Thread Subject: how to smooth a triangulated surface?

Hi all,

Suppose I have a triangulated surface (e.g., created by using isosurface), how can I efficiently smooth the surface? Thanks for any good input!

"Pinpress" <nospam__@yahoo.com> wrote in message news:gsj703$rf1$1@fred.mathworks.com...
> Hi all,
>
> Suppose I have a triangulated surface (e.g., created by using isosurface), how can I
> efficiently smooth the surface? Thanks for any good input!
>
Just a suggestion. If it really is an isosurface, you'll probably
have better results smoothing the volume data before doing
the isosurface. It tends to be simpler and more robust than
messing with the surface data.


    -Mike Garrity
    -The MathWorks

Thanks Mike.

Yes, the isosurface was already based on a smoothed volume (using smooth3). However, I would still like to further smooth the resulting triangular surface. Just imaging that I created a phantom 3D image volume of a sphere using the following code:

stack = zeros(100,100,100);
[x,y,z] = meshgrid(1:size(stack,2), 1:size(stack,1), 1:size(stack,3));
dis = dismap_pointsets_openmp([x(:) y(:) z(:)], size(stack)/2); %% just the distance relative to the center
ind = find(dis<40);
stack(ind) = 1;

When I create isosurface, I will get a somewhat jagged sphere. Because the "real", or "idealized" surface is a perfect sphere, I was wondering if there is any way to "smooth" the resulting triangulated surface.

Thanks for any further input!


"Michael Garrity" <mgarrity@mathworks.com> wrote in message <gskf9d$eh7$1@fred.mathworks.com>...
>
> "Pinpress" <nospam__@yahoo.com> wrote in message news:gsj703$rf1$1@fred.mathworks.com...
> > Hi all,
> >
> > Suppose I have a triangulated surface (e.g., created by using isosurface), how can I
> > efficiently smooth the surface? Thanks for any good input!
> >
> Just a suggestion. If it really is an isosurface, you'll probably
> have better results smoothing the volume data before doing
> the isosurface. It tends to be simpler and more robust than
> messing with the surface data.
>
>
> -Mike Garrity
> -The MathWorks
>
>

"Pinpress" <nothing@nothing.edu> wrote in message <gskimp$9ot$1@fred.mathworks.com>...
> Thanks Mike.
>
> Yes, the isosurface was already based on a smoothed volume (using smooth3). However, I would still like to further smooth the resulting triangular surface. Just imaging that I created a phantom 3D image volume of a sphere using the following code:
>
> stack = zeros(100,100,100);
> [x,y,z] = meshgrid(1:size(stack,2), 1:size(stack,1), 1:size(stack,3));
> dis = dismap_pointsets_openmp([x(:) y(:) z(:)], size(stack)/2); %% just the distance relative to the center
> ind = find(dis<40);
> stack(ind) = 1;
>
> When I create isosurface, I will get a somewhat jagged sphere. Because the "real", or "idealized" surface is a perfect sphere, I was wondering if there is any way to "smooth" the resulting triangulated surface.
>
> Thanks for any further input!

I'll argue that the problem is NOT that you have a
non-smooth iso-surface. The problem is you are
creating the approximately spherical surface in a
poor way.

You are interpolating a boolean expression. There
is no reason this should be smooth. Fix the problem,
not the symptom.

John

Hi John,

I agree that if my only problem is to use a triangulated surface to represent a sphere, then I will have much better methods than what I suggested earlier. However, this is just a simple phantom image of a real world problem -- when we have a bunch of medical images of human anatomies, for example, this would be what we would go through to have the structure's outer boundary surface. In real cases, it'll be much harder to parametrize the surface (unlike the sphere case).

I understand that medical images are inherently pixel- or voxel-based, which is discretized and not continuous. Therefore, my original intention was to construct a simple surface and see if I can find a way to smooth the triangulated surface and then apply the method to my real problems.

Thanks.

>
> I'll argue that the problem is NOT that you have a
> non-smooth iso-surface. The problem is you are
> creating the approximately spherical surface in a
> poor way.
>
> You are interpolating a boolean expression. There
> is no reason this should be smooth. Fix the problem,
> not the symptom.
>
> John