Random Initial parameter selection for registration about simpleitk-notebooks

[zivy]

Hello Subhajit,

Registration is cast as an optimization task, with some subtleties that differ from standard optimization:

a. Most of the time the function will not be convex, as you pointed out.
b. Ideally the global optimum of the optimized function will coincide with the correct transformation parameters.
c. For many similarity measures (optimized functions) 'b' is not satisfied and the correct transformation parameters correspond to a local optimum. This makes the goal of registration different from the goal of standard optimization.

Given the above observations, registration robustness and accuracy are highly dependent on the initialization. Even more than you pointed to, as your initial parameter values need to be close to the correct local optimum.

Two common strategies for initialization:

1. Center or guesstimate based on prior knowledge a reasonable alignment for both volumes (t = CenteredTransformInitializer) get the parameter values for this transformation (t.GetParameters), perturbe them within some known bounds (numpy.random + t.SetParameters) and run the registration multiple times. You will need to analyze the results to select the solution.

2. Use the Exhaustive optimizer in a bounded region in parameter space to generate a sampling of the similarity measure in the region of interest and then start the registration from the k>=1 best locations. If you are familiar with evolutionary algorithm optimization terminology then the first step is similar to exploration and the second to exploitation.

Hopefully this answered your question.

As you also mentioned the different components of registration and their settings, this falls under the category of meta-optimization and is a different story. This paper may be of interest to you.

For further information please consult the registration literature.
regards
Ziv

[subhajitchatu]

Thanks @zivy for your valuable feedbacks. Is there any function in SimpleITK for evolutionary algorithm optimization? Because ITK has support for this one plus one evolutionary multimodal algorithm with Mutual information I guess. How can I use this in python platform?

Thanks

[zivy]

The 1+1 optimizer is also part of the registration framework in SimpleITK. The ImageRegistrationMethod class has a SetOptimizerAsOnePlusOneEvolutionary method. The meaning of the parameter values are described in the ITK documentation.