Assessing average displacement resulting from a linear transform

Community SlicerDMRI
1

Hi,

Is there a way in Slicer to calculate the mean DTI distortion (e.g. as mean transform needed to align DTI to T2w, like the root mean square deviation).

I found this:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5118068/#R34 ->

From the paper:

"We also calculated the root mean square (RMS) deviation for each subject, which combines the six rigid body parameters into a single estimator of mean displacement [Jenkinson, 1999; Reuter et al., 2015]:

RMS = sqrt{r∗r ∕ 5 + tr[(M−I)T(M − I)] + tTt},

where t is the translation vector, M is (here) the 3×3 rotation matrix, I is the identity matrix, tr[] is the trace operator, and r is the approximate spherical radius of the brain (here, estimated from the data to be 65 mm). The rigid body parameters and RMS values of the navigator logs were also examined."

I have a slicer transform file (.h5) for each of my subjects and wonder if there is a way to calculate the RMS (or a similar measure) from them.

Thanks, Lorenz

2

This formula in Taylor2016 incorrect (since it would give non-zero value for an identity matrix), don’t use this:

image

The formula in Reuter2015 (the paper that Taylor2016 cites) looks correct:

image

You can get the value in Slicer by copy-pasting the following code into the Python console:

transformNode = getNode('MyLinearTransform')
r = 15

import numpy as np
import math
transformMatrix = slicer.util.arrayFromTransformMatrix(transformNode)
t = transformMatrix[0:3,3]
M = transformMatrix[0:3,0:3]
RMS = math.sqrt(r * r / 5.0 * np.trace( (M-np.eye(3)).T @ (M-np.eye(3)) ) + np.dot(t,t))
print(RMS)
3

Thank you very much! This is very helpful!

I tried copy-pasted the code and filled in the name of my transform. I get the following error. How can I fix this?

>>> transformNode = getNode('003_transform')
>>> r = 15
>>> import numpy as np
>>> import math
>>> transformMatrix = slicer.util.arrayFromTransformMatrix(transformNode)
Traceback (most recent call last):
File "<console>", line 1, in <module>
AttributeError: 'module' object has no attribute 'arrayFromTransformMatrix'

Thanks again,
Lorenz

4

This script works in recent Slicer Preview Releases. If you need to use latest Slicer Stable Release (4.10.2) then you can copy the slicer.util.arrayFromTransformMatrix method from here.

5

It used it in the newest nightly release and it worked. Thank you very much again! I appreciate it a lot. - Lorenz

1 Like
6

Hi, one last question regarding the formula as I am writing this up: what does T stand for? Havent found a definition in those papers. Thanks, Lorenz

7

matrix.T it means transpose of matrix.

8

Perfect. Thank you very much!