How to create a Radius vs. Intensity plot of an image (matrix)

I have an intensity matrix size=[86 86] and I need to find the radii of all positions in the matrix with respect to a corner. The matlab index values are all exactly 0.25cm apart. How do I find the total intensity summed over all matrix positions with the same radius?

I need to create a plot of Radius (x) vs. Intensity (y).

Let any given position in the matrix be P(i,j) and the corner location P(a,b).

I know Radius = sqrt((i-a)^2 + (j-b)^2)

I am assuming I will also need to create a nested FOR loop so that I can calculate the radius at every matrix position (FOR i<=84 and j<=84).

Can anyone help?

Answer 1

[Image Analyst]

Try using accumarray()

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

%===============================================================================
% Read in a standard MATLAB gray scale demo image.
folder = fileparts(which('cameraman.tif')); % Determine where demo folder is (works with all versions).
baseFileName = 'moon.tif';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- didn't find it there.  Check the search path for it.
  fullFileNameOnSearchPath = baseFileName; % No path this time.
  if ~exist(fullFileNameOnSearchPath, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.  
% numberOfColorBands should be = 1.
[rows, columns, numberOfColorBands] = size(grayImage);
if numberOfColorBands > 1
  % It's not really gray scale like we expected - it's color.
  % Convert it to gray scale by taking only the green channel.
  grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the original gray scale image.
subplot(1, 2, 1);
imshow(grayImage, []);
axis on;
title('Original Grayscale Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 

% Get distances for every pixel
[c, r] = meshgrid(1:rows, 1:columns);
calibrationFactor = 0.25;  % There are 0.25 real world units per index.
distances = sqrt((c-1).^2 + (r-1).^2) * calibrationFactor;
% Round it to the nearest single unit (nearest 4 pixel)
distances = round(distances);
% Add 1 so we can use that as indexes in accumarray
distances = distances + 1;
% Now get sum of intensity at each distance
out = accumarray(distances(:), grayImage(:));
subplot(1, 2, 2);
plot(out, 'b-', 'LineWidth', 3);
grid on;
xlabel('Distance', 'FontSize', fontSize);
ylabel('Sum of gray levels', 'FontSize', fontSize);
title('GL sum vs. distance', 'FontSize', fontSize, 'Interpreter', 'None');

[Image Analyst]

jnrivera -- did that work for you?