Topology-Preserved Diffusion Distance for Histogram Comparison

In most previous works, histograms are simply treated as n-dimensional arrays or even reshaped into vectors when measuring the distances between them. However many histograms have their intrinsic topologies, such as HSV histogram (cone), shape context (polar), orientation histogram (circle). The topologies are important for so-called cross-bin distance, because they determine the similarities between histogram bins, and influence the crossbin distances between histograms. In this paper, we proposed the topologypreserved diffusion distance to take the topology into account. This method extracts the distance by measuring the heat diffusion process defined on the topology of the histogram. Moreover, a fast implementation with time complexity O(N) is developed. Experiments on image retrieval and interest point matching show the effectiveness and efficiency of the proposed method.