如何用hough变换方法检测图像中的圆

Hough变换是实现图像边缘检测的一种有效方法，其基本思想是将测量空间的一点变换到参量空间中的一条曲线或一个曲面，而具有同一参量特征的点交换后在参量空间中相交，通过判断交点处的积累程度来完成特征曲线的检测，基于参量性质的不同，Hough变换可以检测直线、圆、椭圆、双曲线、抛物线等。同时，将概率论、模糊集理论、分层迭代的思想和级联的方法应用于Hough变换的过程中，大大地提高了Hough变换的效率，改善了Hough变换的性能。

实验主要使用的函数

MATLAB内部常数pi：圆周率 p（= 3.1415926...）

MATLAB常用基本数学函数:

abs(x)：纯量的绝对值或向量的长度；

round(x)：四舍五入至最近整数；

floor(x)：地板函数，即舍去正小数至最近整数；

MATLAB常用三角函数

sin(x)：正弦函数

cos(x)：余弦函数；

向量的常用函数

max(x): 向量x的元素的最大值。

MATLAB图像类型转换函数：

rgb2gray:将一副真彩色图像转换成灰度图像；

im2bw:通过设定高度阈值将真彩色，索引色，灰度图转换成二值图像；

MATLAB图形图像文件的读取和显示函数

imread(filename)；

MATLAB二进制图像及其显示

imshow（f1）。

用double对二值图像双精度化

图形处理：

sobel算子检测边缘

hough变换检测圆

分别显示灰度图像：

figuresubplot

Sobel:算子边缘检测图像

hough变换检测后的图像

实验相关代码

I=imread('*.jpg')f=rgb2gray(I)

f1=im2bw(f,200/255)

BW1=double(f1)

BW=edge(BW1,'sobel',0.4)

r_max=50

r_min=10step_r=10step_angle=pi/12p=0.7

[m,n] = size(BW)

size_r = round((r_max-r_min)/step_r)+1

size_angle = round(2*pi/step_angle)

hough_space = zeros(m,n,size_r)

[rows,cols] = find(BW)

ecount = size(rows)

for i=1:ecount

for r=1:size_r

for k=1:size_angle

a = round(rows(i)-(r_min+(r-1)*step_r)*cos(k*step_angle))

b = round(cols(i)-(r_min+(r-1)*step_r)*sin(k*step_angle))

if(a>0&&a<=m&&b>0&&b<=n)

hough_space(a,b,r) = hough_space(a,b,r)+1

end

end

end

end

max_para = max(max(max(hough_space)))

index = find(hough_space>=max_para*p)

length = size(index)

hough_circle = false(m,n)

for i=1:ecount

for k=1:length

par3 = floor(index(k)/(m*n))+1

par2 = floor((index(k)-(par3-1)*(m*n))/m)+1

par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m

if((rows(i)-par1)^2+(cols(i)-par2)^2<(r_min+(par3-1)*step_r)^2+5&&...

(rows(i)-par1)^2+(cols(i)-par2)^2>(r_min+(par3-1)*step_r)^2-5)

hough_circle(rows(i),cols(i)) = true

end

end

end

for k=1:length

par3 = floor(index(k)/(m*n))+1

par2 = floor((index(k)-(par3-1)*(m*n))/m)+1

par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m

par3 = r_min+(par3-1)*step_r

fprintf(1,'Center %d %d radius %d\n',par1,par2,par3)

para(:,k) = [par1,par2,par3]

end

subplot(221),imshow(f)

subplot(222),imshow(BW)

subplot(223),imshow(hough_circle)

代码如下：

function [accum, varargout] = CircularHough_Grd(img, radrange, varargin)

%Detect circular shapes in a grayscale image. Resolve their center

%positions and radii.

%

% [accum, circen, cirrad, dbg_LMmask] = CircularHough_Grd(

% img, radrange, grdthres, fltr4LM_R, multirad, fltr4accum)

% Circular Hough transform based on the gradient field of an image.

