**Abstract**: Correspondence techniques start from the assumption, based on the Lambertian reflection model, that the apparent brightness of a surface is independent of the observer's angle of view. From this, a grey value constancy assumption is derived, which states that a change in brightness of a particular image pixel is proportional to a change in its position. This constancy assumption can be extended directly for vector valued images, such as RGB. It is clear that the grey value constancy assumption does not hold for surfaces with a non-Lambertian behaviour and, therefore, the underlying image representation is crucial when using real image sequences under varying lighting conditions and noise from the imaging device. In order for the correspondence methods to produce good, temporally coherent results, properties such as robustness to noise, illumination invariance, and stability with respect to small geometrical deformations are all desired properties of the representation.

In this paper, we study how different image representation spaces complement each other and how the chosen representations benefit from the combination in terms of both robustness and accuracy. The model used for establishing the correspondences, based on the calculus of variations, is itself considered robust. However, we show that considerable improvements are possible, especially in the case of real image sequences, by using an appropriate image representation. We also show how optimum (or near optimum) parameters, related to each representation space, can be efficiently found.

**Introduction:** ...In this paper, we study how combinations of different image representations behave with respect to both illumination errors and noise, ranking the results accordingly. We believe that such information is useful to the part of the visual community that concentrates on applications, such as obstacle detection in vehicle related scenarios, segmentation, and so on. Although other authors address similar issues, we find these to be slightly limited in scope due to a reduced `test bench', e.g.\ a small number of test images or image representations. Also, in most of the cases, the way in which the parameters related to the model(s) have been chosen is not satisfactorily explained. Therefore, the main contribution of our paper is an analysis of the different image representations supported by a more detailed and systematical evaluation methodology. For example, we show how optimum (or near optimum) parameters for the algorithm, related to each

representation space, can be found. This is a small but important contribution in the case of real, non controlled, scenarios. The standard image representation is the RGB-space, the others being (obtained via image transformations): gradient, gradient magnitude, log-derivative, HSV, \( r\phi\theta \), and phase component of an image filtered using a bank of Gabor filters....

**Authors:** J. Ralli, J. Díaz, P. Guzmán and E. Ros