Homotopy-based computation of defocus blur and affine transform

This paper presents a homotopy-based algorithm for simultaneous recovery of defocus blur and the affine transformation between two images of the same scene. One of the images (and its partial derivatives) is expressed as a function of the second image, partial derivatives of the two images, blur difference, 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. The proposed algorithm is tested using synthetic and real images. The results confirm that dense and accurate estimation can be obtained.