Extracting affine deformations from image patches. I. Finding scale and rotation

Image deformations due to relative motion between an observer and an object may be used to infer 3-D structure. Up to the first order, these deformations can be written in terms of an affine transform. A novel approach is adopted to measuring affine transforms which correctly handles the problem of corresponding deformed patches. The patches are filtered using Gaussians and derivatives of Gaussians and the filters deformed according to the affine transform. The problem of finding the affine transform is therefore reduced to that of finding the appropriate deformed filter to use. In the special case where the affine transform can be written as a scale change and an in-plane rotation, the Gaussian and first derivative equations are solved for the scale. The robustness of the method is demonstrated experimentally