Thread Subject: how to fit an analytical surface

Hi,

I was able to segment an anatomical structure from MR images, and I am in need to fit that into an analytical surface to simplify my subsequent operation. It is the tentorium of a human brain. Of course, if it's simple (like a sphere, ellipsoid, etc.) then I can proceed. The problem is that I don't know what would be the best analytical surface to fit to. Anyone has any idea where to start?

Thanks a lot!

"Pinpress" <nospam__@yahoo.com> wrote in message <hbocfi$ik1$1@fred.mathworks.com>...
> Hi,
>
> I was able to segment an anatomical structure from MR images, and I am in need to fit that into an analytical surface to simplify my subsequent operation. It is the tentorium of a human brain. Of course, if it's simple (like a sphere, ellipsoid, etc.) then I can proceed. The problem is that I don't know what would be the best analytical surface to fit to. Anyone has any idea where to start?
>
> Thanks a lot!

And how would we be able to guess which of
the infinitely many possible forms it might take
on?

The crystal ball is blurry at best.

Thanks for the reply -- Maybe what I would start with, is a 2nd order polynomial in the form of:

z = a*x^2 + b*y^2 + c*x + d*y +e

Is there an existing routine in matlab curve fitting toolbox that would compute the coefficients? I need the surface to be smooth, but not necessarily passing through all the given (x,y,z) points.

Thanks again!

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <hboebh$hkj$1@fred.mathworks.com>...
> "Pinpress" <nospam__@yahoo.com> wrote in message <hbocfi$ik1$1@fred.mathworks.com>...
> > Hi,
> >
> > I was able to segment an anatomical structure from MR images, and I am in need to fit that into an analytical surface to simplify my subsequent operation. It is the tentorium of a human brain. Of course, if it's simple (like a sphere, ellipsoid, etc.) then I can proceed. The problem is that I don't know what would be the best analytical surface to fit to. Anyone has any idea where to start?
> >
> > Thanks a lot!
>
> And how would we be able to guess which of
> the infinitely many possible forms it might take
> on?
>
> The crystal ball is blurry at best.

"Pinpress" <nospam__@yahoo.com> wrote in message <hbof5q$a9u$1@fred.mathworks.com>...
> Thanks for the reply -- Maybe what I would start with, is a 2nd order polynomial in the form of:
>
> z = a*x^2 + b*y^2 + c*x + d*y +e
>
> Is there an existing routine in matlab curve fitting toolbox that would compute the coefficients? I need the surface to be smooth, but not necessarily passing through all the given (x,y,z) points.
>

A polynomial model is a common choice. This
just reflects the idea that many functions will
be well approximated by a truncated Taylor
series.

I believe the curve fitting toolbox does allow
this class of model, at least if you have the
current version. If not, then you can download
polyfitn from the file exchange.

A problem you may quickly trip over is in the
form of the model. A surface fit with a tool
like the curvefitting toolbox, or my own
polyfitn, will presume a form like this:

z = a*x^2 + b*y^2 + c*x + d*y +e

However, you mentioned a model of the form
of an ellipse or a sphere. These "models" do
not fit into the general form above. Very
important here is the question of where the
noise enters into the model.

John

Hi John,

Indeed -- the problem is to get a good model first before fitting the data. The previous model I had in mind did not work quite well -- I have tried your polyfitn tool found in file exchange.

The tentorium has a shape depicted in the following image:

http://en.wikipedia.org/wiki/File:Falxcerebri.jpg

See the green part? That's actually half of the tentorium. In 3D, it should be able to fit into a

z = f(x, y)

function, if "z" is from inferior to superior direction. But I just haven't figured out what type of function form would work the best yet.

Any help from anyone would be appreciated!

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <hboh1c$82f$1@fred.mathworks.com>...
> "Pinpress" <nospam__@yahoo.com> wrote in message <hbof5q$a9u$1@fred.mathworks.com>...
> > Thanks for the reply -- Maybe what I would start with, is a 2nd order polynomial in the form of:
> >
> > z = a*x^2 + b*y^2 + c*x + d*y +e
> >
> > Is there an existing routine in matlab curve fitting toolbox that would compute the coefficients? I need the surface to be smooth, but not necessarily passing through all the given (x,y,z) points.
> >
>
> A polynomial model is a common choice. This
> just reflects the idea that many functions will
> be well approximated by a truncated Taylor
> series.
>
> I believe the curve fitting toolbox does allow
> this class of model, at least if you have the
> current version. If not, then you can download
> polyfitn from the file exchange.
>
> A problem you may quickly trip over is in the
> form of the model. A surface fit with a tool
> like the curvefitting toolbox, or my own
> polyfitn, will presume a form like this:
>
> z = a*x^2 + b*y^2 + c*x + d*y +e
>
> However, you mentioned a model of the form
> of an ellipse or a sphere. These "models" do
> not fit into the general form above. Very
> important here is the question of where the
> noise enters into the model.
>
> John