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While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric…

Computer Vision and Pattern Recognition · Computer Science 2024-02-20 Christian Reiser , Stephan Garbin , Pratul P. Srinivasan , Dor Verbin , Richard Szeliski , Ben Mildenhall , Jonathan T. Barron , Peter Hedman , Andreas Geiger

The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…

Data Structures and Algorithms · Computer Science 2026-03-31 Joshua Brakensiek , Neng Huang , Aaron Potechin , Uri Zwick

In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…

Computer Vision and Pattern Recognition · Computer Science 2017-05-03 Christian Mostegel , Rudolf Prettenthaler , Friedrich Fraundorfer , Horst Bischof

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Optimization and Control · Mathematics 2025-10-27 Evan Markou , Thalaiyasingam Ajanthan , Stephen Gould

We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…

Machine Learning · Computer Science 2012-06-18 Arthur Choi , Adnan Darwiche

We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this…

Computational Geometry · Computer Science 2007-05-23 Jeff Erickson , Sariel Har-Peled

Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to…

Computer Vision and Pattern Recognition · Computer Science 2025-07-15 Ofir Itzhak Shahar , Gur Elkin , Ohad Ben-Shahar

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…

Computer Vision and Pattern Recognition · Computer Science 2017-11-30 V. Estellers , F. R. Schmidt , D. Cremers

We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…

Numerical Analysis · Mathematics 2016-04-08 Charles L. Epstein , Michael O'Neil

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…

Computational Geometry · Computer Science 2010-01-21 Nina Amenta , Marshall Bern , David Eppstein

A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…

Optimization and Control · Mathematics 2026-02-16 Patrick Jung

We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…

Numerical Analysis · Mathematics 2019-11-06 Qing Pan , Timon Rabczuk , Gang Xu , Chong Chen

Recent advances in optimizing Gaussian Splatting for scene geometry have enabled efficient reconstruction of detailed surfaces from images. However, when input views are sparse, such optimization is prone to overfitting, leading to…

Computer Vision and Pattern Recognition · Computer Science 2025-11-19 Meiying Gu , Jiawei Zhang , Jiahe Li , Xiaohan Yu , Haonan Luo , Jin Zheng , Xiao Bai

Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves or each…

Graphics · Computer Science 2021-07-06 Chris Yu , Caleb Brakensiek , Henrik Schumacher , Keenan Crane

3D Gaussian Splatting (3DGS) has emerged as a leading technique for novel view synthesis, demonstrating exceptional rendering efficiency. \replaced[]{Well-reconstructed surfaces can be characterized by low configurational entropy, where…

Computer Vision and Pattern Recognition · Computer Science 2025-12-05 Hong Kuang , Jianchen Liu

We present a novel coarse-to-fine framework that derives a semi-regular multiscale mesh representation of an original input mesh via remeshing. Our approach differs from the conventional mesh wavelet transform strategy in two ways. First,…

Image and Video Processing · Electrical Eng. & Systems 2018-10-09 Hao-Chiang Shao

We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…

Graphics · Computer Science 2021-05-07 Kacper Pluta , Michal Edelstein , Amir Vaxman , Mirela Ben-Chen

A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been…

Graphics · Computer Science 2025-05-08 Yiling Pan , Zhixin Xu , Bin Wang , Bailin Deng

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

Optimization and Control · Mathematics 2023-08-17 Roland Herzog , Estefanía Loayza-Romero

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling…

Numerical Analysis · Mathematics 2018-11-14 Jan Van Langenhove , Didier Lucor , Frédéric Alauzet , Anca Belme