# Calculate the distance between two objects automatically using matlab.

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Lakshya
on 25 Aug 2014

Commented: Image Analyst
on 17 Sep 2022 at 13:32

hi there!

i am currently doing project on image processing in matlab, in which I'm assigned to calculate the Euclidean distance between two object automatically.here is the image link https://imageshack.com/i/pcUJ9tQgj i first converted the image to binary using 'im2bw', then i applied 'canny' edge detection method and obtained the edges, and by using 'find' function i got the corresponding pixel values. And i am not able to processed further, problem is i have to get array of pixel coordinates for object A and object B separately. and the code has to find which pixel coordinates is nearer between both objects and calculate the nearer distance. I'd very much appreciate your input.

Sincrely, lakshya

##### 0 Comments

### Accepted Answer

Image Analyst
on 25 Aug 2014

You forgot to attach your image, which people usually do when they want image processing advice. So I don't know if edge detection is what you want to do or not. Perhaps it is if you have something like phase contrast or DIC microscopy images, but if you have objects of one intensity on a background of a different intensity then you can probably use thresholding. That method is explained in my Image Segmentation Tutorial http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A31862 I find the blobs' centroids. From that you can find the distances between the centroids.

You didn't really explain your definition of distance clearly. I think you mean Euclidean /Pythagorean distance, but there's a chance you mean the Hausdorf distance. See this page to understand the Hausdorf distance: http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/98/normand/main.html, though chances are you've never heard of it.

In my File Exchange there are also color segmentation methods. How you do your task really depends on what your images look like.

##### 24 Comments

### More Answers (5)

Ahmed Mehar
on 1 Jul 2015

You Can calculate the Distance of multiple Objects of Center point by using this code:

k=2; for i=1:1:length(g)-1 x(i) = g(i).Centroid(1); y(i) = g(i).Centroid(2);

x(k)=g(k).Centroid(1); y(k)=g(k).Centroid(2);

distance=sqrt((x(i)-x(k))^2+(y(i)-y(k))^2);

##### 0 Comments

Vihan P
on 23 Apr 2021

##### 5 Comments

Image Analyst
on 26 Apr 2021

@Vihan P, see code adapted for your image. I also did it both ways, using sqrt(), where I just plotted one of the closest pairs, and pdist2() where I plotted all 3 of the closest pairs.

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;

fprintf('Beginning to run %s.m ...\n', mfilename);

fontSize = 13;

% Check that user has the Image Processing Toolbox installed.

hasIPT = license('test', 'image_toolbox');

if ~hasIPT

% User does not have the toolbox installed.

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 a standard MATLAB color demo image.

folder = pwd; %'C:\Users\Lakshya\Documents\Temporary';

baseFileName = 'knee.png';

% Get the full filename, with path prepended.

fullFileName = fullfile(folder, baseFileName);

if ~exist(fullFileName, 'file')

% 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.', fullFileName);

uiwait(warndlg(errorMessage));

return;

end

end

grayImage = imread(fullFileName);

% Get the dimensions of the image. numberOfColorBands should be = 3.

[rows, columns, numberOfColorBands] = size(grayImage);

% Display the original image.

subplot(2, 2, 1);

imshow(grayImage);

axis on;

title('Original Gray Scale Image', 'FontSize', fontSize);

% Enlarge figure to full screen.

set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

% Binarize the image

binaryImage = imbinarize(grayImage);

% Display the image.

subplot(2, 2, 2);

imshow(binaryImage);

title('Binary Image', 'FontSize', fontSize);

% Fill the outline to make it solid so we don't get boundaries

% on both the inside of the shape and the outside of the shape.

binaryImage = imfill(binaryImage, 'holes');

% Display the image.

subplot(2, 2, 3);

imshow(binaryImage);

% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.

