Detect touching/overlapping circles/ellipses with OpenCV and Python

Question

i want to measure the circularity of circles (difference of the "circles" height and width or ellipse parameters). The circles are given in pictures as shown here:

After doing usual stuff like color2gray, thresholding and border detection, I get the following picture as shown:

With this, I already tried a lot of different things:

• List item Watershed with findContour (similar to this question) -> openCV detects the space between the circles as a closed contour and not the circles since they stick together not forming a closed contour
• same problem with fitEllipse. I get ellipses fitted on the black background contour and not in between.
• just trying to apply hough transforamtion (as in the code and the third picture shown) as well leads to strange results:

See the code here:

import sys
import cv2
import numpy
from scipy.ndimage import label

# Application entry point
#img = cv2.imread("02_adj_grey.jpg")
img = cv2.imread("fuss02.jpg")

# Pre-processing.
img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)    
cv2.imwrite("SO_0_gray.png", img_gray)

#_, img_bin = cv2.threshold(img_gray, 0, 255, cv2.THRESH_OTSU | cv2.THRESH_BINARY)
_, img_bin = cv2.threshold(img_gray, 170, 255, cv2.THRESH_BINARY)
cv2.imwrite("SO_1_threshold.png", img_bin)

#blur = cv2.GaussianBlur(img,(5,5),0)
img_bin = cv2.morphologyEx(img_bin, cv2.MORPH_CLOSE, numpy.ones((3, 3), dtype=int))
cv2.imwrite("SO_2_img_bin_morphoEx.png", img_bin)

border = img_bin - cv2.erode(img_bin, None)
cv2.imwrite("SO_3_border.png", border)


circles = cv2.HoughCircles(border,cv2.cv.CV_HOUGH_GRADIENT,50,80, param1=80,param2=40,minRadius=10,maxRadius=150)
print circles

cimg = img
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.putText(cimg,str(i[0])+str(',')+str(i[1]), (i[0],i[1]), cv2.FONT_HERSHEY_SIMPLEX, 0.4, 255)

cv2.imwrite("SO_8_cimg.png", cimg)

Does anyone have an idea to improve my algorhitm or a complete different approach? I have been trying many different approaches but without luck so far. Thanks everyone for your help.

Answer 1

Here's my attempt at detecting the circles. In summary

• perform a BGR->HSV conversion and use the V channel for processing

V channel:

• threshold, apply morphological closing, then take the distance transform (I'll call it dist)

dist image:

• create a template. From the sizes of the circles in the image, a ~75 pixel radius disk looks reasonable. Take its distance transform and use it as the template (I'll call it temp)

temp image:

• perform template matching: dist * temp

dist * temp image:

• find the local maxima of the resulting image. Location of the maxima correspond to circle centers and max values correspond to their radii

Thresholding template matched image:

Detecting circles as local maxima:

I did this in C++ as I'm most comfortable with it. I think you can easily convert this to python if you find this useful. Note that the above images are not to scale. Hope this helps.

EDIT: Added the Python version

C++:

    double min, max;
    Point maxLoc;

