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A Feasibility Study for a Persistent Homology-Based k-Nearest Neighbor Search Algorithm in Melanoma Detection

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Abstract

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 \(=\) 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 Number 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.

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Acknowledgments

The support by ARCES, CA-MI S.r.l., IRST-IRCCS and the National Institute of High Mathematics “F. Severi” (INdAM) is gratefully acknowledged.

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Authors and Affiliations

  1. Università di Bologna, Bologna, Italy

    Massimo Ferri

  2. CA-MI S.r.l., Pilastro, Parma, Italy

    Ivan Tomba & Andrea Visotti

  3. Skin Cancer Unit IRCCS-IRST Istituto Scientifico Romagnolo per la Cura e lo Studio dei Tumori, Meldola, Forlì, Italy

    Ignazio Stanganelli

  4. Clinica Dermatologica, Università di Parma, Parma, Italy

    Ignazio Stanganelli

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  1. Massimo Ferri
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  4. Ignazio Stanganelli
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Correspondence to Ivan Tomba.

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Ferri, M., Tomba, I., Visotti, A. et al. A Feasibility Study for a Persistent Homology-Based k-Nearest Neighbor Search Algorithm in Melanoma Detection. J Math Imaging Vis 57, 324–339 (2017). https://doi.org/10.1007/s10851-016-0680-6

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