An image dependent gamut mapping method for mapping source colors of an image to destination colors reproducible by a printing apparatus, each source color having a lightness component within a range between a source white point and a source black point, and each destination color having a lightness component within a range between a destination white point and a destination black point. A composed transfer function maps the source white point onto the destination white point and the source black point onto the destination black point, applying the composed transfer function on each lightness component of source colors of at least a part of the image. The transfer function is composed of linear mappings. The steepness of each linear mapping is determined by a mathematical optimization problem intended to preserve lightness and contrast in the image produced by the printing apparatus under the conditions of at least one constraint.