Shape Representation via Best Orthogonal Basis Selection

We formulate the problem of finding a statistical representation of shape as a best basis selection problem in which the goal is to choose the basis for optimal shape representation from a very large library of bases. In this work, our emphasis is on applying this basis selection framework using the wavelet packets library to estimate the probability density function of a class of shapes from a limited number of training samples. Wavelet packets offer a large number of complete orthonormal bases which can be searched for the basis that optimally allows the analysis of shape details at different scales. The estimated statistical shape distribution is capable of generalizing to shape examples not encountered during training, while still being specific to the modeled class of shapes. Using contours from two-dimensional MRI images of the corpus callosum, we demonstrate the ability of this approach to approximate the probability distribution of the modeled shapes, even with a few training samples.