Symmetry axis computation for almost-symmetrical and asymmetrical objects: application to pigmented skin lesions

The detection of symmetry axes through the optimization of a given symmetry measure, computed as a function of the mean-square error between the original and reflected images, is investigated in this paper. A genetic algorithm and an optimization scheme derived from the self-organizing maps theory are presented. The notion of symmetry map is then introduced. This transform allows us to map an object into a symmetry space where its symmetry properties can be analyzed. The locations of the different axes that globally and locally maximize the symmetry value can be obtained. The input data are assumed to be vector-valued, which allow to focus on either shape. color or texture information. Finally, the application to skin cancer diagnosis is illustrated and discussed.