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.