    Mat im = imread("04Bxy.jpg");
    Mat hsv;
    Mat channels[3];
    // bgr -> hsv
    cvtColor(im, hsv, CV_BGR2HSV);
    split(hsv, channels);
    // use v channel for processing
    Mat& ch = channels[2];
    // apply Otsu thresholding
    Mat bw;
    threshold(ch, bw, 0, 255, CV_THRESH_BINARY | CV_THRESH_OTSU);
    // close small gaps
    Mat kernel = getStructuringElement(MORPH_ELLIPSE, Size(3, 3));
    Mat morph;
    morphologyEx(bw, morph, CV_MOP_CLOSE, kernel);
    // take distance transform
    Mat dist;
    distanceTransform(morph, dist, CV_DIST_L2, CV_DIST_MASK_PRECISE);
    // add a black border to distance transformed image. we are going to do
    // template matching. to get a good match for circles in the margin, we are adding a border
    int borderSize = 75;
    Mat distborder(dist.rows + 2*borderSize, dist.cols + 2*borderSize, dist.depth());
    copyMakeBorder(dist, distborder, 
            borderSize, borderSize, borderSize, borderSize, 
            BORDER_CONSTANT | BORDER_ISOLATED, Scalar(0, 0, 0));
    // create a template. from the sizes of the circles in the image, 
    // a ~75 radius disk looks reasonable, so the borderSize was selected as 75
    Mat distTempl;
    Mat kernel2 = getStructuringElement(MORPH_ELLIPSE, Size(2*borderSize+1, 2*borderSize+1));
    // erode the ~75 radius disk a bit
    erode(kernel2, kernel2, kernel, Point(-1, -1), 10);
    // take its distance transform. this is the template
    distanceTransform(kernel2, distTempl, CV_DIST_L2, CV_DIST_MASK_PRECISE);
    // match template
    Mat nxcor;
    matchTemplate(distborder, distTempl, nxcor, CV_TM_CCOEFF_NORMED);
    minMaxLoc(nxcor, &min, &max);
    // threshold the resulting image. we should be able to get peak regions.
    // we'll locate the peak of each of these peak regions
    Mat peaks, peaks8u;
    threshold(nxcor, peaks, max*.5, 255, CV_THRESH_BINARY);
    convertScaleAbs(peaks, peaks8u);
    // find connected components. we'll use each component as a mask for distance transformed image,
    // then extract the peak location and its strength. strength corresponds to the radius of the circle
    vector<vector<Point>> contours;
    vector<Vec4i> hierarchy;
    findContours(peaks8u, contours, hierarchy, CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE, Point(0, 0));
    for(int idx = 0; idx >= 0; idx = hierarchy[idx][0])
    {
        // prepare the mask
        peaks8u.setTo(Scalar(0, 0, 0));
        drawContours(peaks8u, contours, idx, Scalar(255, 255, 255), -1);
        // find the max value and its location in distance transformed image using mask
        minMaxLoc(dist, NULL, &max, NULL, &maxLoc, peaks8u);
        // draw the circles
        circle(im, maxLoc, (int)max, Scalar(0, 0, 255), 2);
    }

Python:

import cv2

im = cv2.imread('04Bxy.jpg')
hsv = cv2.cvtColor(im, cv2.COLOR_BGR2HSV)
th, bw = cv2.threshold(hsv[:, :, 2], 0, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU)
kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (3, 3))
morph = cv2.morphologyEx(bw, cv2.MORPH_CLOSE, kernel)
dist = cv2.distanceTransform(morph, cv2.cv.CV_DIST_L2, cv2.cv.CV_DIST_MASK_PRECISE)
borderSize = 75
distborder = cv2.copyMakeBorder(dist, borderSize, borderSize, borderSize, borderSize, 
                                cv2.BORDER_CONSTANT | cv2.BORDER_ISOLATED, 0)
gap = 10                                
kernel2 = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (2*(borderSize-gap)+1, 2*(borderSize-gap)+1))
kernel2 = cv2.copyMakeBorder(kernel2, gap, gap, gap, gap, 
                                cv2.BORDER_CONSTANT | cv2.BORDER_ISOLATED, 0)
distTempl = cv2.distanceTransform(kernel2, cv2.cv.CV_DIST_L2, cv2.cv.CV_DIST_MASK_PRECISE)
nxcor = cv2.matchTemplate(distborder, distTempl, cv2.TM_CCOEFF_NORMED)
mn, mx, _, _ = cv2.minMaxLoc(nxcor)
th, peaks = cv2.threshold(nxcor, mx*0.5, 255, cv2.THRESH_BINARY)
peaks8u = cv2.convertScaleAbs(peaks)
contours, hierarchy = cv2.findContours(peaks8u, cv2.RETR_CCOMP, cv2.CHAIN_APPROX_SIMPLE)
peaks8u = cv2.convertScaleAbs(peaks)    # to use as mask
for i in range(len(contours)):
    x, y, w, h = cv2.boundingRect(contours[i])
    _, mx, _, mxloc = cv2.minMaxLoc(dist[y:y+h, x:x+w], peaks8u[y:y+h, x:x+w])
    cv2.circle(im, (int(mxloc[0]+x), int(mxloc[1]+y)), int(mx), (255, 0, 0), 2)
    cv2.rectangle(im, (x, y), (x+w, y+h), (0, 255, 255), 2)
    cv2.drawContours(im, contours, i, (0, 0, 255), 2)

cv2.imshow('circles', im)