Gamut mapping color constancy algorithms (originally introduced by Forsyth[For90]) attempt to map RGBs of surfaces viewed under an unknown light to corresponding RGBs under a known reference illuminant. With respect to a reference light source the set of all observable RGBs occupies a 3-dimensional convex region, or gamut, of RGB space. If a triple of 3 simple scalar factors defines the map from image colors to reference conditions then it has been shown that the set of all maps taking RGBs into the reference gamut is also a convex set. Gamut mapping algorithms work in 2 stages. First, the set of feasible maps is computed then in a second stage an optimal member of this map set is chosen. Here we show that feasible map set does not need to be computed. Rather we combine the final map selection stage with the enforcement of the constraint that image colors are mapped inside the reference gamut. The main contribution of this paper is to show that this combined computation can be set up as a simple convex programming problem. Two main advantages result from this reformulation of gamut mapping. First, several reasonable designations of ‘optimal’ map can be formulated and tested within the convex programming framework. If we maximize the sum of the triplet of map parameters then color constancy is shown to be a linear programming problem. Maximizing the Euclidean magnitude of the mapping triplet gives a quadratic programming formulation and maximizing the volume of the mapped image gamut (Forsyth’s original gamut mapping algorithm) is also possible The second advantage is that convex programming provides a fast solution to the color constancy problem. Indeed, we show that linear programming color constancy is a strictly more efficient implementation of gamut mapping compared to previous methods. Experiments indicate that, for the Simon Fraser Data set (synthetic and real images), linear programming color constancy provides the best performance over all the convex programming methods tested.
|Number of pages||8|
|Publication status||Published - Oct 2003|
|Event||IEEE workshop on color and photometric methods in computer vision (part of the 9th International Conference on Computer Vision) - Nice, France|
Duration: 1 Oct 2003 → …
|Conference||IEEE workshop on color and photometric methods in computer vision (part of the 9th International Conference on Computer Vision)|
|Period||1/10/03 → …|