How to discover intersecting circles

I have two types of intersecting circles in images, created by the Matlab imfindcircles function, which returns a matrix of centroid (x, y) and a vector with the radii of the circles (r):

1- Concentric circles;

2 - Circles intersecting.

I need to identify all of these cases and apply two functions to treat these intersections, one for case 1 (function1) and one for case 2 (function2). These functions will have as parameters a matrix containing the centroides and the radii of the circles in each case. I just need a program that reports the parameters of the two functions and when to call one or the other.

Answer 1

[Image Analyst]

Try this:

% Create sample data.
numCircles = 10;
xy = rand(numCircles, 2);
radii = 0.1 * rand(numCircles, 1) + 0.1;
viscircles(xy, radii);
% Label them so we know what circle is what.
for k = 1 : numCircles
	text(xy(k, 1), xy(k, 2), num2str(k));
end
axis square;
% See if any intersect
for k = 1 : numCircles
	% Compute the distance between centers.
	distances = sqrt((xy(k, 1) - xy(:, 1)).^2 + (xy(k, 2) - xy(:, 2)) .^2);
	sumOfRadii = radii(k) + radii(:);
	intersectingIndexes = distances < sumOfRadii;
	% Don't compare circle to itself.  Of course that one intersects!
	intersectingIndexes(k) = false;
	% Convert to linear indexes
	intersectingIndexes = find(intersectingIndexes);
	for k2 = 1 : length(intersectingIndexes)
		fprintf('Circle %d intersects with circle #%d.\n', k, intersectingIndexes(k2));
	end
end

You see

Circle 1 intersects with circle #2.

Circle 1 intersects with circle #5.

Circle 1 intersects with circle #7.

Circle 2 intersects with circle #1.

Circle 2 intersects with circle #5.

Circle 3 intersects with circle #7.

Circle 3 intersects with circle #9.

Circle 5 intersects with circle #1.

Circle 5 intersects with circle #2.

Circle 6 intersects with circle #10.

Circle 7 intersects with circle #1.

Circle 7 intersects with circle #3.

Circle 8 intersects with circle #9.

Circle 9 intersects with circle #3.

Circle 9 intersects with circle #8.

Circle 10 intersects with circle #6.

and it's trivial to find out if one circle is completely contained within another. See if you can do it.

Answer 2

[KSSV]

1. You have center C and Radius R of circles. You can form the coordinates i.e (x,y) points of circle using:

m = 500 ; 
th = linspace(0,2*pi,m) ; 
x = C(1)+R*cos(th) ; 
y = C(2)+R*sin(th) ; 

2. You can get the point of intersections using Interx: https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

3. You can find whether a circle is lying inside other circle using inpolygon.

4. You can get the nearest points to a given point using knnsearch.