Subpixel registration directly from the phase difference

Abstract

This paper proposes a new approach to subpixel registration,under local/global shifts or rotation, using the phase-differencematrix. We establish the exact relationship between the continuousand the discrete phase difference of two shifted images and showthat their discrete phase difference is a 2-dimensional sawtoothsignal. As a result, the exact shifts or rotations can bedetermined to subpixel or subangle accuracy by counting thenumber of cycles of the phase-difference matrix along thefrequency axes. The subpixel portion is represented by a fractionof a cycle corresponding to the noninteger part of the shift orrotation. The rotation angle is estimated by applying our methodusing a polar coordinate system. The problem is formulated as anoverdetermined system of equations and is solved by imposing aregularity constraint. The tradeoff for imposing the constraintis determined by exploiting the rank constraint leading to aclosed-form expression for the optimal regularization parameter.