Journal of Mathematical Imaging and Vision

, Volume 57, Issue 3, pp 324–339 | Cite as

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

  • Massimo Ferri
  • Ivan TombaEmail author
  • Andrea Visotti
  • Ignazio Stanganelli


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.


Melanocytic lesion Persistent Betti Numbers Filtering function Image retrieval 



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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Massimo Ferri
    • 1
  • Ivan Tomba
    • 2
    Email author
  • Andrea Visotti
    • 2
  • Ignazio Stanganelli
    • 3
    • 4
  1. 1.Università di BolognaBolognaItaly
  2. 2.CA-MI S.r.l.Pilastro, ParmaItaly
  3. 3.Skin Cancer Unit IRCCS-IRST Istituto Scientifico Romagnolo per la Cura e lo Studio dei TumoriMeldola, ForlìItaly
  4. 4.Clinica DermatologicaUniversità di ParmaParmaItaly

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