I am interested in image processing (in 3D). I often see two different ways of measuring local expansion or contraction of a deformation: the Jacobian determinant or the divergence (but usually the Jacobian determinant), e.g., [1,2]. I have a good intuitive sense of the divergence operator, but although I know the maths behind the Jacobian and its determinant, I don't have a good intuitive understanding of it.
What are the differences between divergence and Jacobian determinant with respect to measuring the local expansion? Why is the Jacobian determinant (seemingly) the more popular method?
[1] Williams, Christopher L., et al. "A mass-conserving 4D XCAT phantom for dose calculation and accumulation." Medical physics 40.7 (2013): 071728.
[2] Gigengack, Fabian, et al. "Motion correction in dual gated cardiac PET using mass-preserving image registration." Medical Imaging, IEEE Transactions on 31.3 (2012): 698-712.