Partial-to-Partial Shape Matching with Geometric Consistency

• URL: http://arxiv.org/abs/2404.12209v2
• Date: Fri, 10 May 2024 08:12:01 GMT
• Title: Partial-to-Partial Shape Matching with Geometric Consistency
• Authors: Viktoria Ehm, Maolin Gao, Paul Roetzer, Marvin Eisenberger, Daniel Cremers, Florian Bernard,
• Abstract summary: 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.
• Score: 47.46502145377953
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges 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. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. 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, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA methods on both an established intra-class dataset and our novel inter-class dataset.

Related papers

• Beyond Complete Shapes: A quantitative Evaluation of 3D Shape Matching Algorithms [41.95394677818476]
  Finding correspondences between 3D shapes is an important problem in computer vision, graphics and beyond. We provide a generic and flexible framework for the procedural generation of challenging partial shape matching scenarios. We manually create cross-dataset correspondences between seven existing (complete geometry) shape matching datasets, leading to a total of 2543 shapes.
  arXiv  Detail & Related papers  (2024-11-05T21:08:19Z)
• 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)
• Zero-Shot 3D Shape Correspondence [67.18775201037732]
  We propose a novel zero-shot approach to computing correspondences between 3D shapes. We exploit the exceptional reasoning capabilities of recent foundation models in language and vision. Our approach produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.
  arXiv  Detail & Related papers  (2023-06-05T21:14:23Z)
• 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)
• Deep Confidence Guided Distance for 3D Partial Shape Registration [14.315501760755609]
  We present a novel non-iterative learnable method for partial-to-partial 3D shape registration. We present Confidence Guided Distance Network (CGD-net), where we fuse learnable similarity between point embeddings and spatial distance between point clouds.
  arXiv  Detail & Related papers  (2022-01-27T08:40:05Z)
• 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.