使用 python 实现霍夫圆变换

Question

我正在实施霍夫圆变换并在仅包含一个圆周的二值图像上尝试我的代码，但是对于我尝试的任何半径，我得到相同数量的累积点，这是代码：

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)

为什么会发生这种行为？

Answer 1

你必须像你一样找出圆心。你必须找到每个边缘坐标

您可以在 detectCircles 函数中检查 python 霍夫圆的实现 https://github.com/PavanGJ/Circle-Hough-Transform/blob/master/main.py

另外，看一下 Matlab 函数的霍夫圆实现

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

使用 python 实现霍夫圆变换

Hough Circle Transform Implementation using python

image-processing

computer-vision

hough-transform