Hough Circle Transform

Goals

In this chapter:

We will learn to use Hough Transform to find circles in an image.
We will see these functions: cv2.HoughCircles()

Theory

A circle is represented mathematically as:

(x - x_center)² + (y - y_center)² = r²

where (x_center, y_center) is the center of the circle, and r is the radius. From the equation, we can see we have 3 parameters, so we need a 3D accumulator for hough transform, which would be highly ineffective. So OpenCV uses a more trickier method, Hough Gradient Method, which uses the gradient information of edges.

Hough Circle Transform in OpenCV

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:

import numpy as np
import cv2 as cv

img = cv.imread('opencv-logo-white.png', cv.IMREAD_GRAYSCALE)
assert img is not None, "file could not be read, check with os.path.exists()"
img = cv.medianBlur(img, 5)
cimg = cv.cvtColor(img, cv.COLOR_GRAY2BGR)

circles = cv.HoughCircles(img, cv.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
    cv.circle(cimg, (i[0], i[1]), i[2], (0, 255, 0), 2)
    # draw the center of the circle
    cv.circle(cimg, (i[0], i[1]), 2, (0, 0, 255), 3)

cv.imshow('detected circles', cimg)
cv.waitKey(0)
cv.destroyAllWindows()

Function Parameters

image: 8-bit, single-channel, grayscale input image.
method: Detection method — currently only cv2.HOUGH_GRADIENT is supported.
dp: Inverse ratio of the accumulator resolution to the image resolution. For example, dp=1 means the accumulator has the same resolution as the input image, dp=2 means half as big.
minDist: Minimum distance between the centers of the detected circles. Too small a value may result in multiple circles being detected; too large a value may miss some circles.
param1: First method-specific parameter. For HOUGH_GRADIENT, it is the higher threshold of the two passed to Canny edge detector (the lower one is twice smaller).
param2: Second method-specific parameter. For HOUGH_GRADIENT, it is the accumulator threshold. Smaller value means more (false) circles may be detected.
minRadius: Minimum circle radius.
maxRadius: Maximum circle radius.