% Plot the borders of all the coins on the original grayscale image using the coordinates returned by bwboundaries.

hold on;

boundaries = bwboundaries(binaryImage);

numberOfBoundaries = size(boundaries, 1);

for k = 1 : numberOfBoundaries

thisBoundary = boundaries{k};

plot(thisBoundary(:,2), thisBoundary(:,1), 'r', 'LineWidth', 3);

end

title('Filled Binary Image with Boundaries', 'FontSize', fontSize);

hold off;

% Define object boundaries

numberOfBoundaries = size(boundaries, 1)

boundary1 = boundaries{1};

boundary2 = boundaries{2};

boundary1x = boundary1(:, 2);

boundary1y = boundary1(:, 1);

x1=1;

y1=1;

x2=1;

y2=1;

overallMinDistance = inf; % Initialize.

index1 = 1;

index2 = 1;

for k = 1 : length(boundary2)

boundary2x = boundary2(k, 2);

boundary2y = boundary2(k, 1);

% For this blob, compute distances from boundaries to edge.

allDistances = sqrt((boundary1x - boundary2x).^2 + (boundary1y - boundary2y).^2);

% Find closest point, min distance.

[minDistance(k), indexOfMin] = min(allDistances);

if minDistance(k) < overallMinDistance

overallMinDistance = minDistance(k);

x1 = boundary1x(indexOfMin);

y1 = boundary1y(indexOfMin);

x2 = boundary2x;

y2 = boundary2y;

index2 = k;

index1 = indexOfMin;

end

end

% Report to command window.

fprintf('Min Distance from sqrt() method = %f at index %d of boundary 1 and index %d of boundary 2.\n', ...

overallMinDistance, index1, index2);

hFig = figure;

h1 = subplot(1, 2, 1);

imshow(binaryImage);

axis on;

title('Closest Distance from sqrt()', 'FontSize', fontSize);

h2 = subplot(1, 2, 2);

imshow(binaryImage);

axis on;

title('Closest Distances from pdist2()', 'FontSize', fontSize);

hFig.WindowState = 'maximized';

hold on;

% Draw a line between point 1 and 2

line(h1, [x1, x2], [y1, y2], 'Color', 'y', 'LineWidth', 3);

%======================================================================================

% For comparison, use pdist2()

allDistances2 = pdist2(boundary1, boundary2);

minDistance2 = min(allDistances2(:));

% Find all points that have that min distance - there may be several that have it.

[r, c] = find(allDistances2 == minDistance2)

boundary1x = boundary1(:, 2);

boundary1y = boundary1(:, 1);

boundary2x = boundary2(:, 2);

boundary2y = boundary2(:, 1);

for k = 1 : length(r)

% Report to command window.

index1 = r(k);

index2 = c(k);

fprintf('Min Distance from pdist2() method = %f at index %d of boundary 1 and index %d of boundary 2.\n', ...

minDistance2, index1, index2);

xLine = [boundary1x(index1), boundary2x(index2)];

yLine = [boundary1y(index1), boundary2y(index2)];

line(h2, xLine, yLine, 'Color', 'm', 'LineWidth', 1.5);

end

You can't see the magenta lines in the right image very well, but they're there.

Rhandrey Maestri
on 17 Sep 2022 at 11:16

Edited: Rhandrey Maestri
on 17 Sep 2022 at 11:19

Following this code. Can you tell me how to detect the bubble border(black region) and the tube wall(this black line near the bubble). And then calculate the distance between the border of the bubble and the closest wall pixel near this bubble?

Also if I know that the inside diameter is 15 mm. Can I have this distances in mm?

Appreciate

##### 1 Comment

Image Analyst
on 17 Sep 2022 at 13:32

@Rhandrey Maestri, start a new question with this since it's sufficiently different. In there, show us how you processed the horizontal profile

horizontalProfile = mean(grayImage);

plot(horizontalProfile, 'b-');

to find the two valleys, and how you used thresholding to get the bubble, then how you use find() to find the edges, row-by-row, of the inner walls and the outer bubble walls. If you still need help, I'll help you there.

There is a variety of ways to do this, and it could be easier if you knew that the walls and bubbles were in approximately the same location every time, like just mask off the middle part and deal with only the central part, then threshold and take the 3 largest blobs with bwareafilt.

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