mlsanityData to 7 Oct 2026

Wormhole Loss for Partial Shape Matching

arXiv 2410.22899 ↗First posted 30 Oct 2024cs.CVcited by 12

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Abstract (arXiv)

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of whether distances measured between pairs of surface points should influence the matching process. The approach we propose treats surfaces as manifolds equipped with geodesic distances, and addresses the partial shape matching challenge by introducing a novel criterion to meticulously search for consistent distances between pairs of points. The new criterion explores the relation between intrinsic geodesic distances between the points, geodesic distances between the points and surface boundaries, and extrinsic distances between boundary points measured in the embedding space. It is shown to be less restrictive compared to previous measures and achieves state-of-the-art results when used as a loss function in training networks for partial shape matching.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 22 of its 64 references that are in the map. First posted on arXiv 30 Oct 2024.

Builds on

22 of 64 references.

References · 22

  1. 2017Attention Is All You Needcited by 59,932
  2. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  3. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  4. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 163
  5. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  6. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  7. 2018Unsupervised Deep Learning for Structured Shape Matchingcited by 81
  8. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  9. 2015Partial Functional Correspondencecited by 61
  10. 2021DPFM: Deep Partial Functional Mapscited by 58
  11. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  12. 2020Correspondence Learning via Linearly-invariant Embeddingcited by 48
10 more
  1. 2017Efficient Deformable Shape Correspondence via Kernel Matchingcited by 25
  2. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  3. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  4. 2022SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondencecited by 13
  5. 2013Spectral Generalized Multi-Dimensional Scalingcited by 11
  6. 2018Intrinsic Isometric Manifold Learning with Application to Localizationcited by 11
  7. 2019Correspondence-Free Region Localization for Partial Shape Similarity via Hamiltonian Spectrum Alignmentcited by 11
  8. 2024Finsler-Laplace-Beltrami Operators with Application to Shape Analysiscited by 10
  9. 2019Deep Eikonal Solverscited by 9
  10. 2020Unsupervised Scale-Invariant Multispectral Shape Matchingcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 6.

12 papers.

  1. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  2. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  3. 2025Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embeddingcited by 7
  4. 2026Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunitiescited by 4
  5. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  6. 2025Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patchescited by 2
  7. 2026An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matchingcited by 1
  8. 2026SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signalscited by 1
  9. 2026Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matchingcited by 1
  10. 2025Learning Eigenstructures of Unstructured Data Manifoldscited by 0
  11. 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler Worldcited by 0
  12. 2026NHO: A Neural Hamiltonian Operator for Anchor-based Region Localization and Dense Correspondencecited by 0