mlsanityData to 14 Oct 2026

Finsler-Laplace-Beltrami Operators with Application to Shape Analysis

arXiv 2404.03999 ↗First posted 5 Apr 2024cs.CVcited by 10

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Abstract (arXiv)

The Laplace-Beltrami operator (LBO) emerges from studying manifolds equipped with a Riemannian metric. It is often called the Swiss army knife of geometry processing as it allows to capture intrinsic shape information and gives rise to heat diffusion, geodesic distances, and a multitude of shape descriptors. It also plays a central role in geometric deep learning. In this work, we explore Finsler manifolds as a generalization of Riemannian manifolds. We revisit the Finsler heat equation and derive a Finsler heat kernel and a Finsler-Laplace-Beltrami Operator (FLBO): a novel theoretically justified anisotropic Laplace-Beltrami operator (ALBO). In experimental evaluations we demonstrate that the proposed FLBO is a valuable alternative to the traditional Riemannian-based LBO and ALBOs for spatial filtering and shape correspondence estimation. We hope that the proposed Finsler heat kernel and the FLBO will inspire further exploration of Finsler geometry in the computer vision community.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 14 of its 47 references that are in the map. First posted on arXiv 5 Apr 2024.

Builds on

14 of 47 references.

References · 14

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  3. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,475
  4. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  5. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 161
  6. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  7. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  8. 2016Learning shape correspondence with anisotropic convolutional neural networkscited by 95
  9. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  10. 2021DPFM: Deep Partial Functional Mapscited by 58
  11. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  12. 2021Field Convolutions for Surface CNNscited by 14
2 more
  1. 2016Global Minimum for a Finsler Elastica Minimal Path Approachcited by 11
  2. 2020Generalized Nonlinear and Finsler Geometry for Roboticscited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 5; 2026: 2.

10 papers.

  1. 2024Wormhole Loss for Partial Shape Matchingcited by 12
  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 8
  4. 2025Laplace-Beltrami Operator for Gaussian Splattingcited by 5
  5. 2024Metric Convolutions: A Unifying Theory to Adaptive Image Convolutionscited by 3
  6. 2024LBONet: Supervised Spectral Descriptors for Shape Analysiscited by 1
  7. 2025Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operatorscited by 1
  8. 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler Worldcited by 1
  9. 2026Finsler Geometry, Graph Neural Networks, and Youcited by 1
  10. 2025Learning Eigenstructures of Unstructured Data Manifoldscited by 0