finding x-y coordinate of object with specific distance

hello,

I have a binary image with five objects in it, I've found the distances between each pair, I gonna find the x-y coordinates of the two objects which have the special distances (for example the biggest distances), how can I do that? Thank you for your help in advance.

[Marry M]

I'm waiting for your help, thank you

Answer 1

[Walter Roberson]

With PairWiseDistanceArray being your 5 x 5 distance array where the index (I,J) is the distance between object #I and object #J, then:

[maxdistance, maxidx] = max(PairWiseDistanceArray(:));
[object1idx, object2idx] = ind2sub(size(PairWiseDistanceArray),maxidx);

The maximum distance was maxdistance and it was between object #object1idx and object #object2idx

[Marry M]

thank you for your suggestion, is it possible to find objects which the distance between them is (55)?

[Walter Roberson]

No. That never happens on the coordinate plane if you are using Euclidean distance. 55 is an integer, and the only integer distances less than 100 that can occur are: 5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97. See https://en.wikipedia.org/wiki/Pythagorean_triple

All non-integral distances that occur between integer coordinates are irrational numbers.

[Marry M]

ok, thank you. how can i find pairs with distances less than 100, with the code you proposed?

[Walter Roberson]

With PairWiseDistanceArray being your 5 x 5 distance array where the index (I,J) is the distance between object #I and object #J, then:

[r, c] = find(PairWiseDistanceArray < 100);
mask = r < c;
obj1 = r(mask);
obj2 = c(mask);

Now obj1 and obj2 are vectors with obj1(K) being less than distance 100 from obj2(K), and duplicates have been eliminated.

[Image Analyst]

Walter, the centroids are rarely exact integer coordinates. They're almost always located in between pixel centers.

Marry, see the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Walter Roberson]

The poster did not say how the coordinates were found. Centroids were not mentioned. One of my mental questions when I first read the topic was "Oh? How exactly is the distance between blobs being determined when blobs are often irregularly shaped?". To get any further in the question I had to assume that some method of assigning the coordinates had been arbitrarily determined.

Coordinates determined by centroids of a finite set of integral points are always rational values, and rational values have the same restrictions on pythagorean triples: there are a few but every other distance is irrational.

[Marry M]

I used 'nchoosek' and distance functions for finding distances between different pairs, with the code Walter Roberson suggested, i can not find the x and y coordinates of centres which have special distances (here less than 100 ).!!

[Walter Roberson]

Please show your code.

[Marry M]

Regarding the code, I Want to find 1) distance between each two centres 2) find distances less than 100, 3) find x-y coordinates of centres with distances less than 100:

co=[ centrex, centreY]; % x-y coordinate of centres

paircentre = nchoosek(1:size(centrex, 2), 2);

    distcentre= sqrt(sum((centrex (:, paircentre(:, 1)) - centrex (:, paircentre(:, 2))) .^ 2, 1)+ sum((centreY (:, paircentre(:, 1)) - centreY (:, paircentre(:, 2))) .^ 2, 1));   % distance between pairs 

cd1= distcentre <100; 

    [tr, tc] = find(cd1);

    mask = tr < tc;

    obj1 = tr(mask);

    obj2 = tc(mask);

xp1 = min(obj2); % x-coordinate of centre of object 1

xp2 = max(obj2);% x-coordinate of centre of object 2

the code does not give the best result, how can I find y-coordinates as well?

Thank you

[Walter Roberson]

obj1 and obj2 are not the x and y coordinates, they are the object number.

xp1 = centrex(obj1);
xp2 = centrex(obj2);
yp1 = centreY(obj1);
yp2 = centreY(obj2);

[Marry M]

ok, thank you.