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

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

Research output: Contribution to journalArticlepeer-review

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 1 2007

Keywords

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

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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