1. An image dependent gamut mapping method for mapping source colors of an image to destination colors reproducible by a printing apparatus, said source colors and destination colors being part of a color space comprising a lightness axis, each source color having a lightness component within a range between a source white point and a source black point on the lightness axis, and each destination color having a lightness component within a range between a destination white point and a destination black point on the lightness axis, said method comprising the steps of determining a composed transfer function that maps the source white point onto the destination white point and the source black point onto the destination black point; and applying the composed transfer function on each lightness component of source colors of at least a part of the image; wherein said step of determining comprises the steps of: dividing the lightness axis between the source white point and the source black point into a plurality of pieces; defining for each piece resulting from said step of dividing, a linear mapping from said piece to a part of the lightness components of the destination colors, said linear mapping having a steepness, the value of which has to be determined; defining the composed transfer function as a composed linear mapping consisting of the plurality of linear mappings from said step of defining the linear mapping; and determining the steepness of each linear mapping of the composed transfer function by the steps of: defining a first measure in the color space for the distance between the lightness component of a source color and the lightness component of a corresponding destination color; defining a second measure in the color space for the distance between a lightness contrast of neighboring source colors and a lightness contrast of corresponding neighboring destination colors; defining a first constraint for the steepnesses in order to establish that the mapped lightness components of the source colors lie on the lightness axis between the destination black point and the destination white point; and computing, by means of mathematical optimization for said part of the image, the values of the steepnesses of the pieces, wherein said optimization takes the first measure, the second measure and the first constraint into account.