Characterizing Images by the Gromov-Hausdorff Distances Between Derived Hierarchies

A hierarchy is a series of nested partitions in which a coarser partition results from merging regions of finer ones. Each hierarchy derived from an image provides a particular structural description of the image content, depending upon the criteria for merging neighboring regions. Distinct hierarchies derived from a same image reflect its various facets and the distances between them nicely characterize its content. In this paper the hierarchies are constructed with the versatile stochastic watershed algorithm and their inter-distances are measured with the Gromov-Hausdorff distance. Experiments conducted on images simulated by dead leaves model illustrate the advantages of our approach in terms of learning efficiency and understandability of the results.