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.
Statistical Shape Models Using Elastic-String Representations
Computer Vision – ACCV 2006 ; 6 ; 612-621
Lecture Notes in Computer Science ; 3851 , 6
2006-01-01
10 pages
Article/Chapter (Book)
Electronic Resource
English
Mixture Model , Shape Model , Nonparametric Model , Shape Space , Geodesic Path Computer Science , Computer Imaging, Vision, Pattern Recognition and Graphics , Pattern Recognition , Image Processing and Computer Vision , Artificial Intelligence (incl. Robotics) , Algorithm Analysis and Problem Complexity
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