% NOTE:Operates on grayscale images, NOT B/W bitmaps.

% NO loops in the implementation of Circular Hough transform,

% which means faster operation but at the same time larger

% memory consumption.

%

%%%%%%%% INPUT: (img, radrange, grdthres, fltr4LM_R, multirad, fltr4accum)

%

% img: A 2-D grayscale image (NO B/W bitmap)

%

% radrange:The possible minimum and maximum radii of the circles

% to be searched, in the format of

% [minimum_radius , maximum_radius] (unit: pixels)

% **NOTE**: A smaller range saves computational time and

% memory.

%

% grdthres:(Optional, default is 10, must be non-negative)

% The algorithm is based on the gradient field of the

% input image. A thresholding on the gradient magnitude

% is performed before the voting process of the Circular

% Hough transform to remove the 'uniform intensity'

% (sort-of) image background from the voting process.

% In other words, pixels with gradient magnitudes smaller

% than 'grdthres' are NOT considered in the computation.

% **NOTE**: The default parameter value is chosen for

% images with a maximum intensity close to 255. For cases

% with dramatically different maximum intensities, e.g.

% 10-bit bitmaps in stead of the assumed 8-bit, the default

% value can NOT be used. A value of 4% to 10% of the maximum

% intensity may work for general cases.

%

% fltr4LM_R: (Optional, default is 8, minimum is 3)

% The radius of the filter used in the search of local

% maxima in the accumulation array. To detect circles whose

% shapes are less perfect, the radius of the filter needs

% to be set larger.

%

% multirad: (Optional, default is 0.5)

% In case of concentric circles, multiple radii may be

% detected corresponding to a single center position. This

% argument sets the tolerance of picking up the likely

% radii values. It ranges from 0.1 to 1, where 0.1

% corresponds to the largest tolerance, meaning more radii

% values will be detected, and 1 corresponds to the smallest

% tolerance, in which case only the "principal" radius will

% be picked up.

%

% fltr4accum: (Optional. A default filter will be used if not given)

% Filter used to smooth the accumulation array. Depending

% on the image and the parameter settings, the accumulation

% array built has different noise level and noise pattern

% (e.g. noise frequencies). The filter should be set to an

% appropriately size such that it's able to suppress the

% dominant noise frequency.

%

%%%%%%%% OUTPUT: [accum, circen, cirrad, dbg_LMmask]

%

% accum: The result accumulation array from the Circular Hough

% transform. The accumulation array has the same dimension

% as the input image.

%

% circen: (Optional)

% Center positions of the circles detected. Is a N-by-2

% matrix with each row contains the (x, y) positions

% of a circle. For concentric circles (with the same center

% position), say k of them, the same center position will

% appear k times in the matrix.

%

% cirrad: (Optional)

% Estimated radii of the circles detected. Is a N-by-1

% column vector with a one-to-one correspondance to the

% output 'circen'. A value 0 for the radius indicates a

% failed detection of the circle's radius.

%

% dbg_LMmask: (Optional, for debugging purpose)

% Mask from the search of local maxima in the accumulation

% array.

%

%%%%%%%%% EXAMPLE #0:

% rawimg = imread('TestImg_CHT_a2.bmp')

% tic

% [accum, circen, cirrad] = CircularHough_Grd(rawimg, [15 60])

% toc

% figure(1)imagesc(accum)axis image

% title('Accumulation Array from Circular Hough Transform')

% figure(2)imagesc(rawimg)colormap('gray')axis image

% hold on

% plot(circen(:,1), circen(:,2), 'r+')

% for k = 1 : size(circen, 1),

% DrawCircle(circen(k,1), circen(k,2), cirrad(k), 32, 'b-')

% end

% hold off

% title(['Raw Image with Circles Detected ', ...

% '(center positions and radii marked)'])

% figure(3)surf(accum, 'EdgeColor', 'none')axis ij

% title('3-D View of the Accumulation Array')

%

% COMMENTS ON EXAMPLE #0:

% Kind of an easy case to handle. To detect circles in the image whose

% radii range from 15 to 60. Default values for arguments 'grdthres',

% 'fltr4LM_R', 'multirad' and 'fltr4accum' are used.

