Hough Transform For Circle Detection - with unknown radius (I)

In previous 2 examples, the generalized Hough Transform has been applied to find for the circle with known radius. We were using the circle equation --> (x-a)^2 + (y-b)^2 = R^2 to map the pixel to a-b domain.For detection circle with unknown radius, another parameter need to be make as variable, which is, the radius R.Let's see how to perform this:


1. Reading image and the convert to binary image.

I = imread('aaa.png');
I =im2bw(double(I),0.5);
[y,x]=find(I);
[sy,sx]=size(I);
imshow(I);

2. Find all the require information for the transformatin. the 'totalpix' is the numbers of '1' in the image.
totalpix = length(x);

3. Preallocate memory for the Hough Matrix. Try to play around with the R, or the radius to see the different results.

HM = zeros(sy,sx,50);
R = 1:50;
R2 = R.^2;
sz = sy*sx;

4. Performing Hough Transform. Notice the accumulator is located in the inner for loop. This portion of codes will map the original image to the a-b domain.

for cnt = 1:totalpix
for cntR = 1:50
b = 1:sy;
a = (round(x(cnt) - sqrt(R2(cntR) - (y(cnt) - [1:sy]).^2)));
b = b(imag(a)==0 & real(a)>0);
a = a(imag(a)==0 & real(a)>0);
ind = sub2ind([sy,sx],b,a);
HM(sz*(cntR-1)+ind) = HM(sz*(cntR-1)+ind) + 1;
end
end


5. Find for the maximum value for each layer, or in other words, the layer with maximum value will indicate the correspond R for the circle.

for cnt = 1:50
H(cnt) = max(max(HM(:,:,cnt)));
end
plot(H,'*-');

6. Extract the information from the layer with maximum value, and overlap with the original image.

[maxval, maxind] = max(H);
[B,A] = find(HM(:,:,maxind)==maxval);
imshow(double(I));
plot(mean(A),sy-mean(B),'xr')
xnumb(mean(A),sy-mean(B),maxind,100)
h = gce();
h.font_foreground = 255;