Clarify direction of JacobianDet and Deformation fields?

[andrewsilberfeld]

Hello,

I'm seeking confirmation for the exact direction of the interpretation for the JacobianDeterminant and the Deformation field images as implemented in Elastix. My understanding from reading the Elastix and ITK documentation has been that since the jacDet field and Deformation fields are defined in the fixed image space, they are thus interpreted to represent the change in volume or position that will occur for that fixed-image-domain voxel when mapped to the moving image. However, as I haven't been formally educated in the matrix math concepts underlying this, I want to formally ask here, instead of extrapolating based on my understanding. Is my interpretation correct? For context, the Elx manual just says the jacobian determinant indicates "local compression" or "local expansion" while the ITK documentation uses the terms "input" and "output", which I believe respectively mean "fixed image" and "moving image" (based on how the transform is defined: a point in fixed is the input and mapped to the moving as output).

Is this all correct?

2 examples:

1. Does a Jacobian determinant value of 0.8 in the fixed image domain means that the same point in the moving image is 20% smaller than in the fixed image (or just 8/10ths of the volume in the fixed image...)? ... "local compression"?
2. Does a deformation field value of -4.9 for the Y component indicate that the point in the fixed image will be translated negatively by 4.9 pixels in the Y direction when mapping to the moving image?