…

Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a…

Real-world 3D data may contain intricate details defined by salient surface gaps. Automated reconstruction of these open surfaces (e.g., non-watertight meshes) is a challenging problem for environment synthesis in mixed reality…