Related papers: 1-Lipschitz Neural Distance Fields
Reconstruction of 3D open surfaces (e.g., non-watertight meshes) is an underexplored area of computer vision. Recent learning-based implicit techniques have removed previous barriers by enabling reconstruction in arbitrary resolutions. Yet,…
Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and…
Input gradients have a pivotal role in a variety of applications, including adversarial attack algorithms for evaluating model robustness, explainable AI techniques for generating Saliency Maps, and counterfactual explanations.However,…
Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…
The neural implicit representation has shown its effectiveness in novel view synthesis and high-quality 3D reconstruction from multi-view images. However, most approaches focus on holistic scene representation yet ignore individual objects…
In this paper, we consider the fundamental problem of approximation of functions on a low-dimensional manifold embedded in a high-dimensional space, with noise affecting both in the data and values of the functions. Due to the curse of…
Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional…
Deep neural networks and Vision Transformers achieve state-of-the-art performance in computer vision but are highly vulnerable to adversarial perturbations. Standard defenses often incur high computational cost or lack formal guarantees. We…
Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
Implicit representations of 3D objects have recently achieved impressive results on learning-based 3D reconstruction tasks. While existing works use simple texture models to represent object appearance, photo-realistic image synthesis…
It is important to estimate an accurate signed distance function (SDF) from a point cloud in many computer vision applications. The latest methods learn neural SDFs using either a data-driven based or an overfitting-based strategy. However,…
We propose a method, HotSpot, for optimizing neural signed distance functions. Existing losses, such as the eikonal loss, act as necessary but insufficient constraints and cannot guarantee that the recovered implicit function represents a…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Explicit neural surface representations allow for exact and efficient extraction of the encoded surface at arbitrary precision, as well as analytic derivation of differential geometric properties such as surface normal and curvature. Such…