The largest rectangle inside object

How can I get the largest rectangle inside an object with a given center point?

Can it be done by using simple functions in Matlab and without any for s?

[Walter Roberson]

"Can it be done by using simple functions in Matlab and without any for s?"

I would tend to doubt that is possible without "for".

[Milad]

Yes, in the end for will be used. But it's better if I don't write any for s and use the built-in functions because they are faster and nicer.

[Image Analyst]

It's not easy, but I think it would involve bwdist(). Then you have to decide whether the rectangle can be rotated (harder) or parallel with image edges (easier).

Answer 1

[Image Analyst]

You might try this:

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 short g;
format compact;
fontSize = 25;

%===============================================================================
% Get the name of the image the user wants to use.
baseFileName = 'UVvcw.jpg';
% Get the full filename, with path prepended.
folder = pwd
fullFileName = fullfile(folder, baseFileName);

% Check if file exists.
if ~exist(fullFileName, 'file')
  % The file doesn't exist -- didn't find it there in that folder.
  % Check the entire search path (other folders) for the file by stripping off the folder.
  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

%===============================================================================
% Read in demo image.
grayImage = imread(fullFileName);
% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage)
if numberOfColorChannels > 1
  % It's not really gray scale like we expected - it's color.
  % Use weighted sum of ALL channels to create a gray scale image.
%   grayImage = rgb2gray(grayImage);
  % ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
  % which in a typical snapshot will be the least noisy channel.
  grayImage = grayImage(:, :, 2); % Take green channel.
end

% Display the original image.
subplot(2, 2, 1);
imshow(grayImage, []);
axis on;
caption = sprintf('Original Image, %s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
drawnow;
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.

% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0.05 1 0.95]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')

% Find the white surround.
binaryImage = grayImage > 128;
% Fill the image to get rid of black spot at center.
binaryImage = imfill(binaryImage, 'holes');
% Take the largest blob only.
% binaryImage = bwareafilt(binaryImage, 1);

% Display the image.
subplot(2, 2, 2);
imshow(binaryImage, []);
axis on;
caption = sprintf('Binary Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;

% Take the largest blob only.
edtImage = bwdist(~binaryImage);
% Display the image.
subplot(2, 2, 3);
imshow(edtImage, []);
axis on;
caption = sprintf('Distance Transform Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;

% Find the max of the EDT:
maxDistance = max(edtImage(:));
[rowCenter, colCenter] = find(edtImage == maxDistance)
hold on;
plot(colCenter, rowCenter, 'r+', 'MarkerSize', 30, 'LineWidth', 2);

% Get the boundary of the blob.
boundaries = bwboundaries(binaryImage);
b = boundaries{1}; % Extract from cell.
x = b(:, 2);
y = b(:, 1);
% Get distances from center to each of the edge pixels.
distances = sqrt((x - colCenter).^2 + (y - rowCenter).^2);
% Find the min distance.
[minDistance, indexOfMin] = min(distances)
% Find x and y of the min
xMin = x(indexOfMin)
yMin = y(indexOfMin)
plot(xMin, yMin, 'co', 'MarkerSize', 10, 'LineWidth', 2);
% Get the delta x and delta y from center to corner
dx = abs(colCenter - xMin)
dy = abs(rowCenter - yMin)
% Get edges of rectangle by adding and subtracting deltas from center.
row1 = rowCenter - dy
row2 = rowCenter + dy
col1 = colCenter - dx
col2 = colCenter + dx
% Make a box so we can plot it.
xBox = [col1, col2, col2, col1, col1];
yBox = [row1, row1, row2, row2, row1];
plot(xBox, yBox, 'r-', 'LineWidth', 2);

% Now, for fun, plot it over the binary image.
% Display the image.
subplot(2, 2, 4);
imshow(binaryImage, []);
axis on;
caption = sprintf('Binary Image with largest rectangle');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hold on;
plot(xBox, yBox, 'r-', 'LineWidth', 2);

[Milad]

This doesn't work for rectangle shaped objects.

[Milad]

Can you please complete this code?