Hi, Feng,

From the text you attached, it already answered your question as:

According to the polar decomposition
theorem [21], a non-singular Jacobian matrix can be decomposed into a rotation matrix (R)
and a symmetric positive definite matrix (U or V), such that J = RU = VR.

In practice, if you decompose your J by using QR, the U or V as referred above should represent only shape change, i.e., discarding Q since it encodes orientation.

Please fix me if I am wrong.

Best,

Xiaowei Song

On Wed, Mar 29, 2017 at 3:24 AM, FENG LIU <[log in to unmask]> wrote:

Dear CAT and SPM experts,

I have a question about the TBM analysis.

Now I have obtained the Jacobian determinant images by using the CAT12 toolbox. Could I directly use these images to perform a TBM analysis?

In the last paragraph of page 10 (attached), it wrote "Because a Jacobian matrix encodes both local shape (zooms and shears) and orientation, it is necessary to remove the latter before making inferences." So, how should I do in a right way?

Any help would be greatly appreciate.

Best,
Feng

Xiaowei Song