[Insight-users] Searching for Optimal Path in 3D vectorfieldImage?

[Zachary Pincus]

There's a ton of literature on fiber tracing in vector images, with 
methods for dealing with this exact problem. (I don't know if you're 
looking at diffusion tensor images, but a lot of the literature is in 
regards to tracing fibers in such images, so that might be a place to 
start.)

One idea would be to borrow some tricks from the robot people and build 
a probabilistic model of what a fiber does. Start at a point, then 
estimate the strength and direction of the fiber based on the principal 
components at that point. Then take a step defined by this strength and 
direction, and *UPDATE* the estimate based on the new principal 
components at that location. (You could also maintain estimates of 
local curvature to help better follow bendy fibers.)

After a few updates, you get a good guess as to where the fiber is 
going. If you hit a region of crossing fibers, then the "update" adds 
only noise to your previous estimate, but you *still* have that 
estimate to carry you through.

The simplest way to implement something like this is with the tried and 
true Kalman filter (for which there is a LOT if literature), or you 
could be more fancy and use something like a Bayes/Particle filter to 
model state.

Zach Pincus

Department of Biochemistry and Program in Biomedical Informatics
Stanford University School of Medicine


On Jul 1, 2004, at 10:22 AM, Patrick (Peng) Cheng wrote:

> Hi,
> The problem is: sometimes you can't just follow the principal vector 
> direction.
> Coz sometimes fiber cross each other, so the singal overload on each 
> other, and the major vector direction
> may not be the direction you want to go if you want to find out the 
> connectivity between two region. (we already know there is certain 
> connection)
> How do I find the optimal path then? coz if I follow the principal 
> direction, I found I can't reach the ending region at last.
> thanks a lot
>
> ---------------------------
> Peng (Patrick) Cheng
> Biomedical Engineering
> University of Iowa
> Tel:(319) 400-7442
> Email: peng-cheng at uiowa.edu
>
> ===========2004-07-01 10:07:11 You wrote in your letter:==============
>
>> You could follow the principal direction of the tensor with the 
>> largest
>> corresponding eigenvalue.  In areas with very low anisotropy this 
>> would not
>> make sense so, in those areas the fiber should stop!
>>
>> It can still be done using streamlines...
>>
>> Greetz,
>>
>>
>> Toon.
>>
>> ----- Original Message -----
>> From: "Patrick (Peng) Cheng" <peng-cheng at uiowa.edu>
>> To: "Toon Huysmans" <denhuys at hotmail.com>; "insight-users"
>> <insight-users at itk.org>
>> Sent: Thursday, July 01, 2004 6:41 PM
>> Subject: Re: Re: [Insight-users] Searching for Optimal Path in 3D 
>> vector
>> fieldImage?
>>
>>
>>> Thanks Toon,
>>> Yeah, the thing is there are three direction to follow at each voxel 
>>> with
>> different weight not only one.
>>> I want to find the optimal path between two points. It's kinda like
>> dynamic programming
>>> But I don't know how to do it in 3D
>>> ---------------------------
>>> Peng (Patrick) Cheng
>>> Biomedical Engineering
>>> University of Iowa
>>> Tel:(319) 400-7442
>>> Email: peng-cheng at uiowa.edu
>>>
>>> ===========2004-07-01 08:52:46 You wrote in your 
>>> letter:==============
>>>
>>>>   Use the vector as a velocity and direction of movement, then 
>>>> integrate
>>>> the a position over time, this should run trough the corresponding 
>>>> fiber
>> i
>>>> think.  Maybe you can use streamlines:
>>>>
>>>>    vtkStreamer
>>>>
>>>> Greetings,
>>>>
>>>> Toon.
>>>>
>>>> ----- Original Message -----
>>>> From: "Patrick (Peng) Cheng" <peng-cheng at uiowa.edu>
>>>> To: "insight-users" <insight-users at itk.org>
>>>> Sent: Thursday, July 01, 2004 4:45 PM
>>>> Subject: [Insight-users] Searching for Optimal Path in 3D vector 
>>>> field
>>>> Image?
>>>>
>>>>
>>>>> Hi everybody,
>>>>> I am doing a fiber tracking on a 3D vector image. I want to find 
>>>>> out
>> the
>>>> connectivity between two regions.
>>>>> So I am trying to find the optimal path which follows the vector 
>>>>> field.
>>>>> Can anybody give some hint or clue to do this?
>>>>> ---------------------------
>>>>> Peng (Patrick) Cheng
>>>>> Biomedical Engineering
>>>>> University of Iowa
>>>>> Tel:(319) 400-7442
>>>>> Email: peng-cheng at uiowa.edu
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Insight-users mailing list
>>>>> Insight-users at itk.org
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