Geometrically Consistent Partial Shape Matching

• URL: http://arxiv.org/abs/2309.05013v1
• Date: Sun, 10 Sep 2023 12:21:42 GMT
• Title: Geometrically Consistent Partial Shape Matching
• Authors: Viktoria Ehm, Paul Roetzer, Marvin Eisenberger, Maolin Gao, Florian Bernard, Daniel Cremers
• Abstract summary: 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.
• Score: 50.29468769172704
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property of matchings is geometric consistency, which means that neighboring triangles in one shape are consistently matched to neighboring triangles in the other shape. Moreover, while in practice one often has only access to partial observations of a 3D shape (e.g. due to occlusion, or scanning artifacts), there do not exist any methods that directly address geometrically consistent partial shape matching. In this work we fill this gap by proposing to integrate state-of-the-art deep shape features into a novel integer linear programming partial shape matching formulation. Our optimization yields a globally optimal solution on low resolution shapes, which we then refine using a coarse-to-fine scheme. We show that our method can find more reliable results on partial shapes in comparison to existing geometrically consistent algorithms (for which one first has to fill missing parts with a dummy geometry). Moreover, our matchings are substantially smoother than learning-based state-of-the-art shape matching methods.

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)
• 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)
• 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)
• Spectral Unions of Partial Deformable 3D Shapes [31.93707121229739]
  We introduce the first method to compute compositions of non-rigidly deforming shapes, without requiring to solve first for a dense correspondence between the given partial shapes. Our approach is data-driven, and can generalize to isometric and non-isometric deformations of the surface.
  arXiv  Detail & Related papers  (2021-03-31T14:19:18Z)
• 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.