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

• Published in: Journal of mathematical imaging and vision Vol. 57; no. 3; pp. 324 - 339
• Main Authors: Ferri, Massimo, Tomba, Ivan, Visotti, Andrea, Stanganelli, Ignazio
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2017; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Computer Science; Feasibility studies; Homology; Image Processing and Computer Vision; Image segmentation; Lesions; Mathematical Methods in Physics; Parameters; Pattern recognition; Search algorithms; Signal,Image and Speech Processing; Topology; Persistent Betti Numbers; Melanocytic lesion; Filtering function; Image retrieval
• ISSN: 0924-9907; 1573-7683; 1573-7683
• DOI: 10.1007/s10851-016-0680-6

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.