Combination of graph theoretic grouping and time-frequency analysis for image segmentation

We introduce a nonparametric approach to multiscale segmentation of images using a hierarchical matrix analysis framework called diffusion wavelets. This approach benefits from the advantages of both graph theory and wavelet transform. Till now a broad range of multiscale transforms like wavelets (and other x-lets) have been introduced for image segmentation task. The graph theoretic formulation of grouping is also well-known to deal with this problem. The combination of multiscale transforms and graph based partitioning results in a scale-spectral method exploring through different scales of the image, over a great deal of spectral methods in graph partitioning. The method constructs multiscale basis functions and a series of dilation and orthogonalizations build a hierarchy, automatically. At each level, a set of basis functions is built by applying dyadic powers of a diffusion operator on the bases at the lower level. Two approaches are proposed for multiscale segmentation of images using diffusion wavelets. The first method is based on extended bases functions at each level and designing a competition between the bases value for partitioning. The second approach is defining a new distance for each level and clustering based on such distances.