MATLAB: Straighten edges of black rectangle in binary image

cornerfilteringimage processingImage Processing Toolbox

I have a binary image that represents a 'rectangle'. The rectangle is not perfect because a top view of the box was taken (then converted to a binary image). My objective is to find four corner points of the black rectangle. In order for the corner function to work the edges must be completely straight.
http://i38.tinypic.com/w0lwro.jpg
clc; clear;
image = imread('0148pm.jpg');
g = rgb2gray(image)
level = graythresh(g);
binary = im2bw(image,level);
imwrite(binary,'imageBinary.jpg');
% Iinv = ~binary; %Invert your binary image
% Iinv = bwareaopen(Iinv,20); %Get rid of small areas (below your size criterion)
% I = ~Inv; %Invert back
imshow(I);
% fill = bwmorph(binary,'hbreak');
% 

% f = bwmorph(fill,'majority');
% 
% k = bwmorph(f,'close');
%corner algorithm///////////////////////////////////////////////////
% C = corner(k,'MinimumEigenvalue', 4)
% imtool(k);
% hold on
% plot(C(:,1), C(:,2), 'r*');
%end corner algorithm///////////////////////////////////////////////

Best Answer

Another way that is pretty easy way, probably the most straightforward is to simply find the centroid of the square and divide it up into quadrants around the centroid. The examine all the points to see which is farthest from the centroid. Like this code:
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures if you have the Image Processing Toolbox.
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 = 'C:\Users\User\Documents\Temporary';
baseFileName = 'w0lwro.jpg';
% 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.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, '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);
% Display the original gray scale image.


subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% 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') 
% Let's compute and display the histogram.
[pixelCount, grayLevels] = imhist(grayImage);
subplot(2, 2, 2); 
bar(pixelCount);
grid on;
title('Histogram of original image', 'FontSize', fontSize);
xlim([0 grayLevels(end)]); % Scale x axis manually.
binaryImage = grayImage < 128;
% Get rid of small blobs, smaller than two rows of pixels.
binaryImage = bwareaopen(binaryImage, 2*rows);
% Display the original gray scale image.
subplot(2, 2, 3);
imshow(binaryImage, []);
title('Binary Image', 'FontSize', fontSize);
% Label the image.
[labeledImage, numberOfBlobs] = bwlabel(binaryImage);
% Find the centroid
measurements = regionprops(labeledImage, 'Centroid');
% Put a cross at the centroid.
xCentroid = measurements.Centroid(1);
yCentroid = measurements.Centroid(2);
fprintf('X Centroid = %.3f, Y Centroid = %.3f', xCentroid, yCentroid);
hold on;
plot(xCentroid, yCentroid, 'r+', 'MarkerSize', 30);
% Find out how far the centroid is from points in each quadrant
% First get all the points.
[rows columns] = find(binaryImage);
xCorners = [0 0 0 0]; % X coordinate of corners in each quadrant.

yCorners = [0 0 0 0]; % X coordinate of corners in each quadrant.
maxDistance = [0 0 0 0]; % Distance of furthers X coordinate from centroid in each quadrant.
for k = 1 : length(columns)
  rowk = rows(k);
  colk = columns(k);
  distanceSquared = (colk - xCentroid)^2 + (rowk - yCentroid)^2;
  if rowk < yCentroid
    % It's in the top half
    if colk < xCentroid
      % It's in the upper left quadrant
      if distanceSquared > maxDistance(1)
        % Record the new furthest point in quadrant #1.
        maxDistance(1) = distanceSquared;
        xCorners(1) = colk;
        yCorners(1) = rowk;
      end
    else
      % It's in the upper right quadrant
      if distanceSquared > maxDistance(2)
        % Record the new furthest point in quadrant #2.
        maxDistance(2) = distanceSquared;
        xCorners(2) = colk;
        yCorners(2) = rowk;
      end
    end
  else
    % It's in the bottom half.
    if colk < xCentroid
      % It's in the lower left quadrant
      if distanceSquared > maxDistance(3)
        % Record the new furthest point in quadrant #3.
        maxDistance(3) = distanceSquared;
        xCorners(3) = colk;
        yCorners(3) = rowk;
      end
    else
      % It's in the lower right quadrant
      if distanceSquared > maxDistance(4)
        % Record the new furthest point in quadrant #4.
        maxDistance(4) = distanceSquared;
        xCorners(4) = colk;
        yCorners(4) = rowk;
      end
    end
  end
end
% Display in command window.
xCorners
yCorners
figure;
% Display the original gray scale image.
hImage = imshow(binaryImage, []);
title('Binary Image', 'FontSize', fontSize);
hold on;
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Place markers at the corners
plot(xCorners, yCorners,  'rs', 'MarkerSize', 10, 'LineWidth', 3);
impixelinfo(hImage);
% Plot centroid again
plot(xCentroid, yCentroid, 'r+', 'MarkerSize', 30, 'LineWidth', 3);
Results:
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