Mesh Topological Optimization for Improving Piecewise-Linear Image Registration

This paper presents a mutual-information based optimization algorithm for improving piecewise-linear (PWL) image registration. PWL-registration techniques, which are well-suited for registering images of the same scene with relative local distortions, divide the images in conjugate triangular patches that are individually mapped through affine transformations. For this process to be accurate, each pair of corresponding image triangles must be the projections of a planar surface in space; otherwise, the registration incurs in errors that appear in the resultant registered image as local distortions (distorted shapes, broken lines, etc.). Given an initial triangular mesh onto the images, we propose an optimization algorithm that, by swapping edges, modifies the mesh topology looking for an improvement in the registration. For detecting the edges to be swapped we employ a cost function based on the mutual information (MI), a metric for registration consistency more robust to image radiometric differences than other well-known metrics such as normalized cross correlation (NCC). The proposed method has been successfully tested with different sets of test images, both synthetic and real, acquired from different angles and lighting conditions.