[ITK-users] 3D/2D registration with itkRayCastInterpolateImageFunction

[Siavash Khallaghi]

Hi Charles,

Your results /suggest/ that the optimizer does not converge to the solution.
Based on your results, I cannot conclusively say why this happens. This is
why I asked you to plot the metric.

The identity test and metric test basically tell you this: "If you start the
registration from these initial parameters, you will converge to some final
parameters." The final parameters being /Best (x, y)/ in your notation.
However, this experiment does not tell you /why/ you converge to these
parameters.

To make it more clear, I will make you an analogy. Think of the registration
as a sledge that takes you from one point on the mountain (A) to the lowest
point in the valley (B). The goal is to arrive at the lowest valley. During
your trip from A to B, you only see glimpses of your position through your
goggles (observer values). After some iterations you arrive at B (final
parameters). If you did not have a map of what the curvature of the mountain
looks like, you have no idea why you ended up at B. You also have no idea if
you are indeed at the lowest valley (global minima). This is your problem.

What I would like to ask you to do, is to plot the metric for a range of
values around the true solution. For example, if the solution is at
x-translation = 0.0 mm an you start at x = 6.0 mm, you should plot the
metric between [-10.0, +10.0] mm (+4 mm for padding). Do this for other
transformation parameters as well. Keep the projection constant during this
experiment.

For example, if your metric looks like the attached image, we can safely say
that the registration gets stuck at a local minima around 8.0 mm. If that is
the case, you have to: 1) make your metric more convex; 
and/or 2) start closer to the solution. There are solutions to both of these
problems.

<http://itk-users.7.n7.nabble.com/file/n36026/metric_pm10.png> 

Siavash





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