A hybrid Eulerian-Lagrangian approach for thickness, correspondence, and gridding of annular tissues

Kelvin R. Rocha, Anthony J. Yezzi, Jerry Ladd Prince

Research output: Contribution to journalArticle

Abstract

We present a novel approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace's equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations are efficiently computed within an Eulerian framework and combined with a Lagrangian approach so that correspondences trajectories are partially constructed when necessary. Examples are presented in order to compare the performance of this method with those of the pure Lagrangian and pure Eulerian approaches. Results show that the proposed technique takes advantage of both the speed of the Eulerian approach and the accuracy of the Lagrangian approach.

Original languageEnglish (US)
Pages (from-to)636-648
Number of pages13
JournalIEEE Transactions on Image Processing
Volume16
Issue number3
DOIs
StatePublished - Mar 2007

Fingerprint

Correspondence
Trajectories
Tissue
Trajectory
Harmonic functions
Laplace equation
Partial differential equations
Gradient Flow
Laplace's equation
Harmonic Functions
Expand
Partial differential equation
Necessary

Keywords

  • Correspondence
  • Correspondence trajectory
  • Partial differential equations (PDEs)
  • Thickness

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

A hybrid Eulerian-Lagrangian approach for thickness, correspondence, and gridding of annular tissues. / Rocha, Kelvin R.; Yezzi, Anthony J.; Prince, Jerry Ladd.

In: IEEE Transactions on Image Processing, Vol. 16, No. 3, 03.2007, p. 636-648.

Research output: Contribution to journalArticle

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