[Insight-users] Estimate a sphere

[Fabian Torres]

Hi

I would try to explain my problem

I would like to estimate a sphere from some points in a space.

To do that I have several ultrasound images of he surface of a sphere
located into a 3D space
I manually select some points of the surface in each image and create a non
linear equation system using this pons and the general equation of the
sphere


0 = (x - cx)^2 + (y-cy)^2  + (z-cz)^2 -r^2 (general equation of a sphere
where x,y,z are the surface points; cx,cy,cz is the center of the sphere
and r is the radius of the sphere)

So from this non-linear equation I would like to obtaine the corresponding
values pf cx,cy,cz znd r.


I have implemented this on MatLab using a function call lsqnonlin that
solves nonlinear least-squares curve fiting problems of the form


                          min||f(x)|| = min(f1(x)^2 + .... + fn(x)^2)

This is the documantation of this function for any reference
http://www.mathworks.com/help/optim/ug/lsqnonlin.html


Now I have to implement it on c++ usin itk and vtk.

I already have the surface points so now I´m trying to solve the equation
system

I try using the vnl_levenberg_marquardt algorithm for this. But I do not
get the expected results. since I know the exact position of the sphere and
its dimentions I do know that the estimated parameters using this method do
not correspond to the real valueas, also my MatLab implementation gives me
realy accurate results.

So my questions are.

Do i have to use vnl_levenberg_marquardt?
Is there any function similar to lsqnonlin implemented on itk, vnl or vtk?
I`m I doing something wrong?


Thanks for your time

-- 
Fabián Torres Robles
Maestria en Ciencias en Ingeniería Electrónica
Ingeniería en Sistemas Electrónicos
tel. 58081280, 0445534661338
e-mail fabian.trobles at gmail.com, dae.wong at gmail.com
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