The establishment of automatic diagnostic systems able to detect and classify skin lesions at the initial stage are getting really relevant and effective in providing support for medical personnel during clinical assessment. Image segmentation has a determinant part in computer-aided skin lesion diagnosis pipeline because it makes possible to extract and highlight information on lesion contour texture as, for example, skewness and area unevenness. However, artifacts, low contrast, indistinct boundaries, and different shapes and areas contribute to make skin lesion segmentation a challenging task. In this paper, a fully automatic computer-aided system for skin lesion segmentation in dermoscopic images is indicated. Adopting this method, noise and artifacts are initially reduced by the singular value decomposition; afterward lesion decomposition into a frame of bit-plane layers is performed. A specific procedure is implemented for redundant data reduction using simple Boolean operators. Since lesion and background are rarely homogeneous regions, the obtained segmentation region could contain some disjointed areas classified as lesion. To obtain a single zone classified as lesion avoiding spurious pixels or holes inside the image under test, mathematical morphological techniques are implemented. The performance obtained highlights the method validity.