We explore various optimization problems which appear in computer vision and image processing. By exploiting the geometric structure of the underlying search spaces, we develop more efficient and robust ways to find optimal solutions. We present the Nelder-Mead algorithms on Lie groups and describe its application to medical image registration.
A widely used approach to image registration involves finding the transformation that maximizes the mutual information between two images, with the transformation restricted to be either rigid-body (i.e., belonging to SE(3)) or volume-preserving...