Hi Mishkin,
basically, yes. The spherical mapping energy function is pretty much a
subset of the spherical registration one (with the folding geometry
correlation term taken out).
Inflation = spring term + distance term
spherical mapping = distance term + topology term (oriented area)
spherical registration = distance term + topology term + correlation term
the other difference is that the spherical mapping uses long range (1-2cm)
distances, while the others are all local distances (nbrs). The
registration also sometimes includes a small area preservation term.
cheers,
Bruce
On Mon, 25 Feb 2008, Mishkin Derakhshan wrote:
Hi,
After reading the wiki and the references on the wiki, specifically
[1] and [2], I'm still a little confused about how the inflation and
registration to a sphere occurs. ie. what energy functions are being
minimized at each step.
I think it is a 3 step process, where
1. Surfaces are inflated by minimizing the energy function Js. This
creates ?h.inflated.
Js = 1/2V (EE ||xi-xn||^2) + lambda-d*Jd (8) in [1]
2. The inflated surfaces are then projected to a sphere by minimizing
the energy function J. This creates ?h.sphere
J = ???
3. The sphere is registered to the average by minimizing the energy
function J. This creates ?h.sphere.reg.
J = Jp + lambda-d*Jd + lambda-a*Ja (5) in [2]
Is there a step I am missing? Are my energy functions correct?
thanks,
mishkin
[1] Cortical Surface-Based Analysis II: Inflation, Flattening, and a
Surface-Based Coordinate System, Fischl, B., Sereno, M.I., Dale, A.M.,
(1999). NeuroImage, 9(2):195-207.
[2] High-resolution inter-subject averaging and a coordinate system
for the cortical surface, Fischl, B., Sereno, M.I., Tootell, R.B.H.,
and Dale, A.M., (1999). Human Brain Mapping, 8:272-284(1999).
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