Mean vs. reference

Maia R.

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Jan 19, 2021, 11:29:04 AM1/19/21

to scalismo

Hi,

I'm still a bit confused about the difference between the mean mesh and the reference mesh in the API. Are they the same ? When to use each of them if they differ ?

Thank you in advance for your explanation.

Best regards

Behzad Vafaeian

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Jan 19, 2021, 12:05:15 PM1/19/21

to Maia R., scalismo

Hi,

A reference mesh is a (discrete) domain on which the deformation fields sampled by a Gaussian process is applied. The mean mesh is the reference mesh deformed by the mean deformation field.

A sampled mesh or shape = the reference mesh deformed by a sampled deformation field.

The mean mesh or shape = the reference mesh deformed by the mean deformation field.

Note that the deformation field is a random filed (like a random vector) so it has a mean.

This is as per my knowledge. If contains error, please correct me.

Best,

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V R

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Jan 20, 2021, 9:36:44 AM1/20/21

to Behzad Vafaeian, scalismo

Hi,

Thanks.

In fact, they are well explained in the tutorials, I don't know why I asked this question, sorry folks. A moment of doubt.

Best

Maia

Marcel Luethi

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Jan 20, 2021, 10:16:09 AM1/20/21

to Maia R., scalismo

Hi Maia,

As Behzad explained, the reference mesh can be seen as the domain on which the GP is defined.

The GP itself models deformation fields. One particular deformation that you can extract from the GP is the mean deformation field. The mean mesh (or mean shape) is the reference mesh warped with this mean deformation field. This is the mesh you obtain when calling .mean on a StatisticalMeshModel. If this mean deformation of the GP happens to be the zero deformation, the mean mesh and the reference mesh coincide. If you have a non-zero mean, the two are different.

Does this clear up your confusion?

Best regards,

Marcel

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V R

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Jan 20, 2021, 4:39:29 PM1/20/21

to Marcel Luethi, scalismo

Thank you very much for the clarification.

Best regards,

Maia

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