“…However, individual doctors normally assess the ABCD criteria using a dermatoscope in an ad hoc manner. Although many image segmentation techniques (Umbaugh et al 1992, Schmid 1999, Silveira et al 2009, Beuren et al 2012, and quantification and classification methods (Ercal et al 1994, Chen et al 2003, Mastrolonardo et al 2006, Pellacani et al 2006, Situ et al 2008, Ding et al 2010, Coelho et al 2011, Messadi et al 2014, Cheerla and Frazier 2014, Jaworek-Korjakowska 2015, Mendes et al 2016 have been 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 do not investigate criterion D (distance) in further detail since the computation of the parameter is straightforward if the boundary of the lesion is given.…”