[Insight-users] Level Set / Fast Marching explanations

[gatts gatsu]

Hi all,

I would like to have some details on the way it works because I don't fully 
understand it.

First, I was wondering what the "speed" of an image refers to. What do you 
call the speed of an image?

On the figure 9.14 of the itksoftwareguide, numbers are written next to the 
level set surface gamma. I guess that those are the distance between gamma 
and the pixel next to it. However, how is it calculated? For instance, if 
you pick the pixel at the bottom with the value 0.4 and the one at the left 
is -0.4. Why is the first one positive and the second one negative ? They 
both seem to be outside the real gamma. I don't figure out how it is 
computed.

I tried to look at this following url to understand better : 
http://math.berkeley.edu/~sethian/2006/Explanations/level_set_explain.html
If you look at the xample with the cone-shaped surface and the circle. The 
starting front is a circle. The fronts at the next steps are the 
intersection between the surface of the cone-shaped surface and the starting 
front plane.  It seems that in the next steps, the front will still be a 
circle. Why is it keeping the same form if the algorithm allows us to get 
random forms ?

I am sorry to ask you those stupid questions but I would really appreciate 
if someone could give some explanations.

Thanks a lot,
Regards,

Philippe

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