MATLAB: Find euclidean distance between 2 regions

distance

I have two regions R1 and R2
How to find "d(pi; pj)", which denote the Euclidean distance between any two pixels pi and pj.
Then define the distance Di from the ith pixel in R1 to R2 as:
please can someone help me with the explanation to compute distance from 2 regions. I find it difficult in understanding. Please help.

Best Answer

See full demo below:
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;
% Check that user has the specified Toolbox installed and licensed.
hasLicenseForToolbox = license('test', 'image_toolbox');   % license('test','Statistics_toolbox'), license('test','Signal_toolbox')
if ~hasLicenseForToolbox
  % User does not have the toolbox installed, or if it is, there is no available license for it.
  % For example, there is a pool of 10 licenses and all 10 have been checked out by other people already.
  ver % List what toolboxes the user has licenses available for.
  message = sprintf('Sorry, but you do not seem to have the Image Processing Toolbox.\nDo you want to try to continue anyway?');
  reply = questdlg(message, 'Toolbox missing', 'Yes', 'No', 'Yes');
  if strcmpi(reply, 'No')
    % User said No, so exit.
    return;
  end
end
%===============================================================================
% Read in gray scale demo image.
folder = fileparts(which('eight.tif')); % Determine where demo folder is (works with all versions).
baseFileName = 'eight.tif';
% Get the full filename, with path prepended.
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
rgbImage = imread(fullFileName);
% Display the image.


subplot(2, 2, 1);
imshow(rgbImage, []);
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis on;
hp = impixelinfo();
% 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(rgbImage);
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(rgbImage); 
  % 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 = rgbImage(:, :, 1); % Take red channel.
else
  grayImage = rgbImage; % It's already gray scale.
end
% Display the image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Gray Scale Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis on;
%------------------------------------------------------------------------------
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% 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') 
subplot(2, 2, 2);
histogram(grayImage);
grid on;
title('Histogram', 'FontSize', fontSize, 'Interpreter', 'None');
% Create a binary image
binaryImage = grayImage < 200;
% Fill holes and take 2 largest blobs.
binaryImage = bwareafilt(imfill(binaryImage, 'holes'), 2);
% Display the image.
subplot(2, 2, 3);
imshow(binaryImage, []);
title('Binary Image with 2 Regions', 'FontSize', fontSize, 'Interpreter', 'None');
axis on;
%=============================================================================================

% Now we have our two regions and we can begin!
%=============================================================================================
% Get the boundaries.
boundaries = bwboundaries(binaryImage);
b1 = boundaries{1};
b2 = boundaries{2};
% Get the x and y
x1 = b1(:, 2);
y1 = b1(:, 1);
x2 = b2(:, 2);
y2 = b2(:, 1);
% Get distances between each boundary pixel and each one in the other blob.
% We just check the outer boundaries to reduce the number of distances we need to compute.
distances = pdist2([x1,y1], [x2,y2]);
% Find the min distance
minDistance = min(distances(:))
[index1, index2] = find(distances == minDistance)
% Get the locations
x1Min = x1(index1);
y1Min = y1(index1);
x2Min = x2(index2);
y2Min = y2(index2);
% Draw a line between them
hold on;
plot([x1Min, x2Min], [y1Min, y2Min], 'r-', 'LineWidth', 2);
title('Binary Image with 2 Regions with Closest Points Indicated', 'FontSize', fontSize, 'Interpreter', 'None');
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