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Abstract:
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Visualization is an integral component of statistical shape analysis, where the goal is to perform inference on shapes of objects. When interested in identifying shape variation, one typically performs principal component analysis (PCA) to decompose total variation into orthogonal directions of variation. In many cases, shapes observe multiple sources of variation; using PCA to visualize requires decomposition into several plots displaying each mode of variation, without the ability to understand how these components work together. I propose a semi-parametric method (according to a model-based bootstrap) for estimating a confidence region for the elastic shape mean, with the goal of also producing a succinct visual summary of this region. The use of elastic shape representations allows for optimal matching of shape features, yielding more appropriate estimation of shape variation than some other approaches. Discussion of visualization issues is included. The proposed region is estimated for simulated data, as well common shapes from the well-known MPEG-7 dataset.
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