Convexity analysis of active contour problems

Christos Davatzikos, Jerry Ladd Prince

Research output: Contribution to journalArticle

Abstract

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

Original languageEnglish (US)
Pages (from-to)27-36
Number of pages10
JournalImage and Vision Computing
Volume17
Issue number1
DOIs
StatePublished - Jan 1999

Fingerprint

Potential energy

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Convexity analysis of active contour problems. / Davatzikos, Christos; Prince, Jerry Ladd.

In: Image and Vision Computing, Vol. 17, No. 1, 01.1999, p. 27-36.

Research output: Contribution to journalArticle

Davatzikos, Christos ; Prince, Jerry Ladd. / Convexity analysis of active contour problems. In: Image and Vision Computing. 1999 ; Vol. 17, No. 1. pp. 27-36.
@article{27e13f63517d4068b6362093e554f544,
title = "Convexity analysis of active contour problems",
abstract = "A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.",
author = "Christos Davatzikos and Prince, {Jerry Ladd}",
year = "1999",
month = "1",
doi = "10.1016/S0262-8856(98)00087-0",
language = "English (US)",
volume = "17",
pages = "27--36",
journal = "Image and Vision Computing",
issn = "0262-8856",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - Convexity analysis of active contour problems

AU - Davatzikos, Christos

AU - Prince, Jerry Ladd

PY - 1999/1

Y1 - 1999/1

N2 - A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

AB - A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics about their convexity, and suggesting that external potentials involving center-of-mass computations may be better behaved than the usual potentials based on image gradients. Our analysis also provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

UR - http://www.scopus.com/inward/record.url?scp=0032742016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032742016&partnerID=8YFLogxK

U2 - 10.1016/S0262-8856(98)00087-0

DO - 10.1016/S0262-8856(98)00087-0

M3 - Article

AN - SCOPUS:0032742016

VL - 17

SP - 27

EP - 36

JO - Image and Vision Computing

JF - Image and Vision Computing

SN - 0262-8856

IS - 1

ER -