Ordinary Differential Equation and Complex Matrix Exponential for Multi-resolution Image Registration
This work addresses image registration for computer vision applications, offering incremental improvements over existing methods.
The paper tackles multi-resolution image registration by proposing the use of complex matrix exponential (CME) instead of real matrix exponential for computing transformation matrices, and an ordinary differential equation (ODE) as an optimizable dynamical system to adapt transformations to a Gaussian pyramid, resulting in significantly better registration on four benchmark datasets.
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.