Related papers: Faithful Euclidean Distance Field from Log-Gaussia…

We present a fast convolution-based technique for computing an approximate, signed Euclidean distance function $S$ on a set of 2D and 3D grid locations. Instead of solving the non-linear, static Hamilton-Jacobi equation ($\|\nabla S\|=1$),…

Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for…

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural…

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the…

The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…

This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build…

Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…

Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is…

Vision-centric 3D environment understanding is both vital and challenging for autonomous driving systems. Recently, object-free methods have attracted considerable attention. Such methods perceive the world by predicting the semantics of…

We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann…

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

Implicit representations have been widely applied in robotics for obstacle avoidance and path planning. In this paper, we explore the problem of constructing an implicit distance representation from a single image. Past methods for implicit…

This paper proposes a deep-learning-based method for recovering a signed distance function (SDF) of a given hypersurface represented by an implicit level set function. Using the flexibility of constructing a neural network, we use an…

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…

Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or…

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning data. Building upon our prior work, which…

3D Gaussian Splatting offers a strong speed-quality trade-off but struggles to reconstruct semi-transparent surfaces because most methods assume a single depth per pixel, which fails when multiple surfaces are visible. We propose TSPE-GS…