Abstract
To develop statistical models for shapes, we utilize an elastic string representation where curves (denoting shapes) can bend and locally stretch (or compress) to optimally match each other, resulting in geodesic paths on shape spaces. We develop statistical models for capturing variability under the elastic-string representation. The basic idea is to project observed shapes onto the tangent spaces at sample means, and use finite-dimensional approximations of these projections to impose probability models. We investigate the use of principal components for dimension reduction, termed tangent PCA or TPCA, and study (i) Gaussian, (ii) mixture of Gaussian, and (iii) non-parametric densities to model the observed shapes. We validate these models using hypothesis testing, statistics of likelihood functions, and random sampling. It is demonstrated that a mixture of Gaussian model on TPCA captures best the observed shapes.
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© 2006 Springer-Verlag Berlin Heidelberg
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Srivastava, A., Jain, A., Joshi, S., Kaziska, D. (2006). Statistical Shape Models Using Elastic-String Representations. In: Narayanan, P.J., Nayar, S.K., Shum, HY. (eds) Computer Vision – ACCV 2006. ACCV 2006. Lecture Notes in Computer Science, vol 3851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11612032_62
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DOI: https://doi.org/10.1007/11612032_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31219-2
Online ISBN: 978-3-540-32433-1
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