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A Convex Optimization Framework for Regularized Geodesic Distances

Authors:

Michal Edelstein,

Nestor Guillen,

Justin Solomon,

Mirela Ben-ChenAuthors Info & Claims

SIGGRAPH '23: ACM SIGGRAPH 2023 Conference Proceedings

Article No.: 2, Pages 1 - 11

https://doi.org/10.1145/3588432.3591523

Published: 23 July 2023 Publication History

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Abstract

We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical solutions in special cases, as well as corresponding efficient optimization algorithms. Additionally, we show how to generalize the approach to the all pairs case by formulating the problem on the product manifold, which leads to symmetric distances. Our regularized distances compare favorably to existing methods, in terms of robustness and ease of calibration.

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Cited By

Mattos Da Silva LStein OSolomon J(2024)A Framework for Solving Parabolic Partial Differential Equations on Discrete DomainsACM Transactions on Graphics10.1145/366608743:5(1-14)Online publication date: 25-Jun-2024
https://dl.acm.org/doi/10.1145/3666087
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658220
Li YNumerow LThomaszewski BCoros S(2024)Differentiable Geodesic Distance for Intrinsic Minimization on Triangle MeshesACM Transactions on Graphics10.1145/365812243:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658122

Index Terms

A Convex Optimization Framework for Regularized Geodesic Distances
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Shape analysis

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cover image ACM Conferences

SIGGRAPH '23: ACM SIGGRAPH 2023 Conference Proceedings

July 2023

911 pages

ISBN:9798400701597

DOI:10.1145/3588432

Copyright © 2023 Owner/Author.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives International 4.0 License.

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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Association for Computing Machinery

New York, NY, United States

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Published: 23 July 2023

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SIGGRAPH '23: Special Interest Group on Computer Graphics and Interactive Techniques Conference

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Cited By

Mattos Da Silva LStein OSolomon J(2024)A Framework for Solving Parabolic Partial Differential Equations on Discrete DomainsACM Transactions on Graphics10.1145/366608743:5(1-14)Online publication date: 25-Jun-2024
https://dl.acm.org/doi/10.1145/3666087
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658220
Li YNumerow LThomaszewski BCoros S(2024)Differentiable Geodesic Distance for Intrinsic Minimization on Triangle MeshesACM Transactions on Graphics10.1145/365812243:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658122

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