Calculate angular displacement of rotated DICOM data

Hey there,

I would need to know the procedure (mathematical calculations) how to calculate the angular displacement (axis x, y and z) of rotated DICOM data. I already know that it is possible to access the image axis directions in RAS coordinate system from the volume, but I would need the direct calculation only out of the DICOM attributes. I also already know that the attribute (0020, 0037) “ImageOrientationPatient” includes the x and y vectors of the image and z can be calculated with the cross product of x and y. Is there also another attribute necessary to calculate the angles?

Thank you in advanced for any help.

ImageOrientationPatient tag everything you need to compute image axis angles relative to patient axes. There are several parametrizations available for computing angles between coordinate systems. Euler angles wikipedia page gives a nice summary and also formulae that you can use to compute rotation angles from axis vectors.

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Perfect. It’s good to know that only the attribute is needed to calculate the angles. Then I’m not too far off with my approach.
Thank you very much for your help.

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