A hybrid eulerian-lagrangian approach for thickness, correspondence, and gridding of annular tissues

Authors:
Kelvin R. Rocha;Anthony J. Yezzi;Jerry L. Prince
Affiliations:
Georgia Institute of Technology, School of Electrical and Computer Engineering, Atlanta, GA;Georgia Institute of Technology, School of Electrical and Computer Engineering, Atlanta, GA;Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD
Venue:
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Year:
2005

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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 (PDEs) are efficiently computed within an Eulerian framework and combined with a Lagrangian approach so that correspondences trajectories are partially constructed when necessary. Results show that the proposed technique takes advantage of both the speed of the Eulerian PDE approach and the accuracy of the Lagrangian approach.