A feasibility study for a persistent homology based k-Nearest Neighbor   search algorithm in melanoma detection
  Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of holes and their persistence while a parameter ("filtering function") is varied. In this paper, some recent developments in this field are integrated in a k-Nearest Neighbor search algorithm suited for an automatic retrieval of melanocytic lesions. Since long, dermatologists use five morphological parameters (A = Asymmetry, B = Boundary, C = Color, D = Diameter, E = Elevation or Evolution) for assessing the malignancy of a lesion. The algorithm is based on a qualitative assessment of the segmented images by computing both 1 and 2-dimensional Persistent Betti Numbers functions related to the ABCDE parameters and to the internal texture of the lesion. The results of a feasibility test on a set of 107 melanocytic lesions are reported in the section dedicated to the numerical experiments. 
Massimo Ferri, Ivan Tomba, Andrea Visotti, Ignazio Stanganelli
q-bio.QM math.AT