%

%%%%%%%%% EXAMPLE #1:

% rawimg = imread('TestImg_CHT_a3.bmp')

% tic

% [accum, circen, cirrad] = CircularHough_Grd(rawimg, [15 60], 10, 20)

% toc

% figure(1)imagesc(accum)axis image

% title('Accumulation Array from Circular Hough Transform')

% figure(2)imagesc(rawimg)colormap('gray')axis image

% hold on

% plot(circen(:,1), circen(:,2), 'r+')

% for k = 1 : size(circen, 1),

% DrawCircle(circen(k,1), circen(k,2), cirrad(k), 32, 'b-')

% end

% hold off

% title(['Raw Image with Circles Detected ', ...

% '(center positions and radii marked)'])

% figure(3)surf(accum, 'EdgeColor', 'none')axis ij

% title('3-D View of the Accumulation Array')

%

% COMMENTS ON EXAMPLE #1:

% The shapes in the raw image are not very good circles. As a result,

% the profile of the peaks in the accumulation array are kind of

% 'stumpy', which can be seen clearly from the 3-D view of the

% accumulation array. (As a comparison, please see the sharp peaks in

% the accumulation array in example #0) To extract the peak positions

% nicely, a value of 20 (default is 8) is used for argument 'fltr4LM_R',

% which is the radius of the filter used in the search of peaks.

%

%%%%%%%%% EXAMPLE #2:

% rawimg = imread('TestImg_CHT_b3.bmp')

% fltr4img = [1 1 1 1 11 2 2 2 11 2 4 2 11 2 2 2 11 1 1 1 1]

% fltr4img = fltr4img / sum(fltr4img(:))

% imgfltrd = filter2( fltr4img , rawimg )

% tic

% [accum, circen, cirrad] = CircularHough_Grd(imgfltrd, [15 80], 8, 10)

% toc

% figure(1)imagesc(accum)axis image

% title('Accumulation Array from Circular Hough Transform')

% figure(2)imagesc(rawimg)colormap('gray')axis image

% hold on

% plot(circen(:,1), circen(:,2), 'r+')

% for k = 1 : size(circen, 1),

% DrawCircle(circen(k,1), circen(k,2), cirrad(k), 32, 'b-')

% hold off

% title(['Raw Image with Circles Detected ', ...

% '(center positions and radii marked)'])

后续完整请参阅ilovematlab.cn/thread-74414-1-1.htmlO(∩_∩)O谢谢

1楼说的对，识别圆就用Hough圆检测函数cvHoughCircles()；至于识别颜色，无非就是写一个循环函数对每个像素判断，不麻烦。都不用二值化。

函数定义：CvSeq*cvHoughCircles(CvArr*image,void*circle_storage,

intmethod,doubledp,doublemin_dist,doubleparam1=100,doubleparam2=100,intmin_radius=0,intmax_radius=0)。

使用例子：

CvMemStorage*storage=cvCreateMemStorage(0)//定义存储器

cvCvtColor(img,gray,CV_BGR2GRAY)//将原图转换为灰度图处理

cvSmooth(gray,gray,CV_GAUSSIAN,9,9)//平滑图像

CvSeq*circles=cvHoughCircles(gray,storage,CV_HOUGH_GRADIENT,2,gray->height/4,200,100)//调用Hough圆检测函数，其中后面几个参数可以根据实际情况修改

inti//画出检测到的所有圆。

for(i=0i<circles->totali++)

{

float*p=(float*)cvGetSeqElem(circles,i)

cvCircle(img,cvPoint(cvRound(p[0]),cvRound(p[1])),3,

CV_RGB(0,255,0),-1,8,0)

cvCircle(img,cvPoint(cvRound(p[0]),cvRound(p[1])),

cvRound(p[2]),CV_RGB(255,0,0),3,8,0)

}

---