In this paper, we focus on the sub-pixel geometric registration of images with arbitrarily-shaped local intensity variations, particularly due to shadows. Intensity variations tend to degrade the performance of geometric registration, thereby degrading subsequent processing. To handle intensity variations, we propose a model with illumination correction that can handle arbitrarily-shaped regions of local intensity variations. The approach is set in an iterative coarse-to-fine framework with steps to estimate the geometric registration with illumination correction and steps to refine the arbitrarily-shaped local intensity regions. The results show that this model outperforms linear scalar model by a factor of 6.8 in sub-pixel registration accuracy.