Unconstrained digital color correction

The colors a camera sees depends on the color of the viewing illuminant and, unless corrected, this leads to poor color reproduction. There are two strategies to color correction: constrained and unconstrained. The constrained methods rely on simplifying assumptions about the world (e.g. there is a white reeectance is in every scene). If the assumptions hold then good correction is possible but if they do not hold, which is often the case, then poor correction results. In contrast, the unconstrained approach attempts to correct colors without making any world assumptions whatsoever. Rather, correction proceeds by exploiting only the information inherent in the physics of color image formation. Recent work by Finlayson has demonstrated that the unconstrained approach can deliver good color correction. Indeed excellent color correction has been demonstrated for images of everyday scenes. However, Finlayson's algorithm is relatively complex (high computational complexity) and it is also sensitive to image noise. In this research we propose to develop new unconstrained algorithms which are fast and which work well in the presence of noise 1 Background Color constancy is the phenomenon whereby our visual system discounts the color of the viewing illuminant so that we see only surface colorr1]. For example, a white piece of paper looks white whether it is viewed under blue sky or yellow tungsten illuminants. We would like color video cameras (and other color devices) to be equally color constant. That is we would like to design a color correction algorithm which would take the camera colors observed under arbitrary and unknown lighting conditions and correct them to remove any illuminant induced color biases. Thus, if surfaces are observed under yellowish tungsten light then the color correction algorithm should infer this fact and correct the colors accordingly (in this case make them less yellow). In mathematical terms color correction can be written as: x s = Mx (1) In (1) x denotes the rgb vector measured for some surface viewed under an unknown illuminant. The same surface viewed under standard (usually white) lighting conditions induces the rgb vector x s. The mapping M (usually a 3 3 matrix) takes the observed illuminant dependent color and maps it to its corresponding illuminant independent counterpart. Finding M is the goal of color correction algorithms.