A mathematical analysis of the ABCD criteria for diagnosing malignant melanoma

The medical community currently employs the ABCD (asymmetry, border irregularity, color variegation, and diameter of the lesion) criteria in the early diagnosis of a malignant melanoma. Although many image segmentation and classification methods are used to analyze the ABCD criteria, it is rare to see a study containing mathematical justification of the parameters that are used to quantify the ABCD criteria. In this paper, we suggest new parameters to assess asymmetry, border irregularity, and color variegation, and explain the mathematical meaning of the parameters. The suggested parameters are then tested with 24 skin samples. The parameters suggested for the 24 skin samples are displayed in three-dimensional coordinates and are compared to those presented in other studies (Ercal et al 1994 IEEE Trans. Biomed. Eng. 41 837-45, Cheerla and Frazier 2014 Int. J. Innovative Res. Sci., Eng. Technol. 3 9164-83) in terms of Pearson correlation coefficient and classification accuracy in determining the malignancy of the lesions.