Hi Mike,
yes, the jacobian is the ratio of the areas, and distinct from the metric distortion we use in the spherical morph. In general there are only two types of distortion - areal and angular. Minimizing one usually pushes more distortion into the other (e.g.conformal maps minimize angular distortion). The distance minimizes some balance between them, which is one of the reasons we like it
cheers, Bruce
On Fri, 12 Dec 2008, Michael Harms wrote:
Hello, How is the distortion calculated by 'mris_jacobian' defined?
Based on this post http://www.mail-archive.com/freesurfer@nmr.mgh.harvard.edu/msg05419.html
I'm guessing that the output of mris_jacobian lh.white lh.sphere.reg lh.jacobian_white
is identical to the "metric distortion" measure used in Wisco et al. 2007; i.e., area of a triangle on lh.sphere.reg divided by area of a triangle on lh.white, normalized for the total surface area of each surface (which is done automatically by 'mris_jacobian' unless you specify the -noscale flag).
Is this correct?
If so, the Wisco (mris_jacobian) definition of "metric distortion" seems quite different from what is used in the energy functionals that control the inflation and registration processes, where the term for metric distortion is defined using the distance between corresponding vertices in the two surfaces.
Is there some relationship between these two different definitions of distortion?
thanks, Mike H.