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 re-parametrization 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.
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Balov, N., Srivastava, A., Li, C., Ding, Z. (2007). Shape Analysis of Open Curves in ℝ3 with Applications to Study of Fiber Tracts in DT-MRI Data. In: Yuille, A.L., Zhu, SC., Cremers, D., Wang, Y. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2007. Lecture Notes in Computer Science, vol 4679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74198-5_31
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DOI: https://doi.org/10.1007/978-3-540-74198-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74195-4
Online ISBN: 978-3-540-74198-5
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