Clarification on GMM sampling

[naga-karthik]

Hello! Thank you for the amazing work! Really interesting approach using domain randomization for contrast/resolution agnostic brain segmentation !

I had a question about the GMM generative model. In the paper, it is mentioned in section 3.1.2 that an initial synthetic scan G is generated by sampling the GMM conditioned on the (deformed) label map. Now, in my (limited) understanding of GMMs, I know that they follow an expectation-maximization (EM) process to estimate the parameters of the model. I am unable to find any info about the EM algorithm (in the paper and code). Could you please provide some insights on how this GMM was trained? In fact, was it trained? I think I am missing something here.

Thank you!

[BBillot]

Hi,

a GMM is not necessarily trained, it all depends if you already know how to assign the classes. The EM algorithm you mention is a possible way to create classes of Gaussians, but here the classes are already defined by the values in the label map, and the parameters (mean, variance) of these Gaussians are randomised

So the image G is formed exactly as exposed in equations 11 to 13:

1. Assuming our training label map has K classes, we first create K different Gaussians with random means and variance
2. for each voxel of G, we look at the corresponding label value k, and we sample an intensity from the Gaussian number k.

Note that the parameters of the K Gaussians change for each training example.

Hope this helps,
Benjamin