Registration of joint geometric and radiometric image deformations in the presence of noise

We consider the problem of object registration where the observed template simultaneously undergoes an affine transformation of coordinates and a non-linear mapping of the intensities. More generally, the problem is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object. We show that, in the absence of noise, the original high dimensional non-convex search problem that needs to be solved in order to register the observation to the template is replaced by an equivalent problem, expressed in terms of a sequence of two linear systems of equations. A solution to this sequence provides an exact solution to the registration problem. It is further shown that in the presence of noise, the original stochastic registration problem can be mapped, almost surely, to a new deterministic problem in the form of a classic deconvolution problem. Solution of the deconvolution problem reduces the solution of the original estimation problem to the form derived for the noise-free case.