Hough Circle Transform Implementation using python - image-processing

Question

I am implementing the Hough circle transform and trying my code on a binary image that contains only one circle circumference, however for any radius I try, I get the same number of accumulated points, here is the code:
y0array, x0array= np.nonzero(image1)
r=8
acc_cells = np.zeros((100,100), dtype=np.uint64)
for i in range( len(x0array)):
y0= y0array[i]
x0= x0array[i]
for angle in range(0,360):
b = int(y0 - (r * s[angle]) ) //s is an array of sine of angles from 0 to 360
a = int(x0 - (r * c[angle]) ) //c is an array of cosine of angles from 0 to 360
if a >= 0 and a < 100 and b >= 0 and b < 100:
acc_cells[a, b] += 1
acc_cell_max = np.amax(acc_cells)
print(r, acc_cell_max)
Why is this behaviour happening?

Answer 1

You have to find out the center of the circles as you did. you have to find each edge coordinates
You can check python implementation of hough circles in detectCircles function
https://github.com/PavanGJ/Circle-Hough-Transform/blob/master/main.py
Also, take a look at hough circle implementation of Matlab functions
http://www.mathworks.com/matlabcentral/fileexchange/4985-circle-detection-via-standard-hough-transform
function [y0detect,x0detect,Accumulator] = houghcircle(Imbinary,r,thresh)
%HOUGHCIRCLE - detects circles with specific radius in a binary image. This
%is just a standard implementaion of Hough transform for circles in order
%to show how this method works.
%
%Comments:
% Function uses Standard Hough Transform to detect circles in a binary image.
% According to the Hough Transform for circles, each pixel in image space
% corresponds to a circle in Hough space and vise versa.
% upper left corner of image is the origin of coordinate system.
%
%Usage: [y0detect,x0detect,Accumulator] = houghcircle(Imbinary,r,thresh)
%
%Arguments:
% Imbinary - A binary image. Image pixels with value equal to 1 are
% candidate pixels for HOUGHCIRCLE function.
% r - Radius of the circles.
% thresh - A threshold value that determines the minimum number of
% pixels that belong to a circle in image space. Threshold must be
% bigger than or equal to 4(default).
%
%Returns:
% y0detect - Row coordinates of detected circles.
% x0detect - Column coordinates of detected circles.
% Accumulator - The accumulator array in Hough space.
%
%Written by :
% Amin Sarafraz
% Computer Vision Online
% http://www.computervisiononline.com
% amin#computervisiononline.com
%
% Acknowledgement: Thanks to CJ Taylor and Peter Bone for their constructive comments
%
%May 5,2004 - Original version
%November 24,2004 - Modified version,faster and better performance (suggested by CJ Taylor)
%Aug 31,2012 - Implemented suggestion by Peter Bone/ Better documentation
if nargin == 2
thresh = 4; % set threshold to default value
end
if thresh < 4
error('HOUGHCIRCLE:: Treshold value must be bigger or equal to 4');
end
%Voting
Accumulator = zeros(size(Imbinary)); % initialize the accumulator
[yIndex xIndex] = find(Imbinary); % find x,y of edge pixels
numRow = size(Imbinary,1); % number of rows in the binary image
numCol = size(Imbinary,2); % number of columns in the binary image
r2 = r^2; % square of radius, to prevent its calculation in the loop
for cnt = 1:numel(xIndex)
low=xIndex(cnt)-r;
high=xIndex(cnt)+r;
if (low<1)
low=1;
end
if (high>numCol)
high=numCol;
end
for x0 = low:high
yOffset = sqrt(r2-(xIndex(cnt)-x0)^2);
y01 = round(yIndex(cnt)-yOffset);
y02 = round(yIndex(cnt)+yOffset);
if y01 < numRow && y01 >= 1
Accumulator(y01,x0) = Accumulator(y01,x0)+1;
end
if y02 < numRow && y02 >= 1
Accumulator(y02,x0) = Accumulator(y02,x0)+1;
end
end
end
% Finding local maxima in Accumulator
y0detect = []; x0detect = [];
AccumulatorbinaryMax = imregionalmax(Accumulator);
[Potential_y0 Potential_x0] = find(AccumulatorbinaryMax == 1);
Accumulatortemp = Accumulator - thresh;
for cnt = 1:numel(Potential_y0)
if Accumulatortemp(Potential_y0(cnt),Potential_x0(cnt)) >= 0
y0detect = [y0detect;Potential_y0(cnt)];
x0detect = [x0detect;Potential_x0(cnt)];
end
end