How to generate polar shape matrix of binary image?

Hello friends,

I want to know how to generate a polar shape matrix from an binary object. I have done my implement up to drawing polar diagram but I don't get idea how to generate shape matrix. My code is:

if true
% code
J=im2double(imread('images\sample1.jpg'));
K=rgb2gray(J);
I=im2bw(K);
radius_min=0;
radius_max=100;
angle=360;
make_square=0;
clc;
close all;
% Check the argument data
if (nargin < 1)
    error('Error in the number of arguments (it should be >0). Use: I,radius_min,radius_max,angle,make_square');
end 
% Check if there are some arguments by default
if exist('radius_min','var') == 0
    radius_min = 0;
end
if exist('radius_max','var') == 0
    radius_max = 100;
end
if exist('angle','var') == 0
    angle = 60;
end
if exist('make_square','var') == 0
    make_square=0;
end
% Check if the input argument data are valid
if (radius_min < 0)
   error('radius_min sholud be >=0')
end
if (radius_max <= radius_min)
   error('radius_max sholud be >radius_min')
end
if (angle<0 && angle>360)
   error('angle sholud be  0<=angle<=360')
end
if (make_square ~= 0 && make_square ~= 1)
   error('make_square sholud be either 0, or, 1')
end
% Plot the input image (rectangular coordinates)
figure(1)
%I=imadjust(I); %activate if needed
imshow((I));
title('Input image (rectangular coordinates)')
[M N]=size(I);
% If the option make_square==1, the input image is resized
if make_square==1     
  if(M>N) dim=M;
   else dim=N;
  end
  I=imresize(I,[dim dim]);
  [M N]=size(I);         
end
% We rotate pi/2 the input image to have the desired view
I=imrotate(I,90);
% The mapping from cartesian to polar coordinates
theta_max=angle;
step_theta=theta_max/(N-1);
step_r=(radius_max-radius_min)/(M-1);
[r,theta] = meshgrid(radius_min:step_r:radius_max, -theta_max/2:step_theta:theta_max/2);
xx=-r.*cos(theta*pi/180)-radius_min;
yy=-r.*sin(theta*pi/180)-radius_min;
% Map the input image I to the polar coordinates xx,yy and represent as 
% a surface surface (viewed from above)
figure(2);
H=surface(yy,xx,im2double(I),'edgecolor','interp'); 
colormap(gray)
view(0,90)
axis off
title('Output image mapped to polar coordinates')
% figure
% polar(theta,r);
point =[97.31;92.12];         %- the center point  
 nbins_theta  =8; %   - theta divide  
nbins_r  =5;       %- r divide  
h2 = axes('position',[0  0  1  1]);
  gca;  
  hold on;  
   r_bin_edges=linspace(radius_min,radius_max,nbins_r);
  % draw circles  
  th = 0 : pi / 50 : 2 * pi;  
  xunit = cos(th);  
  yunit = sin(th);  
  for i=1:length(r_bin_edges)  
      line(xunit * r_bin_edges(i) + point(1), yunit * r_bin_edges(i) + point(2),...  
          'LineStyle', ':', 'Color', 'k', 'LineWidth', 1);  
  end  
  % draw spokes  
  th = (1:nbins_theta) * 2*pi / nbins_theta;  
  cs = [cos(th);zeros(1,size(th,2))];  
  sn = [sin(th);zeros(1,size(th,2))];  
  line(radius_max*cs + point(1), radius_max*sn + point(2),'LineStyle', ':', ...  
      'Color', 'k', 'LineWidth', 1);    
  axis equal;  
  axis off;  
  hold off; 
end
And the result is :

The further process is to generate polar shape matrix. The concept is If the circles intersect the maximum radius of the shape (line OA) at i1,i2,..., in-1, then starting from i1, i2, ..., in-1 and counter-clockwise, we divide each circle into m equal arcs, each arc being theta = 360/m degrees. Then an m x n matrix - which called shape matrix.

I would be thankful if someone helps me to implement this. Thanks in advance.