We address the problem of object registration when the observation differs from the object both geometrically and radiometrically. The geometric deformations being considered are affine. The radiometric deformations are due to the a-priori lack of knowledge regarding the locations and intensities of the light sources. Hence, to solve the registration problem, a joint solution for the radiometric and the geometric deformations must be offered. A direct approach for solving the joint registration problem as an optimization problem leads to a high-dimensional non-convex search problem. In this paper, we treat the images as vector valued measurements, such that each element of the vector provides the intensity at a specific spectral (color) band. By applying a set of operators, derived in the paper, to the vector valued data the original high-dimensional search problem is replaced by an equivalent problem, expressed in terms of two systems of linear equations. Their solution provides an exact solution to the joint problem.