title: Fractal and integer-dimensional geometric analysis of pigmented skin lesions.
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 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.
authors.affiliation: Department of Pathology, University of Sheffield Medical School, England.
authors.forename: S S
authors.initials: SS
authors.lastname: Cross
authors.forename: A J
authors.initials: AJ
authors.lastname: McDonagh
authors.forename: T J
authors.initials: TJ
authors.lastname: Stephenson
authors.forename: D W
authors.initials: DW
authors.lastname: Cotton
authors.forename: J C
authors.initials: JC
authors.lastname: Underwood
mesh_terms: D000465:Algorithms; D016002:Discriminant Analysis; D017709:Fractals; D006801:Humans; D007091:Image Processing, Computer-Assisted; D017492:Keratosis, Seborrheic / Q000473:pathology / Q000601:surgery; D016014:Linear Models; D008433:Mathematics; D008545:Melanoma / Q000473:pathology / Q000601:surgery; D008838:Microcomputers; D015999:Multivariate Analysis; D009506:Nevus / Q000473:pathology / Q000601:surgery; D018330:Nevus, Intradermal / Q000473:pathology / Q000601:surgery; D009508:Nevus, Pigmented / Q000473:pathology / Q000601:surgery; D010781:Photography; D010859:Pigmentation Disorders / Q000473:pathology* / Q000601:surgery; D015203:Reproducibility of Results; D012878:Skin Neoplasms / Q000473:pathology* / Q000601:surgery