Fractal and Integer-Dimensional Geometric Analysis of Pigmented Skin Lesions

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Abstract
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 κ 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.

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