Analysis of the contour structural irregularity of skin lesions using wavelet decomposition

The boundary irregularity of skin lesions is of clinical significance for the early detection of malignant melanomas and to distinguish them from other lesions such as benign moles. The structural components of the contour are of particular importance. To extract the structure from the contour, wavelet decomposition was used as these components tend to locate in the lower frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to give position and frequency resolution invariance. Energy distributions among different wavelet sub-bands were then analyzed to extract those with significant levels and differences to enable maximum discrimination. Based on the coefficients in the significant sub-bands, structural components from the original contours were modeled, and a set of statistical and geometric irregularity descriptors researched that were applied at each of the significant sub-bands. The effectiveness of the descriptors was measured using the Hausdorff distance between sets of data from melanoma and mole contours. The best descriptor outputs were input to a back projection neural network to construct a combined classifier system. Experimental results showed that thirteen features from four sub-bands produced the best discrimination between sets of melanomas and moles, and that a small training set of nine melanomas and nine moles was optimum

Ideal hierarchical secret sharing schemes

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft