How to compute 3D volume using Linearlization ?!

Hello Everybody;

I want your help for solving a question for volume computation of a cone. Given a set of short axis images, we need to estimate the volume of this cone concerning about the slice thickness; inter-slice gap. assume that the shape is as you see in the attached image. I have to calculate the following:

- distance between the planes containing the contours

- the area of each contour

- the radius of a circle whose area = area of smallest contour

- the volume of each frustum

- the volume of the half sphere

- the total volume

Hint 1: to draw the contours(attached at a mat file) , use the following matlab code:

if true
  % code
load('Contours.mat');
figure,hold on,
for i=1:8, 
  S=DataSet{i};         
  plot3(S(:,1),S(:,2),S(:,3));
end

Your help is highly appreciated...

[John D'Errico]

It would help those who wish to help you, if you actually did attach the mat file that you said you attached.

[Mariam Sheha]

files is now attached, sorry but i thought i did attachment...

Really i need and appreciate your help,,,

Thanks a lot..

[Mariam Sheha]

hello John D'Errico,

Did check the problem?... any ideas??

[Ced]

Naively, I guess I would start by computing the center of each circle, then determining the major axes. Using the knowledge that these are circles (and not ellipses), it should be possible to reconstruct the orientation. Using the area of the smallest circle as reference, you can get the actual size too. Once that is known, computing the volume should not be hard.

But you are probably better off starting in the lecture notes, and then ask specific matlab questions here.

[Mariam Sheha]

Thanks for your answer Ced,

i know how to compute a BW image centroid, area and also orientation. but in the case of these contours i don't know how to deal?!

let's be more specific...

how can i make 3D orientation, compute the center and radius of each of these contours?, then compute area?!

[Ced]

What do you mean by BW image centroid? Not a vision person, sorry, so this might be a trivial question.

But you have the coordinates of the contours (saved in the mat file), so just do the same with them as you would with the BW image I guess.