Registration of Geometric Deformations in the Presence of Varying Illumination

We address the problem of object registration when the observation differs from the object both geometrically and radio-metrically. 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.