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Persistent Homology is a fairly new branch of Computational Topology whichcombines geometry and topology for an effective shape description of use inPattern Recognition. In particular it registers through "Betti Numbers" thepresence of holes and their persistence while a parameter ("filteringfunction") is varied. In this paper, some recent developments in this field areintegrated in a k-Nearest Neighbor search algorithm suited for an automaticretrieval of melanocytic lesions. Since long, dermatologists use fivemorphological parameters (A = Asymmetry, B = Boundary, C = Color, D = Diameter,E = Elevation or Evolution) for assessing the malignancy of a lesion. Thealgorithm is based on a qualitative assessment of the segmented images bycomputing both 1 and 2-dimensional Persistent Betti Numbers functions relatedto the ABCDE parameters and to the internal texture of the lesion. The resultsof a feasibility test on a set of 107 melanocytic lesions are reported in thesection dedicated to the numerical experiments.

A feasibility study for a persistent homology based k-Nearest Neighbor search algorithm in melanoma detection