Shape modelling with Gaussian processes and kernels

[Maia R.]

Hello,

I am working with the tutorials and it is unclear form me how to use multiscale kernels: how to adjust parameters and combination, how can I estimate visually the correctness/quality of a kernel for my model ...

In fact, what would be the best steps to perform a good medelling with analytic kernels.

Thank you very much

Maia

[Marcel Luethi]

Dear Maia

I usually choose the kernels just based on my own prior knowledge of the anatomy. The scale factor that you multiply a kernel with determines the variance of the amplitude of the deformation. Hence a value of 100 means it has a std deviation of 10 mm. So you would consider deformations of 10 mm length as a likeli deformation. A similar argument goes for the standard deviation of the Gaussian kernel. It essentially determines the size of the region (in mm) for which you expect that deformations are still correlated. So if you choose 100 mm as a kernel with, you expect that points which are 100 mm apart, would still be correlated.

Thinking about the deformation you expect in this way gives you a first indication on how to choose the parameters. The second, and maybe more important step is to sample from the model you build and visualily assess the deformations. Would it be likely that the target you try to explain is generated by the model? If not (e.g. because all your samples show only small deformations but your target is much larger than the reference) you need to refine. Otherwise you can proceed to the fitting process and see if it gives adequate results.

Best regards

Marcel

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