Selection for gamut mapping colour constancy

Abstract

The requirement that the sensor responses of a camera to a given surface reflectance be constant under changing illumination conditions has led to the development of the so called colour constancy algorithms. Given an image recorded under an unknown illuminant, the task for a colour constancy algorithm is to recover an estimate of the scene illuminant. One such algorithm developed by D.A. Forsyth, A novel algorithm for colour constancy, International Journal of Computer Vision 5 (1) (1990) 5–36 [1] and later extended by G.D. Finlayson, Color in perspective, IEEE Transactions on Pattern Analysis and Machine Intelligence 18(10) (1996) 1034–1038 [2] exploits the constraint that under a canonical illuminant all surface colours fall within a maximal convex set-the canonical gamut. Given a set of image colours Forsyth’s algorithm recovers the set of mappings which take these colours into the canonical gamut. This feasible set of mappings represents all illuminants, which are consistent with the recorded image colours. In this article we address the question of how best to select a single mapping from this feasible set as an estimate of the unknown illuminant. We develop our approach in the context of Finlayson’s colour-in- perspective algorithm. This algorithm performs a perspective transform on the sensor data to discard intensity information which, without unrealistic constraints (uniform illumination and no specularities) being placed on the world, cannot be recovered accurately. Unfortunately, the feasible set of mappings recovered by this algorithm is also perspectively distorted. Here, we argue that this distortion must be removed prior to carrying out map selection and show that this is easily achieved by inverting the perspective transform. A mean-selection criterion operating on non-perspective mapping space provides good colour constancy for a variety of synthetic and real images. Importantly, constancy performance surpasses all other existing methods.