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

St. Klein, M. Staring, J.P.W. Pluim

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationProgress in Biomedical Optics and Imaging - Proceedings of SPIE
EditorsJ.M. Fitzpatrick, J.M. Reinhardt
Number of pages12
Publication statusPublished - 2005
Externally publishedYes
Event2005 Medical Imaging : Image Processing - San Diego, United States
Duration: 13 Feb 200517 Feb 2005


Conference2005 Medical Imaging : Image Processing
Country/TerritoryUnited States
CitySan Diego


  • Computation time
  • Mutual information
  • Nonrigid registration
  • Optimisation
  • Stochastic gradient descent


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