Jidan,

Here are additions to Donna's comments.

On Dec 28, 2009, at 8:22 AM, Donna Dierker wrote:
> That is way too hard of a question on the Monday morning following a
> long weekend. ;-)
Agreed - but your questions raise important issues.  See further inline comments
> 
> On 12/28/2009 02:55 AM, z丹丹 wrote:
>> Hi Donna,
>> 
>> I want to ask a question related to the spherical registration. When
>> we have the original surface, we need to make it into a sphere to
>> register it to a template sphere. After this step, we will get the
>> deformed sphere. Do you have any way to make this deformed sphere go
>> back into the original surface space?

> 
>> I mean, after this, I can have one original surface, one deformed
>> original surface which is from the deformed shpere, when I superimpose
>> them together, we can know which part deformed a lot.

(i) The distortions associated with deforming a source (individual) sphere to a 
target (template, or atlas) sphere can be visualized using a deformation field, 
as Donna notes. Alternatively, they can be viewed using an areal distortion 
map, computed using Surface: Measurements: Generate Distortion.  This will 
compute the areal distortion (as log 2 values) between the surface in the main 
window and whatever currently loaded surface you choose from the pulldown menu.

If you are using Core 6 landmarks and registering human individuals to the 
PALS-B12 atlas, the sphere-to-sphere distortions are generally pretty modest.  

ii) The issue of evaluating the 'distortions' of the original surface are 
conceptually not so straightforward.  (I assume by 'original' you mean the 3D 
'fiducial' or 'anatomical' surface configuration.)

Caret by default creates a 'deformed' fiducial surface as part of the 
registration process, but in this case 'deformed' is really an unfortunate 
misnomer.  We now routinely describe it as a 'resampled' fiducial surface.  It 
has the same  fundamental shape as the original but is represented by a 
different surface mesh (tessellation) - namely, the 'standard mesh' of the 
target atlas (73,730 nodes for both the PALS-B12 human atlas and the macaque 
F99 atlas).  

Another source of distortions is the mapping between the fiducial surface and 
the spherical surface.  Even after multi-resolution morphing is done, the areal 
distortions between the sphere and the fiducial surface are generally large and 
irregular.  This is because the cortex contains a lot of intrinsic (gaussian) 
curvature (dimples and bulges) rather than being simply folded like a crumpled 
newspaper.  And given the high degree of variability in folding patterns 
(especially humans), the pattern of areal distortions differs markedly across 
individuals.  

I hope this helps, at least to some degree.  If you have additional questions, 
please clarify more specifically what it is you are trying to learn from this 
analysis.  

These issues are very much on my current front burner, as I am in the midst of 
analyzing and writing a paper that introduces a new version of our landmark- 
and surface-based registration algorithm.  

David VE


>> 
>> Thanks a lot.
>> 
>> Jidan
>> 
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