Multi-scale auto-convolution for affine invariant pattern recognition

This paper describes a novel image transform, called the multi-scale auto-convolution, which is invariant with respect to affine transformations of the spatial image coordinates. The transform can be applied directly to image patches without segmentation. Algebraically, the transform is simple requiring only rescaling of the image and computation of two-dimensional convolutions that can be performed efficiently in the frequency domain. Similar transforms can also be derived for other linear distortions of the image. The experiments performed show that classification of complex patterns can be carried out reliably with only a small set of transform coefficients.