Event Location: NSH 3305
Bio: Anand Rangarajan has worked in shape analysis for over twenty years. After receiving the Ph.D. from the University of Southern California in 1991, he worked at Yale University in both the radiology and computer science departments until the advent of the new millennium. Since then, he has been in the computer science department at the University of Florida. His research interests include computer vision, machine learning and the scientific study of consciousness.

Abstract: In shape analysis, classification and indexing, a shape distance is a principal requirement. When shapes are represented using probability densities, distance measures between two probability densities can function as shape distances. Beyond the pairwise shape comparison scenario, when an atlas (or mean shape) is also represented as a probability density function, we have shown that the familiar Jensen-Shannon divergence (and other information-theoretic distance measures) can be pressed into service in this groupwise setting. In all of this previous work, we have continued to rely on spline and diffeomorphism parameterizations of the (usually quotiented out) non-rigid deformations. Recently, we have shown that geodesics or shortest paths based on an information geometry-driven Riemannian metric can play the role of a shape distance. Unfortunately, geodesic computation can be slow and cumbersome for Gaussian mixture models which are typically used to represent the aforementioned shape density functions. Due to this, we switch to Schrodinger distance transform (SDT) or wavelet density representations for square-root densities since the shortest path in this setting is an easily computed geodesic on a hypersphere. Representative applications such as the groupwise registration of hippocampal shapes and indexing on the MPEG 7 dataset showcase these approaches. Finally, we draw upon the highly suggestive relationship between square-root densities and the Schrodinger wave function to show that the phase of the wave function can represent signed distance function information—thereby potentially including grouping into the matching process.