Hough transform : Circle

The classical Hough transform was developed to identify lines in the image, but later the Hough transform has been extended to identify the positions of arbitrary shapes, most commonly circles or ellipses.

"In many cases an edge detector can be used as a pre-processing stage to obtain image points or image pixels that are on the desired curve in the image space. Due to imperfections in either the image data or the edge detector, however, there may be missing points or pixels on the desired curves as well as spatial deviations between the ideal line/circle/ellipse and the noisy edge points as they are obtained from the edge detector. For these reasons, it is often non-trivial to group the extracted edge features to an appropriate set of lines, circles or ellipses. The purpose of the Hough transform is to address this problem by making it possible to perform groupings of edge points into object candidates by performing an explicit voting procedure over a set of parameterized image objects." - wiki - Hough transform.

A circle can be fully defined with three parameters: the center coordinates ($a,ドル $b$) and the radius ($R$):

As the $\theta$ varies from 0ドル$ to 360ドル,ドル a complete circle of radius $R$ is created.

So with the Circle Hough Transform, we expect to find triplets of $(x, y, R)$ from the image. In other words, our purpose is to find those three parameters.

Therefore, we need to construct a 3D accumulator for Hough transform, which would be highly ineffective. So, OpenCV uses more trickier method, Hough Gradient Method which uses the gradient information of edges.

import cv2
import numpy as np
from matplotlib import pyplot as plt
bgr_img = cv2.imread('b.jpg') # read as it is
if bgr_img.shape[-1] == 3: # color image
 b,g,r = cv2.split(bgr_img) # get b,g,r
 rgb_img = cv2.merge([r,g,b]) # switch it to rgb
 gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY)
else:
 gray_img = bgr_img
img = cv2.medianBlur(gray_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)
plt.subplot(121),plt.imshow(rgb_img)
plt.title('Input Image'), plt.xticks([]), plt.yticks([])
plt.subplot(122),plt.imshow(cimg)
plt.title('Hough Transform'), plt.xticks([]), plt.yticks([])
plt.show()

The function we use here is cv2.HoughCircles(). It has plenty of arguments which are well explained in the documentation. So we directly go to the code.

So far so good.

In the following cases, however, the Hough transform finds hidden circles which are not meant to be perceived as circles:

In this Crescent case, we can make it better by blurring more:

img = cv2.medianBlur(gray_img,5) => img = cv2.medianBlur(gray_img,25)

In general, without blurring, the algorithms tends to extract too many circular features. So, to be more successful, the prepocessing seems to be crucial.

With blurring value 51:

img = cv2.medianBlur(gray_img,51)

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