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

Yuchuan Qiao, Baldur van Lew, Boudewijn P.F Lelieveldt and Marius Staring

Abstract

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. Among many classical optimization strategies, stochastic gradient descent is a powerful method to iteratively solve the registration problem. This procedure relies on a proper selection of the optimization step size, which is important for the optimization procedure to converge. This step size 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 has been proposed to automatically choose the step size, but it comes at a high computational cost, dependent on the number of transformation parameters.

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, the fast ASGD method only has linear complexity. Extensive validation has been performed on different datasets with different modalities, inter/intra subjects, different similarity measures and transformation models. To perform a large scale experiment on 3D MR brain data, we have developed efficient and reusable tools to exploit an international high performance computing facility. For all experiments, we obtained similar accuracy as ASGD. Moreover, the estimation time of the fast ASGD method is reduced to a very small value, from 40 seconds to less than 1 second 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 2.5-7x for the experiments in this paper.

Source code

The source code of the methods described in this paper can be found in the image registration toolkit elastix, available at https://github.com/SuperElastix/elastix.

The exact parameter settings used in this paper can be found at the parameter file database of elastix at entry Par0035.

BibTeX entry