Hi all,

heat kernel smoothing and diffusion smoothing are supposed to give 
the same solution to an isotropic heat equation on the cortex. the
difference is that heat kernel smoothing is simpler and there is no
need to worry about the convergence. in diffusion smoothing, there
might be a ringing effect (divergence) on smoothed data if "delta t"
is not small enough. to avoid this problem, you may want to implement
backward Euler scheme in solving the diffusion equation, which i
haven't done. to avoid this instability problem, i developed the heat
kernel smoothing.
i feel heat kernel smoothing is far simpler and better approach than
diffusion smoothing.

SUMA pacakage (AFNI add on) uses diffusion smoothing ported from my
original MATLAB code but they are trying to replace with heat kernel
smoothing soon. :)

i am sorry i will fix the link on diffusion smoothing soon.

moo. 

On 6/29/05, Doug Greve <greve@nmr.mgh.harvard.edu> wrote:
  

Hi Moo,

I actually implemented your diffusion smoother but could not quite get it to
work. It might have been related to the delta t parameter. Can you give some
guidance as to how to set it? What's the difference between heat kernel
smoothing and diffusion smoothing? btw, the link to the "Diffusion smoothing
on cortex" software on your web page is broken.

thanks

doug









Moo K. Chung wrote: 
Dear Dr. Park,
    

I guess you are asking about freesurfer related surface
  

smoothing.
    

Although I am not exactly sure how FreeSurfer is implmenting
  

surface
    

smoothing, the general theory of suface-based smoothing and FWHM
  

can
    

be found in two of my previous publications:

Chung, M.K., Worsley, K.J.
  

, Paus, T., Cherif, C., Giedd, J.N., 
    

Rapoport, J.L, Evans, A.C. 2001. A
  

Unified Statistical Approach to
    

Deformation-Based Morphometry, NeuroImage
  

14:595-606.
    

http://www.math.mcgill.ca/chung/deformation/ni_deformation.pdf

Chung,
  

M.K., Robbins,S., Dalton, K.M., Davidson, Alexander, A.L.,
    

R.J., Evans, A.C.
  

2005. Cortical thickness analysis in autism via heat
    

kernel smoothing.
  

NeuroImage
25:1256-1265.
    

http://www.stat.wisc.edu/~mchung/papers/ni_heatkernel.pdf

These
  

softwares implemented in MATLAB can be found in my
webpage
    

http://www.stat.wisc.edu/~mchung/softwares/sotfwares.html
for
  

other type of triangular meshes.
    

Moo.

On 6/27/05, Hae-Jeong Park, PhD
  

<parkhj@yumc.yonsei.ac.kr> wrote:
    

Hi,
    

I would like to know the relationship between number of iteration in
  

surface
    

smoothing and Gaussian kernel size in FWHM.

Would you give me some
  

information on this? Thank you in advance.
    

Hae-Jeong

--
Hae-Jeong Park,
  

PhD
    

Assistant Professor, Department of Diagnostic Radiology, 
Yonsei
  

University, College of Medicine
    

and Division of Nuclear Medicine, Severance
  

Hospital Director, 
    

Laboratory of Molecular Neuroimging
  

Technology
    

http://neuroimage.yonsei.ac.kr
Tel) 82-2-2228-2363, Fax)
  

82-2-393-3035
    

Cellur) 82-10-4220-1003

  

_______________________________________________
Freesurfer
  

mailing
list
    

Freesurfer@nmr.mgh.harvard.edu
https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer


  

-- 
    

Douglas N. Greve, Ph.D.
MGH-NMR Center
greve@nmr.mgh.harvard.edu
Phone
  

Number: 617-724-2358 
    

Fax: 617-726-7422
  

-- 
Douglas N. Greve, Ph.D.
MGH-NMR Center
greve@nmr.mgh.harvard.edu
Phone Number: 617-724-2358 
Fax: 617-726-7422