[Elastix] Transitivity calculation using elastix

Kierkels, RGJ (rt) r.g.j.kierkels at umcg.nl
Thu Aug 4 21:44:41 CEST 2016

Dear Elastix user,

For B-spline deformable registration evaluation I would like to calculate the inverse consistency and transitivity error. The inverse consistency is straightforward following the instructions in the manual calculating the inverse of the transformation (chapter.6.1.6) . The transitivity error requires transformations T between minimal 3 image sets: ImgA, ImgB and ImgC, having T1, T2 and T3. From each Tx the DVF was calculated using transformix. The transitivity error is then defined as the sum of all DVF. When there is no error the sum should be zero. It is however not correct to sum all DVF directly since their origin is on different images.

The registration problem is as follows (with ImgX' = ImgX deformed):

1.      ImgA(moving) - ImgB(fixed) --> DVF_B and ImgA' (on grid of ImgB)

2.      ImgA'(moving) - ImgC(fixed) --> DVF_C and ImgA'' (on grid of ImgC)

3.      ImgA''(moving) - ImgA(fixed) --> DVF_A (now ImgA''' should equal ImgA)

I would like to sum all DVFs in the grid of ImgB. Therefore, DVF_A (and DVF_C) should be shifted towards the ImgB grid (e.g. using the invese of DVF_B which should then be interpolated to ImgB?).

Is it possible with elastix/transformix to interpolate the DVF to the grid of another image as illustrated above? Perhaps using an InitialTransform? What approach should I follow? Any help is appreciated.

Best regards,

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