Thread Subject: 3d image surface normals

 
   Hi everyone,

I work on 3d face images.I have x,y,z points in raster
form.I need to find the surface normals of these images for
my project. Firstly I need to apply polgonal mesh I
think.But I can not any idea how to do this and obtain
surface normals.Is there any one to help me???

"kıvılcım " <kvlcm_helhel@mathworks.com> wrote in
message <fous72$b2o$1@fred.mathworks.com>...
>
> Hi everyone,
>
> I work on 3d face images.I have x,y,z points in raster
> form.I need to find the surface normals of these images for
> my project. Firstly I need to apply polgonal mesh I
> think.But I can not any idea how to do this and obtain
> surface normals.Is there any one to help me???
---------
  Here is a possible answer to your question. Suppose A is a 9 by 3 array with
each row containing the (x,y,z) coordinates of one of nine points in your
raster data, where these points consist of one point where you seek the
surface normal, along with its eight neighboring points. That is, within your
raster form, the nine points presumably form a square when projected onto
the x,y plane, with the central point being the one for which a normal is to be
found.

  The normal to an orthogonal least squares best-fitting plane through these
nine points can be regarded as a first order approximation to the surface
normal direction at the central point. If that is a suitable approximation for
you, this problem can be easily solved using matlab's svd function.

 [U,S,V] = svd(A,0); % "economy" version of svd
 n = V(:,3); % Choose eigenvector with least eigenvalue
 n = sign(n(3))*n; % Choose "upwards" as plus direction

  The vector n will be a unit vector orthogonal to the best-fitting plane. That
is, it consists of the three direction cosines of the approximate normal
direction. (The adjustment in the last line is due to the ambiguity as to which
of two opposite directions is chosen by svd. The above ensures that n has a
positive z-component.)

  Of course, you will need to repeat all of this for each point in the surface
data.

Roger Stafford