Circular Hough Transform misses circles

Question

I've read a lot about the Circular Hough transform on Stack Overflow, but I seem to be missing something. I wrote a program that is supposed to detect the circles of a "Bull's Eye" target. However, even after playing with the parameters, the algorithm is quite bad - it ignores most of the circles and one time it finds a circle but seems to "wander off". I've even tried applying an "Unsharp Mask" to no avail. I have added my code, the image I started with and the output. I hope someone can point me at the right direction.

import cv2
import cv2.cv as cv
import numpy as np
import math
# Load Image
img = cv2.imread('circles1.png',0)
# Apply Unsharp Mask
tmp = cv2.medianBlur(img,5)
img = cv2.addWeighted(img,1.5,tmp,-0.5,0)
cimg = cv2.cvtColor(img,cv2.COLOR_GRAY2BGR)

# Hough Transform
circles = cv2.HoughCircles(img,cv.CV_HOUGH_GRADIENT,1,5,
                            param1=100,param2=100,minRadius=0,maxRadius=0)

circles = np.uint16(np.around(circles))

# Go over circles, eliminating the ones that are not cocentric enough
height, width = img.shape
center = (width/2,height/2)
for i in circles[0,:]:
    # draw the outer circle
    if math.sqrt((center[0]-i[0])**2 + (center[1]-i[1])**2) < 15:
        cv2.circle(cimg,(i[0],i[1]),i[2],(0,255,0),1)
        # 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()

Quick explanation: I load the image, apply Unsharp Mask, use the Hough Transfrom to detect circles, then draw the circles that are close to the center (I found that the other circles are false circles).

I tried playing with the parameters, and this is the best I got. I feel like this is a simple enough problem which has me buffled. I appriciate any help.

My input image:

My output image:

Answer 1

As I mentioned in my comment, you'll need to run successive iterations of cv2.HoughCircles for different range of radii to ensure that you get all of the circles. With the way the Circular Hough Transform works, specifying a minimum and maximum radius that has quite a large range will be inaccurate and will also be slow. They don't tell you this in the documentation, but for the Circular Hough Transform to work successfully, the following two things need to be valid:

maxRadius < 3*minRadius
maxRadius - minRadius < 100

With the above, blindly making the minimum radius very small and the maximum radius very large won't give you great results. Therefore, what you could do is start at... say...radius=1, then iterate up to radius=300 in steps of 20. Between each chunk of 20, run cv2.HoughCircles and update your image with these contours.

Doing this requires very little modification to your code. BTW, I removed the unsharp masking it because I was getting poor results with it. I also changed a couple of parameters in cv2.HoughCircles slightly to get this to work as best as possible given your situation:

import cv2
import cv2.cv as cv
import numpy as np
import math
# Load Image
img = cv2.imread('circles1.png',0)
cimg = cv2.cvtColor(img,cv2.COLOR_GRAY2BGR)

# Specify different radii
radii = np.arange(0,310,10)

# For each pair of radii...
for idx in range(len(radii)-1):
    # Get the minimum and maximum radius
    # Note you need to add 1 to each minimum
    # as the maximum of the previous pair covers this new minimum
    minRadius = radii[idx]+1
    maxRadius = radii[idx+1]

    # Hough Transform - Change here
    circles = cv2.HoughCircles(img,cv.CV_HOUGH_GRADIENT,1,5,
                               param1=25,param2=75,minRadius=minRadius,maxRadius=maxRadius)

    # Skip if no circles are detected - Change here
    if circles is None:
        continue

    circles = np.uint16(np.around(circles))

    # Go over circles, eliminating the ones that are not cocentric enough
    height, width = img.shape
    center = (width/2,height/2)
    for i in circles[0,:]:
        # draw the outer circle
        if math.sqrt((center[0]-i[0])**2 + (center[1]-i[1])**2) < 15:
            cv2.circle(cimg,(i[0],i[1]),i[2],(0,255,0),1)
            # 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()

I get this figure:

Unfortunately it isn't perfect as it doesn't detect all of the circles. You'll have to play around with the cv2.HoughCircles function until you get good results.

---

However, I wouldn't recommend using cv2.HoughCircles here. May I suggest using cv2.findContours instead? This finds all of the contours in the image. In this case, these will be the black circles. However, you need to reverse the image because cv2.findContours assumes non-zero pixels are object pixels, so we can subtract 255 from the image assuming a np.uint8 type:

# Make copy of original image
cimg2 = cv2.cvtColor(img, cv2.COLOR_GRAY2BGR)

# Find contours
contours,_ = cv2.findContours(255 - img, cv2.RETR_LIST, cv.CV_CHAIN_APPROX_NONE)

# Draw all detected contours on image in green with a thickness of 1 pixel
cv2.drawContours(cimg2, contours, -1, color=(0,255,0), thickness=1)

# Show the image
cv2.imshow('detected circles', cimg2)
cv2.waitKey(0)
cv2.destroyAllWindows()

This is what I get: