Sunday, September 09, 2007

Wavelet Transform For Deformable Registration

I finished working on the itk::WaveletTransform and now have it working with the itk::OnePlusOneEvolutionaryOptimizer it uses the Daubechies wavelets now and is able to do the wavelet transformation much faster. The following video shows the registration moving along using a transform with 128 parameters and 1200 points. Parts of the border of the ellipse can be seen to change their location as the coefficients of the wavelets are changed. Video also here.

This registration was created by using parameters that were found by using a tracing of the border of the skull using MultiTrace. The tracing was inputted into the IGUI program to get the intensity profile data to fit and find optimal parameters. A picture of the IGUI program with the tracing mesh follows.
This is the data that is used to fit the data in the preceding video. Although one consequence of using this exact data is that the models used to fit the intensity profiles may not work anymore since many of the intensity profiles are not normal to the skull anymore. To remedy this models that change the length of the sampling interval may need to be developed and ones that take into account a smaller neighborhood of data and one with more ambiguities. Another improvement would be to change the optimizer to factor in the information from gradient descent, which the itk::IntensityProfileMetric is still calculating. The optimizer would need to be changed to make sure that the there were localized gradient directions calculated or to treat each wavelet function as a seperate and independent optimization problem. Because of the problems with the current optimization methodology the registration depicted in the video seems to stay still and have a hard time finding the correct exact positioning although if run long enough it would probably converge to the correct answer.

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