A Convex Optimization Framework for Regularized Geodesic Distances

Michal Edelstein; Nestor Guillen; Justin Solomon; Mirela Ben-Chen

doi:https://doi.org/10.1145/3588432.3591523

A Convex Optimization Framework for Regularized Geodesic Distances

Michal Edelstein, Nestor Guillen, Justin Solomon, Mirela Ben-Chen

Computer Science

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Proceedings - SIGGRAPH 2023 Conference Papers
Editors	Stephen N. Spencer
ISBN (Electronic)	9798400701597
DOIs	https://doi.org/10.1145/3588432.3591523
State	Published - 23 Jul 2023
Event	2023 Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2023 - Los Angeles, United States Duration: 6 Aug 2023 → 10 Aug 2023

Publication series

Name	Proceedings - SIGGRAPH 2023 Conference Papers

Conference

Conference	2023 Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2023
Country/Territory	United States
City	Los Angeles
Period	6/08/23 → 10/08/23

Keywords

convex optimization
geodesic distance
triangle meshes

All Science Journal Classification (ASJC) codes

Software
Computer Vision and Pattern Recognition
Computer Graphics and Computer-Aided Design

Access to Document

https://doi.org/10.1145/3588432.3591523

Cite this

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title = "A Convex Optimization Framework for Regularized Geodesic Distances",

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.",

keywords = "convex optimization, geodesic distance, triangle meshes",

author = "Michal Edelstein and Nestor Guillen and Justin Solomon and Mirela Ben-Chen",

note = "Publisher Copyright: {\textcopyright} 2023 Owner/Author.; 2023 Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2023 ; Conference date: 06-08-2023 Through 10-08-2023",

year = "2023",

month = jul,

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doi = "https://doi.org/10.1145/3588432.3591523",

language = "الإنجليزيّة",

series = "Proceedings - SIGGRAPH 2023 Conference Papers",

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booktitle = "Proceedings - SIGGRAPH 2023 Conference Papers",

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Edelstein, M, Guillen, N, Solomon, J & Ben-Chen, M 2023, A Convex Optimization Framework for Regularized Geodesic Distances. in SN Spencer (ed.), Proceedings - SIGGRAPH 2023 Conference Papers., 2, Proceedings - SIGGRAPH 2023 Conference Papers, 2023 Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2023, Los Angeles, United States, 6/08/23. https://doi.org/10.1145/3588432.3591523

TY - GEN

T1 - A Convex Optimization Framework for Regularized Geodesic Distances

AU - Edelstein, Michal

AU - Guillen, Nestor

AU - Solomon, Justin

AU - Ben-Chen, Mirela

PY - 2023/7/23

Y1 - 2023/7/23

N2 - 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.

AB - 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.

KW - convex optimization

KW - geodesic distance

KW - triangle meshes

UR - http://www.scopus.com/inward/record.url?scp=85167964786&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/3588432.3591523

DO - https://doi.org/10.1145/3588432.3591523

M3 - منشور من مؤتمر

T3 - Proceedings - SIGGRAPH 2023 Conference Papers

BT - Proceedings - SIGGRAPH 2023 Conference Papers

A2 - Spencer, Stephen N.

T2 - 2023 Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2023

Y2 - 6 August 2023 through 10 August 2023

ER -

A Convex Optimization Framework for Regularized Geodesic Distances

Abstract

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Keywords

All Science Journal Classification (ASJC) codes

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