Image deformations due to relative motion between an observer and an object may be used to infer 3D structure. Up to 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. The gaussian equations are solved both in the special case where the affine transform can be written as a similarity transform and for the general affine transform. The method is local and can handle arbitrarily large affine deformations. Experiments demonstrate that this technique can find scale changes and optical flow in situations where other methods fail. The experiments also demonstrate the robustness of the technique.
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