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"Comparison of gradient approximation techniques for optimisation of mutual information in nonrigid registration"

Stefan Klein, Marius Staring and Josien P.W. Pluim

Abstract

Nonrigid registration of medical images by maximisation of their mutual information, in combination with a deformation field parameterised by cubic B-splines, has been shown to be robust and accurate in many applications. However, the high computation time is a big disadvantage. This work focusses on the optimisation procedure. Many implementations follow a gradient-descent like approach. The time needed for computing the derivative of the mutual information with respect to the B-spline parameters is the bottleneck in this process. We investigate the influence of several gradient approximation techniques on the number of iterations needed and the computation time per iteration. Three methods are studied: a simple finite difference strategy, the so-called simultaneous perturbation method, and a more analytic computation of the gradient based on a continuous, and differentiable representation of the joint histogram. In addition, the effect of decreasing the number of image samples, used for computing the gradient in each iteration, is investigated. Two types of experiments are performed. Firstly, the registration of an image to itself, after application of a known, randomly generated deformation, is considered. Secondly, experiments are performed with 3D ultrasound brain scans, and 3D CT follow-up scans of the chest. The experiments show that the method using an analytic gradient computation outperforms the other two. Furthermore, the computation time per iteration can be extremely decreased, without affecting the rate of convergence and final accuracy, by using very few samples of the image (randomly chosen every iteration) to compute the derivative. With this approach, large data sets (2563) can be registered within 5 minutes on a moderate PC.

 

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Copyright © 2005 by the authors. Published version © 2005 by SPIE. Personal use of this material is permitted. However, permission to reprint or republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works, must be obtained from the copyright holder.

 

BibTeX entry

@inproceedings{Klein:2005,
author = "{Stefan Klein and Marius Staring and Josien P.W. Pluim}",
title = "{Comparison of gradient approximation techniques for optimisation of mutual information in nonrigid registration}",
booktitle = "{SPIE Medical Imaging: Image Processing}",
editor = "{J.M. Fitzpatrick and J.M. Reinhardt}",
address = "{San Diego, CA, USA}",
series = "{Proceedings of SPIE}",
volume = "{5747}",
pages = "{192 - 203}",
month = "{February}",
year = "{2005}",
}

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