## how can I find the furthest pair of points in a 3D binary matrix?

### Naim (view profile)

on 14 Aug 2017
Latest activity Commented on by Naim

on 15 Aug 2017

### Image Analyst (view profile)

the 3D matrix only contains one object. I want to know which of the two '1' values are the furthest away from each other. I read through all the functions and there doesn't seem to be a way. Is there one I don't know about?

### Products ### Image Analyst (view profile)

on 14 Aug 2017

Just do a brute force triple for loop. I attach a way in 2-D. A vectorized way would be to use find() and pdist2(), if you have the Statistics and Machine Learning Toolbox. Attach your 3-D binary image in a .mat file if you need more help. If you do that, let me know if you have the stats toolbox.

Naim

### Naim (view profile)

on 15 Aug 2017
Hey Image Analyst,
sorry for the late reply. Yes I do have the statistics and machine learning toolbox. I attached the .mat file to this comment. thank you for your help.
Image Analyst

### Image Analyst (view profile)

on 15 Aug 2017
You forgot to say if you tried it yourself. I expect that you did, so you can compare your code to mine and see if you get the same values.
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 = 20;
filename = fullfile(pwd, 'armsegmentation.mat');
arm = s.Arm;
maxValue = max(arm(:))
linearIndexes = find(arm);
for k = 1 : length(linearIndexes)
[yRow(k), xCol(k), zSlice(k)] = ind2sub(size(arm), linearIndexes(k));
end
xyz = [xCol', yRow', zSlice'];
distances = pdist2(xyz, xyz);
imshow(distances, []);
title('Distances between points', 'FontSize', fontSize);
xlabel('Point 1', 'FontSize', fontSize);
ylabel('Point 2', 'FontSize', fontSize);
axis on;
% Find the max distance
maxDistance = max(distances(:))
% Find the indexes where it occurs
[index1, index2] = find(distances == maxDistance)
fprintf('Farthest apart are linear indexes %d and %d.\n',...
index1(1), index2(1));
% Extract the x,y,z of the indexes.
x1 = xyz(index1(1), 1);
y1 = xyz(index1(1), 2);
z1 = xyz(index1(1), 3);
x2 = xyz(index2(1), 1);
y2 = xyz(index2(1), 2);
z2 = xyz(index2(1), 3);
fprintf('Linear index %d is at row = %d, column = %d, and slice %d.\n',...
index1(1), y1, x1, z1);
fprintf('Linear index %d is at row = %d, column = %d, and slice %d.\n',...
index2(1), y2, x2, z2);
fprintf('They are %f voxels apart.\n', maxDistance)
Results:
Farthest apart are linear indexes 2382 and 157.
Linear index 2382 is at row = 107, column = 181, and slice 35.
Linear index 157 is at row = 130, column = 108, and slice 28.
They are 76.857010 voxels apart.
Naim

### Naim (view profile)

on 15 Aug 2017
wow, amazing code that did exactly what I wanted it to do. thanks image analyst!