  Autograd-based software packages have recently renewed interest in image
registration using homography and other geometric models by gradient descent
and optimization, e.g., AirLab and DRMIME. In this work, we emphasize on using
complex matrix exponential (CME) over real matrix exponential to compute
transformation matrices. CME is theoretically more suitable and practically
provides faster convergence as our experiments show. Further, we demonstrate
that the use of an ordinary differential equation (ODE) as an optimizable
dynamical system can adapt the transformation matrix more accurately to the
multi-resolution Gaussian pyramid for image registration. Our experiments
include four publicly available benchmark datasets, two of them 2D and the
other two being 3D. Experiments demonstrate that our proposed method yields
significantly better registration compared to a number of off-the-shelf,
popular, state-of-the-art image registration toolboxes.
