Dear Feng,
in CAT12 this is not possible. It only provides the Jacobian Determinant, which expresses the local volume changes, which might be sufficient for most morphometric analyses.
Best,
Christian
On Sun, 2 Apr 2017 19:24:01 +0800, FENG LIU <[log in to unmask]> wrote:
>Thanks a lot, Xiaowei
>
>But the CAT12 toolbox just generate the Jacobian determinant images rather
>than Jacobian matrix.
>
>Anyone knows how to obtain the Jacobian matrix?
>
>Best,
>Feng
>
>On Wed, Mar 29, 2017 at 10:15 PM, Xiaowei Song <[log in to unmask]>
>wrote:
>
>> 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
>>
>
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