How do I find the largest empty space in such images?

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I would like to find the empty spaces (black regions) in images similar to the one I've posted below, where I have randomly sized blocks scattered in it.

enter image description here

By empty spaces, I refer to such possible open fields ( i have no particular lower bound on the area, but I would like to extract the top 3-4 largest ones present in the image.) There is also no restriction on the geometric shape they can take, but these empty spaces must not contain any of the blue blocks.

enter image description here

What is the best way to go about this?

What I've done till now:

My original image actually looks like this. I identified all the points, grouped them based on a certain distance threshold and applied a convex hull around them. I'm unsure how to proceed further. Any help would be greatly appreciated. Thank you!

enter image description here

opencv image-processing algorithm python
1 Answers

Here is one way in Python/OpenCV using the distance transform to find the largest Euclidean distance between the Xs.

Input:

enter image description here

import cv2
import numpy as np
import skimage.exposure

# read image
img = cv2.imread('xxx.png')

# convert to gray
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

# threshold to binary and invert so background is white and xxx are black
thresh = cv2.threshold(gray, 128, 255, cv2.THRESH_BINARY)[1]
thresh = 255 - thresh

# add black border around threshold image to avoid corner being largest distance
thresh2 = cv2.copyMakeBorder(thresh, 1,1,1,1, cv2.BORDER_CONSTANT, (0))
h, w = thresh2.shape

# create zeros mask 2 pixels larger in each dimension
mask = np.zeros([h + 2, w + 2], np.uint8)

# apply distance transform
distimg = thresh2.copy()
distimg = cv2.distanceTransform(distimg, cv2.DIST_L2, 5)

# remove excess border
distimg = distimg[1:h-1, 1:w-1]

# get max value and location in distance image
min_val, max_val, min_loc, max_loc = cv2.minMaxLoc(distimg)

# scale distance image for viewing
distimg = skimage.exposure.rescale_intensity(distimg, in_range='image', out_range=(0,255))
distimg = distimg.astype(np.uint8)

# draw circle on input
result = img.copy()
centx = max_loc[0]
centy = max_loc[1]
radius = int(max_val)
cv2.circle(result, (centx, centy), radius, (0,0,255), 1)
print('center x,y:', max_loc,'center radius:', max_val)

# save image
cv2.imwrite('xxx_distance.png',distimg)
cv2.imwrite('xxx_radius.png',result)

# show the images
cv2.imshow("thresh", thresh)
cv2.imshow("thresh2", thresh2)
cv2.imshow("distance", distimg)
cv2.imshow("result", result)
cv2.waitKey(0)
cv2.destroyAllWindows()

Distance Transform Image:

enter image description here

Region of Largest Distance to Xs:

enter image description here

Textual Information:

center x,y: (179, 352) radius: 92.5286865234375

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