Optimization

The main purpose of incorporating the itk::WaveletTransform into the segmentation framework is to create deformable registration where the points can fit the outside of the brain with more detail. Some issues with the addition of the itk::WaveletTransform were that it had difficulty being optimized using the itk::OnePlusOneEvolutionaryOptimizer so a few parameters were looked at to make sure that it would work with an optimizer like gradient descent or downhill simplex optimizer. The following graphs represent the metric value of the segmentation as one wavelet parameter is being changed. The graphs also show a diagram of the brain with a region circled in green representing the area that the wavelet parameter is affecting.

For the most part the coefficients have an overall minimum point in the metric value but still has places where the coefficients can get stuck. One way to incorporate gradient descent as the optimizer would be to take the gradient information at each intensity profile and then use that information to find the next set of wavelet coefficients.