Statistical Modeling of Colour Data

Abstract

In this paper we investigate how best to model naturally arising distributions of colour camera data. It has become standard to model single mode distributions of colour data by ignoring the intensity component and constructing a Gaussian model of the chromaticity. This approach is appealing, because the intensity of data can change arbitrarily due to shadowing and shading, whereas the chromaticity is more robust to these effects. However, it is unclear how best to construct such a model, since there are many domains in which the chromaticity can be represented. Furthermore, the applicability of this kind of model is questionable in all but the most basic lighting environments.

We begin with a review of the reflection processes that give rise to distributions of colour data. Several candidate models are then presented; some are from the existing literature and some are novel. Properties of the different models are compared analytically and the models are empirically compared within a region tracking application over two separate sets of data. Results show that chromaticity based models perform well in constrained environments where the physical model upon which they are based applies. It is further found that models based on spherical representations of the chromaticity data provide better performance than those based on more common planar representations, such as the chromaticity plane or the normalised colour space. In less constrained environments, however, such as daylight, chromaticity based models do not perform well, because of the effects of additional illumination components, which violate the physical model upon which they are based.