# extract 3D surface from 3D volume data

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Hi, I have a volumetric data (in the form of (x,y,z,val(x,y,z)) array of data on and within a 3D volume shape. I would like to take only the coordinates and value on the surface.

Does anyone have an idea ?

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### Answers (4)

Sean de Wolski
on 2 Feb 2012

It sounds like you may want to create an isosurface (a volumetric contour map).

doc isosurface

##### 4 Comments

Bjorn Gustavsson
on 3 Feb 2012

Now we can start working!

If you don't take the radius from [0,0,0] but from the center of your points [xC,yC,zC] then you might be set. If you should calculate the center points with the mean or median of the points, like the center of mass (sum(x.*val)/sum(val)), also it is not given that such center even are inside a general 3-D body. But these steps you can judge better yourself.

HTH

YADOLAH GANJKHANLOU
on 3 Jun 2020

if you voxilize the object then yes it is very easy

you can run following code to see how it work:

load('spiralVol.mat');

h = volshow(spiralVol);

B = bwperim(spiralVol);

figure

h = volshow(B);

to voxilize your volume:

Just make a zeros matrix V with your volume's dimention and then make the voxels with x,y,z of your shape to be equal to 1.

you can reverese the above algoritm to extract X,Y,Z of the surface of you volume.

Yadi

Bjorn Gustavsson
on 2 Feb 2012

Algorithm in steps:

- Extract the surface elements in x y z and val

Done! Since we cant know how you define the surface, the shape of the surface or any other facts about it except that it is a surface in 3-D it is not easy for us to give you more than that. If you want to display it you might get somewhere with:

T = delaunay3(X,Y,Z,{'Qt', 'Qbb', 'Qc', 'Qz'} ); and then something like tetramesh

HTH

##### 3 Comments

Bjorn Gustavsson
on 2 Feb 2012

Josiah Yoder
on 27 Jan 2017

Kevin Moerman
on 10 Feb 2012

Could you rephrase/clarify your question? It sounds like you have 3D image data and that you are only interested in a certain surface within this volume.

Do you have intensity data x,y,z,val for a cloud of points or is that an image? And do I understand it correctly that you have coordinates that you know lie on the surface? Like x_s,y_x,z_s? And that you want to find the intensities on the surface points e.g. val_s? This can be achieved through interpolation (e.g. griddata3 or TriScatterInterp). If you want an actual description of the surface like patch data (faces and vertices) for plotting of the possibly closed shape (you don’t need this for determination of val_s on these points) then its more complex. Then you have point cloud onto which you want to draw a surface. You could try the cart2sph approach you suggested but this will produce possible artefacts at the poles and will lead to non-unique solutions at locations with double solutions in the spherical coordinate system (multiple radii solutions for a given angular coordinate set). There’s a number of quick and dirty approaches to getting the surface: 1) Just use the convex hull 2) Do a Delaunay tessellation (the outer surface elements now describe the convex hull again) but delete tetrahedrons which contain edged which are too long (i.e. these might be bridging the gaps that you do not want bridged). Then find the outer triangles to find your surface. This only works if you have a nice even point spacing. Good luck.

Kevin

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