Gamma Comprehensive Normalisation

摘要

The light reflected from an object depends not only on surface reflectance of the object but also on lighting geometry and illuminant color. As a consequence, the raw color recorded by a camera is not a reliable cue for color based tasks such as object recognition and tracking. One solution to this problem is to find color invariants which are independent of illumination. While many invariant functions cancel out dependency due to geometry and light color it is less easy to remove both dependencies. The comprehensive normalisation removes both geometry and color but at the cost of an iterative procedure. In earlier work we showed how the need for iteration could be removed by carrying out normalisations in the log color domain. However, we have found that both these normalisations, though theoretically sound, do not account for all dependencies that might realistically be present. Indeed, in image processing pipelines it is common to raise an image to the power of gamma either to change the contrast (see into shadows or highlights) or to account for display non-linearities. In this paper we ask, "for systems to which gamma functions are applied, how can we make the invariant approach work to facilitate color based object recognition?" Clearly we need to deal with gamma and develop a framework where gamma is removed. This is the major contribution of this paper. We show how a simple extension of the log normalisation strategy also suffices to remove gamma. We tested our method both on linear and nonlinear datasets. While producing similarly results for linear dataset as our previous methods, our new method significantly outperformed previous methods for the nonlinear dataset.