Shape analysis of open curves in R3with applications to study of fiber tracts in DT-MRI data

Authors:
Nikolay Balov;Anuj Srivastava;Chunming Li;Zhaohua Ding
Affiliations:
Department of Statistics, Florida State University, Tallahassee, FL;Department of Statistics, Florida State University, Tallahassee, FL;Institute of Imaging Sciences, Vanderbilt University, Nashville, TN;Institute of Imaging Sciences, Vanderbilt University, Nashville, TN
Venue:
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Year:
2007

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Abstract

Motivated by the problem of analyzing shapes of fiber tracts in DT-MRI data, we present a geometric framework for studying shapes of open curves in R3. We start with a space of unit-length curves and define the shape space to be its quotient space modulo rotation and reparametrization groups. Thus, the resulting shape analysis is invariant to parameterizations of curves. Furthermore, a Riemannian structure on this quotient shape space allows us to compute geodesic paths between given curves and helps develop algorithms for: (i) computing statistical summaries of a collection of curves using means and covariances, and (ii) clustering a given set of curves into clusters of similar shapes. Examples using fiber tracts, extracted as parameterized curves from DT-MRI images, are presented to demonstrate this framework.