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 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. The first contribution of this paper is to present a non-iterative comprehensive normalisation procedure. Iteration is avoided by working with logarithms of RGB images rather than the RGBs themselves. We show that under certain simplifying assumptions, in log colour space two simple projection operators lead to invariance to geometry and light colour in a single step. Although both comprehensive normalisation and the non-iterative normalisation work well in the context of colour based object recognition, neither of them accounts for all dependencies that might realistically be present in images. For example, a power (gamma) function is typically applied to image data as part of the coding process and this function can be device and even image dependent. Thus in a second part of the paper we ask whether we can also remove colour dependency due to gamma? We show that we can and furthermore, that invariance can be achieved by adding a single further step to the non-iterative normalisation procedure. Finally, we demonstrate the efficacy of these new normalisation procedures by conducting a series of object recognition experiments on sets of linear and non-linear images.