Dependence of gradient moment based descriptors on affine distortions of the differentiating kernel

This article investigates how the contribution of different gradient directions to the 2^nd-moment matrix (used in the Harris-detector) change by affine transformations of the low-pass filter used. It will be shown, that the transformation dependence of a Gaussian blurred (low-pass filtered) image´s 2^nd-moment matrix is encapsulated mainly in the 2^nd-moment matrix of the same image filtered by a slightly different uniform blur. Therefore, only one additional component is required per every standard component to predict the change of gradient moment based descriptors. The linear model of this dependence is obtained by numeric methods. The obtained linear model is used to approximate the transformation occurred between the extraction of two descriptors of the same image patch. Results are presented to show advantages and drawbacks of this application.