Gamut mapping transforms the colors of an input image to the colors of a target device so as to exploit the full potential of the rendering device in terms of color rendition. In this paper we present spatial gamut mapping algorithms that rely on a perceptually-based variational framework. Our algorithms adapt a well-known image energy functional whose minimization leads to image enhancement and contrast modification. We show how by varying the importance of the contrast term in the image functional we are able to perform gamut reduction and gamut extension. We propose an iterative scheme that allows our algorithms to successfully map the colors from the gamut of the original image to a given destination gamut while keeping the perceived colors close to the original image. Both subjective and objective evaluations validate the promising results achieved via our proposed algorithms.