Colour constancy with error bars

The colours in images are confounded by the colour of the illuminant: a yellow light leads to colours that are more yellow than they ought to be. Colour constancy algorithms attempt to estimate and correct for the colour of the illuminant. Unfortunately existing colour constancy algorithms do not work very well. The reason for their failure is easy to understand: different collections of reflectances viewed under different lights can induce exactly the same image. It follows that inverting the image formation process, thereby extracting the illuminant, is an ill-posed problem. To circumvent the ill-posedness of the problem authors have sought solutions for certain special cases, e.g. when there is a white reflectance in a scene. Unfortunately these special case scenarios often do not hold in practice; blindly assuming that they do hold also leads to poor colour constancy. In this paper we work with the ill-posedness inherent in the problem. In particular, rather than trying to solve for a unique answer we instead compute the set of all plausible answers. This set is characterised by the set median and associated error bars. For example, our algorithm might estimate that the illuminant colour is white (the median answer) but that it could be a little reddish or bluish (the error bars). We have found that the magnitude of the error bars correlates with the colour diversity in a scene. The more colours there are, the less ill-posed is the recovery problem and so the smaller the error bars. It is proposed that error bars provide useful information for any computer vision module that uses colour (e.g. face trackers)