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A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…

Unsigned Distance Fields (UDFs) can be used to represent non-watertight surfaces. However, current approaches to converting them into explicit meshes tend to either be expensive or to degrade the accuracy. Here, we extend the marching cube…

3D Gaussian Splatting (3DGS) has recently emerged as a powerful paradigm for photorealistic view synthesis, representing scenes with spatially distributed Gaussian primitives. While highly effective for rendering, achieving accurate and…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

Various SDF-based neural implicit surface reconstruction methods have been proposed recently, and have demonstrated remarkable modeling capabilities. However, due to the global nature and limited representation ability of a single network,…

We present SuperNormal, a fast, high-fidelity approach to multi-view 3D reconstruction using surface normal maps. With a few minutes, SuperNormal produces detailed surfaces on par with 3D scanners. We harness volume rendering to optimize a…

Recently, neural implicit surfaces learning by volume rendering has become popular for multi-view reconstruction. However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to…

In visual computing, 3D geometry is represented in many different forms including meshes, point clouds, voxel grids, level sets, and depth images. Each representation is suited for different tasks thus making the transformation of one…

Mobile ground robots require perceiving and understanding their surrounding support surface to move around autonomously and safely. The support surface is commonly estimated based on exteroceptive depth measurements, e.g., from LiDARs.…

In this paper, we present a generalizable method for 3D surface reconstruction from raw point clouds or pre-estimated 3D Gaussians by 3DGS from RGB images. Unlike existing coordinate-based methods which are often computationally intensive…

We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…

In the field of trajectory generation for objects, ensuring continuous collision-free motion remains a huge challenge, especially for non-convex geometries and complex environments. Previous methods either oversimplify object shapes, which…

The aim of Shape From Shading (SFS) problem is to reconstruct the relief of an object from a single gray level image. In this paper we present a new method to solve the problem of SFS using Machine learning method. Our approach belongs to…

We propose a hybrid continuum surface force (CSF) formulation to model the interface interaction within the three-phase volume of fluid (VOF) method. Instead of employing the height function globally, we compute the curvature based on a…

Reconstructing accurate implicit surface representations from point clouds remains a challenging task, particularly when data is captured using low-quality scanning devices. These point clouds often contain substantial noise, leading to…

In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter $r$ (a small positive real number) as…

Shape-from-Focus (SFF) is a passive depth estimation technique that infers scene depth by analyzing focus variations in a focal stack. Most recent deep learning-based SFF methods typically operate in two stages: first, they extract focus…

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…

Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…

Learning-based point cloud registration methods can handle clean point clouds well, while it is still challenging to generalize to noisy, partial, and density-varying point clouds. To this end, we propose a novel point cloud registration…