[Insight-users] Level Set / Fast Marching explanations

[gatts gatsu]

Hi Chris,

First, thanks a lot for answering this quickly.
I have some other questions about what you told me.

>http://www.iua.upf.es/~vcaselles/papers_v/GAC_article.pdf
>http://www.math.ucla.edu/~lvese/PAPERS/IEEEIP2001.pdf

Thank you for those links, I will read them carefully.

>>First, I was wondering what the "speed" of an image refers to. What do you 
>>call the speed of an image?
>
>The velocity at which the wave front (surface or contour) is moving at each 
>grid location.

Let's say that you are using a series of DICOM (representing for instance a 
vessel).
If you take as the level set the contour of this vessel in the first 
picture. To calculate this velocity : is it totally independant of the next 
"slides" (only using the result of the gradient?) ?


>>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.
>
>
>It is a signed distance transform. Negative values are inside, positive 
>values are outside (or vice versa).
>
>Each pixel's intensity value represents its distance from the surface (the 
>zero level set).
>
>The surface is the zero level set. i.e. where the image you refer to is 
>equal to all zeros.
>
>Adding one to the entire image ( a speed image with all values equal to 
>one) would change all zeros to one, and all -l's to zero.
>So where there were -1's, there would now be a surface.
>
Thank you for this explanation I understand it far better now (the only 
question about it is the one that I previously asked about the velocity 
calculation)


>>
>>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 ?
>
>Not random forms, forms driven by the image and internal smoothness forces.
>

What I meant is for instance : the circle can change form transforming into 
half a circle and the other half some kind of rectangle (so that it's still 
related with the previous form). However, how will it be detected with a 
cone-shaped surface?


Concerning the Fast Marching Segmentation (9.3.1 in itksoftwareguide)
"The output of the FastMarchingImageFilter
is a time-crossing map that indicates, for each pixel, how much time it 
would take for
the front to arrive at the pixel location."
I understand for the stopping value since it's a time crossing map. But once 
again, how does it calculate the time of propagation between the front to 
the top left of the image for instance ?

"In the current example we decided to use a Sigmoid function since
it offers a good deal of control parameters that can be customized to shape 
a nice speed image.
The mapping should be done in such a way that the propagation speed of the 
front will be very
low close to high image gradients while it will move rather fast in low 
gradient areas."
We use the sigmoid on the result of the gradient filter. We put the output 
between 0 and 1.
It is said to give a nice speed image. Is the value "1" high enough to 
provide a high speed image ?

Thanks again for taking time to answer to this post.

Regards,

Philippe

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