Discriminating BCC Subtypes Using Entropy and Mutual Information from Dermoscopic Features

Objective: To analyze the frequency and co-occurrence of dermoscopic patterns in BCC lesions and their relationship with histopathologic subtypes, using statistical analysis and Information Theory tools such as entropy, conditional entropy, mutual information, and Hamming weight. Methods: A total of 223 dermoscopic images (256x256 pixels) of histologically confirmed BCC lesions from Hospital Universitario Virgen Macarena (Seville, Spain) were analyzed. Each image was multilabel-annotated for the presence of nine dermoscopic patterns and categorized into one of four BCC subtypes: superficial, nodular, infiltrative, or micronodular. Statistical and information-theoretic methods were applied, including co-occurrence matrices, Bayesian conditional probabilities, and entropy-based metrics. Mutual information quantified the predictive value of individual and paired patterns, and decision trees were built based on diagnostic informativeness. Results: Nodular BCC was highly associated with most dermoscopic patterns, particularly arborizing telangiectasia and blue-gray ovoid nests. Superficial BCC showed stronger associations with maple leaf-like structures and shiny white-red areas. Some patterns, like spoke-wheel areas and white streaks, showed low discriminative power. Mutual information and conditional probabilities identified meaningful pattern-pair dependencies for each subtype. Decision trees revealed that subsets of patterns could enhance subtype classification by accumulating diagnostic information. Conclusions: Information Theory enables a quantitative understanding of dermoscopic patterns and their relationship with BCC subtypes. This framework highlights key diagnostic features, aids in differentiating complex cases, and supports the development of automated, pattern-based diagnostic tools. Further research with larger, more balanced datasets is encouraged.