Shape L'Âne rouge: Sliding wavelets for indexing and retrieval

Adrian M. Peter, Anand Rangarajan, Jeffrey Ho

Abstract: Shape representation and retrieval of stored shape models are becoming increasingly more prominent in fields such as medical imaging, molecular biology and remote sensing. We present a novel framework that directly addresses the necessity for a rich and compressible shape representation, while simultaneously providing an accurate method to index stored shapes. The core idea is to represent point-set shapes as the square root of probability densities expanded in a wavelet basis. We then use this representation to develop a natural similarity metric that respects the geometry of these probability distributions, i.e. under the wavelet expansion, densities are points on a unit hypersphere and the distance between densities is given by the separating arc length. The process uses a linear assignment solver for non-rigid alignment between densities prior to matching; this has the connotation of ldquoslidingrdquo wavelet coefficients akin to the sliding block puzzle LpsilaAne Rouge. We illustrate the utility of this framework by matching shapes from the MPEG-7 data set and provide comparisons to other similarity measures, such as Euclidean distance shape distributions.