Shape analysis on the hypersphere of wavelet densities

We present a novel method for shape analysis which represents shapes as probability density functions and then uses the intrinsic geometry of this space to match similar shapes. In our approach, shape densities are estimated by representing the square-root of the density in a wavelet basis. Under this model, each density (of a corresponding shape) is then mapped to a point on a unit hypersphere. For each category of shapes, we find the intrinsic Karcher mean of the class on the hyper-sphere of shape densities, and use the minimum spherical distance between a query shape and the means to classify shapes. Our method is adaptable to a variety of applications, does not require burdensome preprocessing like extracting closed curves, and experimental results demonstrate it to be competitive with contemporary shape matching algorithms.