Hough 圆环变换
目标
• 学习使用霍夫变换在图像中找圆形（环）。
• 学习函数：cv2.HoughCircles()。
原理
圆形的数学表达式为 ( x － x c e n t e r ) 2 {
{(x－{x}_{center})}^{2}} (x－xcenter)2+ ( y － y c e n t e r ) 2 {
{(y－{y}_{center})}^{2}} (y－ycenter)2 = r 2 {
{r}^{2}} r2，其中（ x c e n t e r {
{x}_{center}} xcenter, y c e n t e r {
{y}_{center}} ycenter）为圆心的坐标，r 为圆的直径。从这个等式中我可以看出：一个圆环需要 3个参数来确定。所以进行圆环霍夫变换的累加器必须是 3 维的，这样的话效率就会很低。所以 OpenCV 用来一个比较巧妙的办法，霍夫梯度法，它可以使用边界的梯度信息。
我们要使用的函数为 cv2.HoughCircles()。文档中对它的参数有详细的解释。这里我们就直接看代码吧。
# -*- coding: utf-8 -*-
"""
Created on Sat Jan 18 19:53:50 2014
@author: duan
"""
import cv2
import numpy as np
img = cv2.imread('opencv_logo.png',0)
img = cv2.medianBlur(img,5)
cimg = cv2.cvtColor(img,cv2.COLOR_GRAY2BGR)
circles = cv2.HoughCircles(img,cv2.HOUGH_GRADIENT,1,20,
param1=50,param2=30,minRadius=0,maxRadius=0)
circles = np.uint16(np.around(circles))
for i in circles[0,:]:
# draw the outer circle
cv2.circle(cimg,(i[0],i[1]),i[2],(0,255,0),2)
# draw the center of the circle
cv2.circle(cimg,(i[0],i[1]),2,(0,0,255),3)
cv2.imshow('detected circles',cimg)
cv2.waitKey(0)
cv2.destroyAllWindows()
#Python: cv2.HoughCircles(image, method, dp, minDist, circles, param1, param2, minRadius, maxRadius)
#Parameters:
#image – 8-bit, single-channel, grayscale input image.
# 返回结果为 Output vector of found circles. Each vector is encoded as a
#3-element floating-point vector (x, y, radius) .
#circle_storage – In C function this is a memory storage that will contain
#the output sequence of found circles.
#method – Detection method to use. Currently, the only implemented method is
#CV_HOUGH_GRADIENT , which is basically 21HT , described in [Yuen90].
#dp – Inverse ratio of the accumulator resolution to the image resolution.
#For example, if dp=1 , the accumulator has the same resolution as the input image.
#If dp=2 , the accumulator has half as big width and height.
#minDist – Minimum distance between the centers of the detected circles.
#If the parameter is too small, multiple neighbor circles may be falsely
#detected in addition to a true one. If it is too large, some circles may be missed.
#param1 – First method-specific parameter. In case of CV_HOUGH_GRADIENT ,
#it is the higher threshold of the two passed to the Canny() edge detector
# (the lower one is twice smaller).
#param2 – Second method-specific parameter. In case of CV_HOUGH_GRADIENT ,
# it is the accumulator threshold for the circle centers at the detection stage.
#The smaller it is, the more false circles may be detected. Circles,
# corresponding to the larger accumulator values, will be returned first.
#minRadius – Minimum circle radius.
#maxRadius – Maximum circle radius.
结果如下：
