Seeing through the blur

This paper addresses the problem of image alignment using direct intensity-based methods for affine and homography transformations. Direct methods often employ scale-space smoothing (Gaussian blur) of the images to avoid local minima. Although, it is known that the isotropic blur used is not optimal for some motion models, the correct blur kernels have not been rigorously derived for motion models beyond translations. In this work, we derive blur kernels that result from smoothing the alignment objective function for some common motion models such as affine and homography. We show the derived kernels remove poor local minima and reach lower energy solutions in practice.