Generation of reference surface

[Ruslan Kosarev]

Dear statismo's developers and users.

 

I would like to discuss one point which concerns of generation of reference surface. For example, I'd like to discuss two ways to build this surface

 

1) A suitable reference surface R0 is selected from the dataset and registered to all other label maps with composition of spatial and non-rigid (transformation with GP model) transformations. As a result, we get a set of transformed surfaces S1,S2,....,Sn. The mean over S1,S2,....,Sn is computed and we get new reference surface R1. Then this surface R1 is registered to all the training set and a new mean is computed as new reference surface. This method is repeated until there is no significant change in the generated mean.

This method is described in Clogenson et al., "A statistical shape model of the human second cervical vertebra". How to choose the surface R0? What does it mean suitable surface?

 

2) The second method is as follows. So, we have a set of surfaces S1,S2,....,Sn. At first we can align them using, for example, center of mass. For each aligned surface we compute signed distance map (using itkSignedMaurerDistanceMapImageFilter) D1, D2,..., Dn. The mean of these distance maps P0 is used as potential to registrate in it surfaces S1,S2,....,Sn with only spatial transform. Then, we compute new potential P1 as mean of distance maps of transformed surfaces and run registration surfaces with P1. This iteration process is repeated several times. As a result we get some level set image (potential) and aligned surfaces. As an example, you may see our screenshort. Then, the surface corresponding to level 0 is used as reference surface R0 and we may continue with the method 1). .

How can you comment these methods? Which one is better?

 

Best regards, 

Ruslan N. Kosarev

[Marcel Luethi]

Dear Ruslan,

If I understand the two methods correctly, I would say that the main difference between the two methods is in the correspondence assumption. In the first method, you assume that there is a perfect 1 to 1 correspondence between your reference and the target shapes (the target shapes may still have artifacts/holes, but a hypothetical clean version of it would be in perfect correspondence). If this assumption is correct in your application, then I would say that the first option is a practical and simple way of finding a good reference.

The second method does not make this assumption. However, it is less clear to me what exactly happens in case there are holes or artifacts in the data. Also, what does the mean of the distance map exactly represent?

I am not an expert in reference generation, and maybe somebody else on this list has more insights. 

Another interesting method for reference generation was recently published by Mutsvangwa et al. If I understand it correctly, it would be somehow in between the two methods you propose.

Mutsvangwa, Tinashe, et al. "An automated statistical shape model developmental pipeline: application to the human scapula and humerus." IEEE Transactions on Biomedical Engineering 62.4 (2015): 1098-1107.

Best regards,

Marcel

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[Ruslan Kosarev]

Dear Marcel, 

I apologize for the late answer.  

As for the first method, of course this is a simple way. In my opinion, this method has two disadvantages. The first disadvantage, it is not clear how to choose suitable surface to use it as reference. The second disadvantage, the resulting shape model can be biased to the particular surface. 

As for the second method, of course, we cannot say that there will be no holes or artifacts in the built surface. Of course, if artifacts will be present, we will not be able to use this surface as the reference. 

Also, what does the mean of the distance map exactly represent? The usage of distance maps can be interpreted as follows, thus we define a surface which is an “average shape” in a sense. 

Thanks for your answer and the link to the article.

Best regards

Ruslan N. Kosarev

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