On the geometric modulation of skin lesion growth: a mathematical model for melanoma

Abstract

Introduction: Early detection of suspicious skin lesions is critical to prevent skin malignancies, particularly the melanoma, which is the most dangerous form of human skin cancer. In the last decade, image processing techniques have been an increasingly important tool for early detection and mathematical models play a relevant role in mapping the progression of lesions. Methods: This work presents an algorithm to describe the evolution of the border of the skin lesion based on two main measurable markers: the symmetry and the geometric growth path of the lesion. The proposed methodology involves two dermoscopic images of the same melanocytic lesion obtained at different moments in time. By applying a mathematical model based on planar linear transformations, measurable parameters related to symmetry and growth are extracted. Results: With this information one may compare the actual evolution in the lesion with the outcomes from the geometric model. First, this method was tested on predefined images whose growth was controlled and the symmetry known which were used for validation. Then the methodology was tested in real dermoscopic melanoma images in which the parameters of the mathematical model revealed symmetry and growth rates consistent with a typical melanoma behavior. Conclusions: The method developed proved to show very accurate information about the target growth markers (variation on the growth along the border, the deformation and the symmetry of the lesion trough the time). All the results, validated by the expected phantom outputs, were similar to the ones on the real images.

Accurate Segmentation of Dermoscopic Images based on Local Binary Pattern Clustering

“…The Border Error (BE) metric, displayed in percentage, is defined in (5), measures the nonoverlapping segmentation regions between the proposed segmentation method (SM) and the dataset ground-truth segmentation (GT).…”

“…Accordingly, amongst all image processing steps commonly used in dermoscopic images, the identification of the region of interest (ROI) is of central importance in the classification framework [4]. In addition to the ROI delineation, this segmentation procedure is also used not only to extract other information regarding the lesion itself, but also about the dynamics of its growing process [5].…”

Computational models of melanoma

“…two-dimensional (2D) patterns of naevi and melanoma can also be subjected to planar linear transformations using two subsequent dermoscopic pictures. Those pictures allow the classification of melanoma growth rates and naevi symmetry [68]. The ABCD criteria for asymmetry, border irregularity, color variation, and diameter of melanoma have been mathematically considered too [69].…”

A mathematical analysis of the ABCD criteria for diagnosing malignant melanoma

“…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.…”