Does non-rigid registration changes the real Geometry?

Hello all,

I have 2 sets of micro CT images (3D):

  1. with the 12-micrometer resolution taken in Axial mode
  2. with the 120-micrometer resolution taken in Helical mode

We can consider the high-res image displays the reality of the scanned specimen. I try to register these two sets of images. When I use the rigid registration I can see an offset created in one direction (fig), but when I use the non-rigid registration it matches better.

My question is:
Does the non-rigid image registration change objects’ geometry (not real anymore!)?

The following image is low-resolution and the red lines are rigid registered high-resolution (binarized)

Thank you

Hello @Faramarz-bagherzadeh,

The answer is “it depends”. You need to incorporate domain knowledge to justify a specific transformation model. Generally speaking, you do not want to over-parameterize which will result in over-fitting. Please take a look at this jupyter notebook for a detailed discussion of registration errors. The most relevant section is titled FRE-TRE, and Occam’s razor.

Specifically to your problem:
Do you know if the sample underwent deformation between the two scans? If yes, then using a non-rigid transformtaion makes sense. Even a static object that contains water may deform if there is water evaporation. If this is the same object in both scans, no deformations, use a rigid transformation.

One last recommendation, use the high resolution (smaller voxel spacing) image as the fixed image in registration.

This is interesting. Can you explain what is the advantage?

In general, I would chose fixed/moving based on what direction I need the use the transform the most. It this does not matter (e.g., because I use a rigid transform) then I would use the sparser (lower-resolution) image as fixed because then I don’t need to interpolate between sparse samples. In the extreme of single-slice to volume registration we could not even find enough samples if the dense image was used as fixed image and the sparse (single-slice) image was used as moving image.