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

TL;DR

This paper explores the use of persistent homology, a topological data analysis method, to enhance k-Nearest Neighbor search for melanoma detection by analyzing lesion features through Betti numbers.

Contribution

It introduces a novel algorithm integrating persistent homology with traditional morphological parameters for improved melanoma lesion retrieval.

Findings

Feasibility demonstrated on 107 lesions

Persistent Betti numbers effectively characterize lesion features

Potential for improved automatic melanoma diagnosis

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 = 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.