How to use voxels of different sizes to measure the volume of a 3D object using Matlab?

Hi Dear Community members,

i want to measure the volume of a cone using voxels. i am new in this field of voxels. Using the first link, a sphre of radius 8 has been voxelized. After voxelization, how can we count the total number of voxels. how to fix the size of voxels?

Using this method of author, how can we voxelize the cone to measure its volume. The attached file has xyz - coordiantes for the cone.

Thanks in advance for all cooperation and guidance.

https://www.mathworks.com/matlabcentral/fileexchange/50802-voxelplotter

https://www.mathworks.com/matlabcentral/answers/55633-how-to-drawing-3d-voxel-data?s_tid=answers_rc1-2_p2_MLT

% This scrypt illustrates the use of VoxelPlotter function to visualize
% voxel data stored in a 3d matrix
clear all
close all
clc
%Generating sinthetic input
gridesize=16;
R=8;
VoxelMat=zeros(gridesize,gridesize,gridesize);
for i=1:gridesize
    for j=1:gridesize
        for k=1:gridesize
            if (i-gridesize/2)^2+(j-gridesize/2)^2+(k-gridesize/2)^2<R^2
                VoxelMat(i,j,k)=1;
            end
        end
    end
end
[vol_handle]=VoxelPlotter(VoxelMat,1); 

view(3);
daspect([1,1,1]);
set(gca,'xlim',[0 gridesize], 'ylim',[0 gridesize], 'zlim',[0 gridesize]);

Answer 1

[Bruno Luong]

Vol estimate = 1.2692e+06

xyz = load('Cone_20000_points.txt');

[minxyz,maxxyz] = bounds(xyz,1);
N = 30*ones(1,3); % resolution, select with care
ijk = min(max(ceil((xyz-minxyz)./(maxxyz-minxyz).*N),1),N);
C = accumarray(ijk,1);
b = C > 0;
p = mean(C(b))
if p < 2 % Sanity check
    warning('Your bin is too small, inaccurate result');
end
Vol = sum(b,'all') * prod((maxxyz-minxyz)./N)

[M.S. Khan]

Thanks Dear Bruno for all your great cooperation as usual.

Please tell me what was the size of the voxel here. Also, how many voxels were counted in total? What will p represent. Please if you dont mind, explain to me the code. i will be vey thankful. can i conclude that : " b " represent the number of voxels. "prod((maxxyz-minxyz)./(N-1)" represent the size of voxel.

[Bruno Luong]

sum(b,'all') gives the number of voxels intesrsecting with the object

prod((maxxyz-minxyz)./N) is the volume (not size) of the voxel

[M.S. Khan]

Thank you for guiding! How will we know what is the size of the voxel? if i want to measure the volume using different size of voxel, how will we change the size of the voxel.

[Bruno Luong]

The sizes in x/y/z directions are

(maxxyz-minxyz)./N

PS: I edit the code I think the correct sizes is devided by N, not by N-1.

[M.S. Khan]

voxel means cube. Its length, width and heigh will be same e.g.5x5x5 or 10x10x10

In this case, if i use : (maxxyz-minxyz)./N --> it will give me voxel size like: 5 x5x6. am i right?

are the resolution and voxel size depending on each other?

I want to voxel size as 10, How will i fix it.

How to show the total count of all voxels used.

Please guide me.

[Bruno Luong]

Let as exercice for you. I have done enough already no?

[M.S. Khan]

Great Dear Bruno, yes i am thinking over it. I know, i am taking a lot of time from you.

[M.S. Khan]

i used below code to count number of voxels and size of voxels. Bruno, could you please look at it:6

number_of_voxels = numel(b) % To count number of voxels using above code. 
%  number_of_voxels = 27000
size_of_voxel = (maxxyz - minxyz)./N
% size_of_voxel= 5.1  5.1  5.93 ==> prod()~= 153

But if i measure volume using above values i.e. 27000 * 153 = 4139568 which is wrong.

[Bruno Luong]

Where you get this

number_of_voxels = numel(b) % To count number of voxels using above code.

from???? If you change the calculation of my code then it's normal you get wrong result.

[M.S. Khan]

Greetings Bruno, sorry for late reply. i was out of station.

Yes true, i got wrong results. Could you pleasue give me some tips how to count the number of voxels and how to measure the size of voxel.

[M.S. Khan]

i could not still figure out, how to measure the total number of voxels used. Please anyone can help me?