A homotopy-based approach for computing defocus blur and affine transform simultaneously

This paper presents a homotopy-based algorithm for a simultaneous recovery of defocus blur and the affine parameters of apparent shifts between planar patches of two pictures. These parameters are recovered from two images of the same scene acquired by a camera evolving in time and/or space and for which the intrinsic parameters are known. Using limited Taylor's expansion one of the images (and its partial derivatives) is expressed as a function of the partial derivatives of the two images, the blur difference, the affine parameters and a continuous parameter derived from homotopy methods. All of these unknowns can thus be directly computed by resolving a system of equations at a single scale. The proposed algorithm is tested using synthetic and real images. The results confirm that dense and accurate estimation of the previously mentioned parameters can be obtained.