computer vision - Counting small circles in an image

Question

The image below has many circles. Click and zoom in to see the circles.

https://drive.google.com/open?id=1ox3kiRX5hf2tHDptWfgcbMTAHKCDizSI

What I want is counting the circles using any free language, such as python.

Is there a function or idea to do it?

Answer 1

Edit: I came up with a better solution, partially inspired by this answer below. I thought of this method originally (as noted in the OP comments) but I decided against it. The original image was just not good enough quality for it. However I improved that method and it works brilliantly for the better quality image. The original approach is first, and then the new approach at the bottom.

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First approach

So here's a general approach that seems to work well, but definitely just gives estimates. This assumes that circles are roughly the same size.

First, the image is mostly blue---so it seems reasonable to just do the analysis on the blue channel. Thresholding the blue channel, in this case, using Otsu thresholding (which determines an optimal threshold value without input) seems to work very well. This isn't too much of a surprise since the distribution of color values is pretty much binary. Check the mask that results from it!

Then, do a connected component analysis on the mask to get the area of each component (component = white blob in the mask). The statistics returned from connectedComponentsWithStats() give (among other things) the area, which is exactly what we need. Then we can simply count the circles by estimating how many circles fit in a given component based on its area. Also note that I'm taking the statistics for every label except the first one: this is the background label 0, and not any of the white blobs.

Now, how large in area is a single circle? It would be best to let the data tell us. So you could compute a histogram of all the areas, and since there are more single circles than anything else, there will be a high concentration around 250-270 pixels or so for the area. Or you could just take an average of all the areas between something like 50 and 350 which should also get you in a similar ballpark.

Really in this histogram you can see the demarcations between single circles, double circles, triple, and so on quite easily. Only the larger components will give pretty rough estimates. And in fact, the area doesn't seem to scale exactly linearly. Blobs of two circles are slightly larger than two single circles, and blobs of three are larger still than three single circles, and so on, so this makes it a little difficult to estimate nicely, but rounding should still keep us close. If you want you could include a small multiplication parameter that increases as the area increases to account for that, but that would be hard to quantify without going through the histogram analytically...so, I didn't worry about this.

A single circle area divided by the average single circle area should be close to 1. And the area of a 5-circle group divided by the average circle area should be close to 5. And this also means that small insignificant components, that are 1 or 10 or even 100 pixels in area, will not count towards the total since round(50/avg_circle_size) < 1/2, so those will round down to a count of 0. Thus I should just be able to take all the component areas, divide them by the average circle size, round, and get to a decent estimate by summing them all up.

import cv2
import numpy as np

img = cv2.imread('circles.png')
mask = cv2.threshold(img[:, :, 0], 255, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)[1]

stats = cv2.connectedComponentsWithStats(mask, 8)[2]
label_area = stats[1:, cv2.CC_STAT_AREA]

min_area, max_area = 50, 350  # min/max for a single circle
singular_mask = (min_area < label_area) & (label_area <= max_area)
circle_area = np.mean(label_area[singular_mask])

n_circles = int(np.sum(np.round(label_area / circle_area)))

print('Total circles:', n_circles)

This code is simple and effective for rough counts.

However, there are definitely some assumptions here about the groups of circles compared to a normal circle size, and there are issues where circles that are at the boundaries will not be counted correctly (these aren't well defined---a two circle blob that is half cut off will look more like one circle---no clear way to count or not count these with this method). Further I just used automatic thresholding via Otsu here; you could get (probably better) results with more careful color filtering. Additionally in the mask generated by Otsu, some circles that are masked have a few pixels removed from their center. Morphology could add these pixels back in, which would give you a (slightly larger) more accurate area for the single circle components. Either way, I just wanted to give the general idea towards how you could easily estimate this with minimal code.

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New approach

Before, the goal was to count circles. This new approach instead counts the centers of the circles. The general idea is you threshold and then flood fill from a background pixel to fill in the background (flood fill works like the paint bucket tool in photo editing apps), that way you only see the centers, as shown in this answer below.

However, this relies on global thresholding, which isn't robust to local lighting changes. This means that since some centers are brighter/darker than others, you won't always get good results with a single threshold.

Here I've created an animation to show looping through different threshold values; watch as some centers appear and disappear at different times, meaning you get different counts depending on the threshold you choose (this is just a small patch of the image, it happens everywhere):

Notice that the first blob to appear in the top left actually disappears as the threshold increases. However, if we actually OR each frame together, then each detected pixel persists:

But now every single speck appears, so we should clean up the mask each frame so that we remove single pixels as they come (otherwise they may build up and be hard to remove later). Simple morphological opening with a small kernel will remove them:

Applied over the whole image, this method works incredibly well and finds almost every single cell. There are only three false positives (detected blob that's not a center) and two misses I can spot, and the code is very simple. The final thing to do after the mask has been created is simply count the components, minus one for the background. The only user input required here is a single point to flood fill from that is in the background (seed_pt in the code).

img = cv2.imread('circles.png', 0)
seed_pt = (25, 25)
fill_color = 0
mask = np.zeros_like(img)
kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (3, 3))
for th in range(60, 120):
    prev_mask = mask.copy()
    mask = cv2.threshold(img, th, 255, cv2.THRESH_BINARY)[1]
    mask = cv2.floodFill(mask, None, seed_pt, fill_color)[1]
    mask = cv2.bitwise_or(mask, prev_mask)
    mask = cv2.morphologyEx(mask, cv2.MORPH_OPEN, kernel)

n_centers = cv2.connectedComponents(mask)[0] - 1
print('There are %d cells in the image.'%n_centers)

There are 874 cells in the image.