Fast Globally Optimal and Geometrically Consistent 3D Shape Matching

• URL: http://arxiv.org/abs/2504.06385v2
• Date: Thu, 10 Apr 2025 07:03:31 GMT
• Title: Fast Globally Optimal and Geometrically Consistent 3D Shape Matching
• Authors: Paul Roetzer, Florian Bernard,
• Abstract summary: We propose a novel formalism for computing globally optimal and geometrically consistent matchings between 3D shapes.<n>Our key idea is to represent the surface of the source shape as a collection of cyclic paths, which are then consistently matched to the target shape.<n>We empirically show that our formalism is efficiently solvable and that it leads to high-quality results.
• Score: 16.65517718538827
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical shape modelling. Yet, in practice, geometric consistency is often overlooked, or only achieved under severely limiting assumptions (e.g. a good initialisation). In this work, we propose a novel formalism for computing globally optimal and geometrically consistent matchings between 3D shapes which is scalable in practice. Our key idea is to represent the surface of the source shape as a collection of cyclic paths, which are then consistently matched to the target shape. Mathematically, we construct a hyper product graph (between source and target shape), and then cast 3D shape matching as a minimum-cost circulation flow problem in this hyper graph, which yields global geometrically consistent matchings between both shapes. We empirically show that our formalism is efficiently solvable and that it leads to high-quality results.

Related papers

• Partial-to-Partial Shape Matching with Geometric Consistency [47.46502145377953]
  Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. We bridge the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world settings by exploiting geometric consistency as a strong constraint. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle product spaces.
  arXiv  Detail & Related papers  (2024-04-18T14:14:07Z)
• Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation [50.376243444909136]
  We present a unified framework to predict both point-wise correspondences and shape between 3D shapes. We combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains.
  arXiv  Detail & Related papers  (2024-02-29T07:26:23Z)
• Geometrically Consistent Partial Shape Matching [50.29468769172704]
  Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics. An often neglected but essential property of matching geometrics is consistency. We propose a novel integer linear programming partial shape matching formulation.
  arXiv  Detail & Related papers  (2023-09-10T12:21:42Z)
• CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes [62.45415756883437]
  Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, $mathcalNP$-hard problem. Existing quantum shape-matching methods do not support multiple shapes and even less cycle consistency. This paper introduces the first quantum-hybrid approach for 3D shape multi-matching.
  arXiv  Detail & Related papers  (2023-03-28T17:59:55Z)
• Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matching [12.740151710302397]
  We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. Existing solutions heavily rely on unrealistic prior assumptions to avoid degenerate solutions. We propose a novel 2D-3D shape matching formalism based on the conjugate product graph between the 2D contour and the 3D shape.
  arXiv  Detail & Related papers  (2022-11-21T15:41:28Z)
• A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching [69.14632473279651]
  We present a scalable algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We propose a novel primal coupled with a Lagrange dual problem that is several orders of magnitudes faster than previous solvers.
  arXiv  Detail & Related papers  (2022-04-27T09:47:47Z)
• Isometric Multi-Shape Matching [50.86135294068138]
  Finding correspondences between shapes is a fundamental problem in computer vision and graphics. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis.
  arXiv  Detail & Related papers  (2020-12-04T15:58:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.