Shaping receptive fields for affine invariance

The Gaussian kernel has played a central role in multi-scale methods for feature extraction and matching. In this paper, a method for shaping the filter using the local image structure is presented. We propose an optimization formulation that densely estimates the filter's affine parameters by minimizing an objective constructed from differential feature responses and seek iterative, approximate solutions. A consequence of shaping the filters is affine invariance of the differential feature vector and it is shown that the shaped responses improve recognition performance.