Fast Automatic Step Size Estimation for Gradient Descent Optimization of Image Registration

Fast automatic image registration is an important prerequisite for image-guided clinical procedures. However, due to the large number of voxels in an image and the complexity of registration algorithms, this process is often very slow. Stochastic gradient descent is a powerful method to iteratively solve the registration problem, but relies for convergence on a proper selection of the optimization step size. This selection is difficult to perform manually, since it depends on the input data, similarity measure and transformation model. The Adaptive Stochastic Gradient Descent (ASGD) method is an automatic approach, but it comes at a high computational cost. In this paper, we propose a new computationally efficient method (fast ASGD) to automatically determine the step size for gradient descent methods, by considering the observed distribution of the voxel displacements between iterations. A relation between the step size and the expectation and variance of the observed distribution is derived. While ASGD has quadratic complexity with respect to the transformation parameters, fast ASGD only has linear complexity. Extensive validation has been performed on different datasets with different modalities, inter/intra subjects, different similarity measures and transformation models. For all experiments, we obtained similar accuracy as ASGD. Moreover, the estimation time of fast ASGD is reduced to a very small value, from 40 s to less than 1 s when the number of parameters is 105, almost 40 times faster. Depending on the registration settings, the total registration time is reduced by a factor of 2.5-7 x for the experiments in this paper.