[FIXED] How to identify a group of pixels as approximately rectangular?

Issue

What is the mathematical logic to consider the group of pixels on left as rectangular?

Solution

Here's the implementation of the idea in the comments. The approach is:

1. Find the rotated rectangular bounding box
2. Calculate the area of this rotated bounding box and the area of the contour
3. Compare the two. If the area of the contour is say at least 80% (or any arbitrary threshold value) of the rotated bounding box area then we consider it as rectangular

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Here's a visualization of the image processing pipeline

Input image -> Threshold -> Detected rotated rectangular bounding box -> Mask

Contour area: 17719.0
Mask area: 20603.0
Compared area percentage: 86.002%
It is a rectangle!

For the other image

Input image -> Threshold -> Detected rotated rectangular bounding box -> Mask

Contour area: 13395.5
Mask area: 19274.5
Compared area percentage: 69.499%
It is not a rectangle!

You didn't specify a language, so here's a simple implementation using Python OpenCV

import cv2
import numpy as np

# Load image, convert to grayscale, Otsu's threshold for binary image
image = cv2.imread('1.png')
mask = np.zeros(image.shape, dtype=np.uint8)
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
thresh = cv2.threshold(gray, 0, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)[1]

# Find contours, find rotated rectangle, find contour area
cnts = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
cnts = cnts[0] if len(cnts) == 2 else cnts[1]
contour_area = cv2.contourArea(cnts[0])
print('Contour area: {}'.format(contour_area))
rect = cv2.minAreaRect(cnts[0])
box = np.int0(cv2.boxPoints(rect))
cv2.drawContours(image, [box], 0, (36,255,12), 3)

# Find area of rotated bounding box and draw onto mask image
mask_area = cv2.contourArea(box)
cv2.drawContours(mask, [box], 0, (255,255,255), -1)
print('Mask area: {}'.format(mask_area))

# Compare areas and calculate percentage
rectangular_threshold = 80
percentage = (contour_area / mask_area) * 100
print('Compared area percentage: {:.3f}%'.format(percentage))
if percentage > rectangular_threshold:
    print('It is a rectangle!')
else:
    print('It is not a rectangle!')

# Display
cv2.imshow('image', image)
cv2.imshow('thresh', thresh)
cv2.imshow('mask', mask)
cv2.waitKey()

Answered By - nathancy

Answer Checked By - Senaida (PHPFixing Volunteer)