[Insight-users] Oblique section (extract 2D plane) filter for ITK

[Dan Mueller]

Hi all,

I am wanting to use an 'oblique section' type filter within ITK. That is, a filter that extracts a 2D plane from a 3D input image at an artibitary angle to the i-j-k axes.

I would like the user to specify the plane center point (in 3D input space), plane size (in output pixel space), and a direction to "look". The extracted 2D plane should be orthogonal to the given direction. (I know oblique sectioning is typically a "visualisation" task; however I'm planning to use it for a segmentation task, so I feel this filter still fits into ITK...)

I guess my first question is: does such a filter already exist within ITK? I couldn't find one, although ResampleImageFilter has similarities with what I am trying to do...

It's relatively simple to create my desired filter: a centered 3D rigid body itk::Transform is setup to map the output plane to the input 3D image (the transform center is set as the plane center), for each index in the ouput 2D image use the itk::Transform to map the point into the 3D image, interpolate the value at the continuous location.

I have nearly managed to implement such a filter with an itk::CenteredEuler3DTransform. Unfortunately, at present, rather than specifying the "look" direction, the user specifies the 3 Euler angles. Can anyone help me or point me to some references which show how to map this "look" direction to the Euler angles?

For example: I have a 3D image, 100x100x100, 1x1x1 spacing (to keep things simple). I want to extract the plane at point [50,50,50], looking in the direction [1,1,1] from this point. I know (from working it out in my head) the Euler angles corresponding to this direction are [0,0.78539,0.78539] (that is a rotation of 45° around the z-axis, followed by a rotation of 45° around the y-axis). My question is, how can I programmatically map direction to Euler angles?

Any thoughts, suggestions, or references would be greatly appreciated!

Cheers

Dan Mueller
d.mueller[at]qut.edu.au