Malignant melanoma is a skin cancer that can be mistaken as a harmless mole in the early stages and is curable only in these early stages. Therefore, dermatologists use a microscope that shows the pigment structures of the skin to classify suspicious skin lesions as malignant or benign. This microscope is called "dermoscope." However, even when using a dermoscope a malignant skin lesion can be mistaken as benign or vice versa. Therefore, it seems desirable to analyze dermoscopic images by computer to classify the skin lesion. Before a dermoscopic image can be classified, it should be segmented into regions of the same color. For this purpose, we propose a segmentation method that automatically determines the number of colors by optimizing a cluster validity index. Cluster validity indices can be used to determine how accurately a partition represents the "natural" clusters of a data set. Therefore, cluster validity indices can also be applied to evaluate how accurately a color image is segmented. First the RGB image is transformed into the L*u*v* color space, in which Euclidean vector distances correspond to differences of visible colors. The pixels of the L*u*v* image are used to train a self-organizing map. After completion of the training a genetic algorithm groups the neurons of the self-organizing map into clusters using fuzzy c-means. The genetic algorithm searches for a partition that optimizes a fuzzy cluster validity index. The image is segmented by assigning each pixel of the L*u*v* image to the nearest neighbor among the cluster centers found by the genetic algorithm. A set of dermoscopic images is segmented using the method proposed in this research and the images are classified based on color statistics and textural features. The results indicate that the method proposed in this research is effective for the segmentation of dermoscopic images.