Related papers: Diffeomorphic Reconstruction Of A 2D Simple Non Pa…

We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…

In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…

3D reconstruction from a single view image is a long-standing prob-lem in computer vision. Various methods based on different shape representations(such as point cloud or volumetric representations) have been proposed. However,the 3D shape…

Algorithms based on gradient descent for computing the elastic shape registration of two simple surfaces in 3-dimensional space and therefore the elastic shape distance between them have been proposed by Kurtek, Jermyn, et al., and more…

Curve reconstruction from unstructured points in a plane is a fundamental problem with many applications that has generated research interest for decades. Involved aspects like handling open, sharp, multiple and non-manifold outlines,…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…

This paper introduces 3DFIRES, a novel system for scene-level 3D reconstruction from posed images. Designed to work with as few as one view, 3DFIRES reconstructs the complete geometry of unseen scenes, including hidden surfaces. 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…

Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to…

Multi-view image-based rendering consists in generating a novel view of a scene from a set of source views. In general, this works by first doing a coarse 3D reconstruction of the scene, and then using this reconstruction to establish…

Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…

A simple method of constructing the 3D surface of non-transparent micro-objects by extending the depth-of-field on the whole attainable surface is presented. The series of images of a sample are recorded by the sequential movement of the…

We present a novel geometric deep learning layer that leverages the varifold gradient (VariGrad) to compute feature vector representations of 3D geometric data. These feature vectors can be used in a variety of downstream learning tasks…

Neural 3D scene reconstruction methods have achieved impressive performance when reconstructing complex geometry and low-textured regions in indoor scenes. However, these methods heavily rely on 3D data which is costly and time-consuming to…

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…

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Reconstructing the shape and appearance of real-world objects using measured 2D images has been a long-standing problem in computer vision. In this paper, we introduce a new analysis-by-synthesis technique capable of producing high-quality…

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…