Shape L'Âne Rouge: Sliding Wavelets for Indexing and Retrieval.

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 "sliding" wavelet coefficients akin to the sliding block puzzle L'Âne 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.