Fractal and integer-dimensional geometric analysis of pigmented skin lesions

Accurate in vivo diagnosis of pigmented skin lesions is required to identify and excise malignant melanomas but to avoid unnecessary excision of benign lesions; the published rates of clinical diagnostic accuracy are about 65%. This study investigates whether fractal geometric analysis of pigmented skin lesions can improve the rate of diagnostic accuracy. Forty-two pigmented skin lesions (15 malignant melanomas, 21 melanocytic naevi, and 6 basal cell papillomas) on patients attending a dermatology clinic were photographed, excised, and sent for histopathological examination. The fractal dimension of the boundary of the lesions was measured using a box-counting method implemented on a microcomputer-based image analysis system. Euclidean geometric parameters were also measured. The fractal dimension of all the lesions was greater than the topological dimension (one), indicating that there is a fractal element to their structure. Using all measured parameters together, multivariate linear discriminant analysis produced a confusion matrix in which 45% of the lesions were assigned to the correct diagnostic group with a kappa statistic of 0.33. There was no significant difference between the fractal dimension of melanocytic naevi and that of malignant melanomas (p = 0.18). Although pigmented skin lesions have a fractal element to their structure, the fractal dimension of their boundaries is not a useful morphometric discriminant between the diagnostic groups of malignant melanomas and benign melanocytic naevi.