Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Shape Analysis: Clustering, Learning, and Testing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Elastic-string models for representation and analysis of planar shapes
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images
International Journal of Computer Vision
An Elasticity Approach to Principal Modes of Shape Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An Elasticity-Based Covariance Analysis of Shapes
International Journal of Computer Vision
Robust diffeomorphic mapping via geodesically controlled active shapes
Journal of Biomedical Imaging
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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.