Find sphere fit on binary matrix

Hi all,

I have a (239,239,85) binary matrix in which the 1's correspond to the mask of a geometrical shape (see attachment). I want to fit a sphere around it, so that it fits best to the binary mask. I have already tried this: https://nl.mathworks.com/matlabcentral/fileexchange/34129-sphere-fit-least-squared, but that does not work since the matrix is singular. Can anybody help me out? Thanks in advance!

[Walter Roberson]

If the matrix is singular then enter the data all lies in the same plane or else you are passing the wrong information to the fitting function.

Answer 1

[KSSV]

load('matrixfit.mat') 

[m,n,p] = size(tumor3) ; 
[X,Y,Z] = ndgrid(1:m,1:n,1:p) ; 

k = tumor3(:) ; 
x = X(:) ;
y = Y(:) ;
z = Z(:) ; 
P = [x(k==1) y(k==1) z(k==1)] ; 

[Center,Radius] = sphereFit(P) ;   % Use that file exchange function 

I got:

Center = [100.8695  103.3629   37.2319] ;
Radius = 3.0785 ;

[Lieke Pullen]

Thank you! This is exactly what I was looking for.

[Walter Roberson]

Are X and Y reversed here? Remember that X is the second index of an array and Y is the first index of an array.

[Lieke Pullen]

I have a follow-up question on plotting the sphere. I have extracted the radius and center via your script, but when I want to draw the sphere, it does not give me the right results, since the center is not at the center of the coordinates given. The script is given below

array_x=239; array_y=239; array_z=85;
sphere=create_sphere(round(Radius),array_x,array_y, array_z, round(Center));

function solid_sphere=create_sphere(radius,array_x,array_y, array_z,Center)
ax=(array_x-1)/2; ay=(array_y-1)/2; az=(array_z-1)/2;
axlin=linspace(-ax,ax,array_x); aylin=linspace(-ay,ay,array_y); azlin=linspace(-az,az,array_z);
[X,Y,Z]=meshgrid(axlin, aylin, azlin);
solid_sphere= sqrt((X+(0.5*Center(1))).^2 + (Y+(0.5*Center(2))).^2 + (Z+(0.5*Center(3))).^2) <= radius ;
end

Can anybody help me out? Thanks in advance!

[Torsten]

Usually,

solid_sphere= sqrt((X-Center(1)).^2 + (Y-Center(2)).^2 + (Z-Center(3)).^2) <= radius ;

Is it different in your case ?

[Lieke Pullen]

I think so, since I have made a linspace varying from -119 to -119 (for x and y), and from -43 to 43 for z. I used the equation you mentioned in the following script:

array_x=239; array_y=239; array_z=85;
sphere=create_sphere(round(Radius),array_x,array_y, array_z, round(Center));

function solid_sphere=create_sphere(radius,array_x,array_y, array_z,Center)
[X,Y,Z]=meshgrid(0:1:array_x-1, 0:1:array_y-1, 0:1:array_z-1);
solid_sphere= sqrt((X-madCenter(1)).^2 + (Y-Center(2)).^2 + (Z-Center(3)).^2) <= radius ;
end

But that also does not give me the right center unfortunately.