Non-iterative Comprehensive Normalisation

The light reflected from an object depends not only on object colours but also on lighting geometry and illuminant colour. As a consequence the raw colour recorded by a camera is not a reliable cue for object based tasks such as recognition and tracking. One solution to this problem is to find functions of image colours that cancel out dependencies due to illumination. While many invariant functions cancel out either dependency due to geometry or dependency due to illuminant colour, only the comprehensive normalisation has been shown (theoretically and experimentally) to cancel both. However, this invariance is bought at the price of an iterative procedure. In this paper we develop a non iterative log comprehensive normalisation procedure. We begin by reviewing the idea that lighting effects due to geometry and light colour can, under certain reasonable simplifying assumptions, both be modelled using simple scalar multipliers. We now take logarithms and turn geometry and light colour dependency into additive processes. We show how in this log color space two simple projection operators lead to invariance to geometry and light colour. Moreover, because projection operators are idempotent, illuminant invariance is achieved in a single step. Experiments demonstrated that log comprehensive normalisation used as a preprocessing step supports accurate colour based object recognition independent of lighting conditions.