[Insight-users] how to calculate point using eigen vector

[Kishore Mosaliganti]

Hi Kana,

You need to arrange the lambda values in the order of decreasing magnitudes.
So based on your convention:
lambda1 = 12.2557
lambda2 = - 560.862
lambda3 = - 1022.66

You may want to use the filter developed in: "Generalizing vesselness with
respect to dimensionality and shape",
http://www.insight-journal.org/browse/publication/175
The basic work consist of Frangi's measures and it is mentioned in the
references of the above article. Specifically, the above paper implements
the filter proposed by Manniesingh et al.:
"Vessel enhancing diffusion: A scale space representation of vessel
structures "

This filter will allow you to first preprocess your images and enhance
tubes.


For your second question, you can follow the center line by looking for the
eigen-vector whose corresponding eigen value has a value closest to 0. The
reason is that along the center-line, there is no gradient in intensity and
hence the lambda1~0. So, you will go in the direction [-0.120 0.010 0.992]



Kishore



On Wed, Mar 10, 2010 at 11:31 AM, Arunachalam Kana <
Kana.Arunachalam at fh-wels.at> wrote:

>  Hi itk users,
>
>
>
> I am trying to write an algorithm to trace centre line of a tube shape in
> 3D CT image.
>
>
>
> I am using the hessian matrix to get the direction of the tube shape.
>
>
>
> The Eigen values and vector of hessian matrix for coordinate [9,5,2]:
>
>
>
> Eigen value: -560.862  -1022.66  12.2557 (not in any order)
>
>
>
> Eigen vectors:   0.701     0.708      0.078
>
>                                 -0.702   0.705     -0.092
>
>                                -0.120   0.010     0.992
>
>
>
> When arranged in |Lambda1| < |Lambda2| < |Lambda3| , i get 12.2557 as
> Lambda1.
>
> If my understanding of literature is right, then the direction of the tube
> centre line will
>
> point in the direction of eigenvector corresponding to 12.2557 which is
> 0.992.
>
>
>
> If i am right so far, then my question is :
>
> 1.       how to calculate the next coordinate to which i have to move from
> [9,5,2]?
>
> 2.       Is there any literature to refer to ?
>
>
>
> Help to solve this problem will be highly appreciated.
>
>
>
> Thank you,
>
> Regards,
>
> Kana
>
>
>
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