Basic functions for early vision

It is commonly agreed on that the first step in early vision consists of projections of the image to a set of basis functions. Usually the spatial distribution of the basis functions is homogeneous and the projection is a convolution but in general this will not be the case. In the literature there is a wealth of different basis functions, each of them optimal with respect to certain criteria. On the other hand, there seems to be a convergence towards derivatives of Gaussians or harmonic modulations of Gaussians (Gabor functions). In this report we discuss the principles and analysing methods underlying the choice of these functions. One of these methods that recently became of exceptional importance is the energy/phase representation. We investigate in detail the quality of succesive orders of derivatives of Gaussians as odd/even pairs for the energy/phase concept. In addition we work out to which extent derivatives of Gaussians can be approximated by Gabor functions.

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