Algorithms for stochastic approximations of curvature flows

Gozde Unal; Delphine Nain; Gerard Ben-Arous; Nahum Shimkin; Allen Tannenbaum; Ofer Zeitouni

Algorithms for stochastic approximations of curvature flows

Gozde Unal, Delphine Nain, Gerard Ben-Arous, Nahum Shimkin, Allen Tannenbaum, Ofer Zeitouni

Mathematics

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

Abstract

Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work [1], we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve shortening flows initiated by convex curves. The present note shows that this theory may be implemented as a new way of evolving curves and as a possible alternative to level set methods.

Original language	English (US)
Title of host publication	IEEE International Conference on Image Processing
Pages	651-654
Number of pages	4
Volume	2
State	Published - 2003
Event	Proceedings: 2003 International Conference on Image Processing, ICIP-2003 - Barcelona, Spain Duration: Sep 14 2003 → Sep 17 2003

Other

Other	Proceedings: 2003 International Conference on Image Processing, ICIP-2003
Country/Territory	Spain
City	Barcelona
Period	9/14/03 → 9/17/03

ASJC Scopus subject areas

Hardware and Architecture
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering

Cite this

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title = "Algorithms for stochastic approximations of curvature flows",

abstract = "Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work [1], we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve shortening flows initiated by convex curves. The present note shows that this theory may be implemented as a new way of evolving curves and as a possible alternative to level set methods.",

author = "Gozde Unal and Delphine Nain and Gerard Ben-Arous and Nahum Shimkin and Allen Tannenbaum and Ofer Zeitouni",

year = "2003",

language = "English (US)",

volume = "2",

pages = "651--654",

booktitle = "IEEE International Conference on Image Processing",

note = "Proceedings: 2003 International Conference on Image Processing, ICIP-2003 ; Conference date: 14-09-2003 Through 17-09-2003",

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TY - GEN

T1 - Algorithms for stochastic approximations of curvature flows

AU - Unal, Gozde

AU - Nain, Delphine

AU - Ben-Arous, Gerard

AU - Shimkin, Nahum

AU - Tannenbaum, Allen

AU - Zeitouni, Ofer

PY - 2003

Y1 - 2003

N2 - Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work [1], we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve shortening flows initiated by convex curves. The present note shows that this theory may be implemented as a new way of evolving curves and as a possible alternative to level set methods.

AB - Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work [1], we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve shortening flows initiated by convex curves. The present note shows that this theory may be implemented as a new way of evolving curves and as a possible alternative to level set methods.

UR - http://www.scopus.com/inward/record.url?scp=0344271954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344271954&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0344271954

VL - 2

SP - 651

EP - 654

BT - IEEE International Conference on Image Processing

T2 - Proceedings: 2003 International Conference on Image Processing, ICIP-2003

Y2 - 14 September 2003 through 17 September 2003

ER -

Algorithms for stochastic approximations of curvature flows

Abstract

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ASJC Scopus subject areas

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