comparing volume of two 3d matrices

I have two 3d matrices called ORIGINAL and RECONSTRUCTED, size 500x500x500.

• ORIGINAL [Solid intensity: 0 black , 1 white]
• RECONSTRUCTED [intensity: 0 black to 1 white]

each matrix contain an object that can be viewed using command : isosurface(Volum,0.5);

How can I compare the size of those two object in Matlab?

Is there a way to combine the two matrix together and draw an isosurface of the two Objects after combination?

Thanks

Answer 1

[Sean de Wolski]

If the objects are convex then you can use the second output of convhulln to give you the volume directly. If not, then you have a few options:

You can just sum the images:

v1 = sum(sum(sum(original)));
v2 = sum(sum(sum(original)));

You could use a more fancy approach such as this:

FEX:mesh2tetra

And there are other ways.

For my masters thesis that did quite a bit of CT volume analysis, I just summed - it was a good enough approximation and there were many other attributes in the image that cause more error than this (reconstruction/downsampling bits/binarizing/noise, etc).

[Alan AF]

Thank you Sean for your brilliant answer

Actually I am interested in measuring the errors resulted from reconstruction, (I.e finding the changes and error that a reconstruction method (such as Wanted Back Projection) suffers from).

the first Matrix contains a sphere that is placed in the middle with solid intensity Original(x,y,z), while the other Matrix is a result from reconstruction that contains sphere shifted to the right with many artefacts and continuous intensity.

I thought of converting the two matrices in to indix imagies matrices with different colours and then combining them but did not know how to do it :(

Is there a way to combine the two matrix together and draw an isosurface of the two Objects after combination? or at least to find visually if the resulted object have different volume.

Many thanks

[Sean de Wolski]

You could do a Venn diagramesque combo, sure.

V = uint8(Original); %original is label 1, background is zero

V(logical(recon))) = 2; % recon is label 2

V(logical(original)&logical(recon)) = 3; %both

Now isosurface based on equality, i.e:

isosurface(V==1,0) %isosurface of first object

Or if you want total isosurface

isosurface(V>0,0);

etc. Logical indexing is your friend!

Is this what you want?