Pixel per mm calculation of an image using camera calibration matrix and object distance is not same as pixel dimension of object in MS Paint - opencv

Question

I want to calculate number of pixels per grid (i.e. pixels per 11 mm) of the checkerboard. I am doing this to validate that mm/pixel calculation I obtain using calibration matrix and formula (below) is same as what I will see when I open the image in MS Paint.
For the checkerboard image (1920x1080 resolution): 11 grid x 7 grid in size with each grid as 11x 11 mm, at a distance of 500 mm (picture below).
I compute a calibration matrix using code:
import cv2
import numpy as np
import pathlib
#from utils import *
import glob
from argparse import ArgumentParser
topview_image_path = 'checkerboard_top\*.png'
camera_orientation = 'topview'
if camera_orientation == 'topview':
image_path = topview_image_path
def calibrate_chessboard(folder):
# Defining the dimensions of checkerboard
CHECKERBOARD = (6,9)
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
# Creating vector to store vectors of 3D points for each checkerboard image
objpoints = []
# Creating vector to store vectors of 2D points for each checkerboard image
imgpoints = []
# Defining the world coordinates for 3D points
objp = np.zeros((1, CHECKERBOARD[0] * CHECKERBOARD[1], 3), np.float32)
objp[0,:,:2] = np.mgrid[0:CHECKERBOARD[0], 0:CHECKERBOARD[1]].T.reshape(-1, 2)
prev_img_shape = None
# Extracting path of individual image stored in a given directory
print("image path:", image_path)
images = glob.glob(image_path)
#images = glob.glob(f'{folder}/*.png')
# if len(images) == 0:
# images = glob.glob(f'{folder}/*.jpg')
# print(images)
for fname in images:
img = cv2.imread(fname)
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
# Find the chess board corners
# If desired number of corners are found in the image then ret = true
ret, corners = cv2.findChessboardCorners(gray, CHECKERBOARD, cv2.CALIB_CB_ADAPTIVE_THRESH + cv2.CALIB_CB_FAST_CHECK + cv2.CALIB_CB_NORMALIZE_IMAGE)
"""
If desired number of corner are detected,
we refine the pixel coordinates and display
them on the images of checker board
"""
if ret == True:
objpoints.append(objp)
# refining pixel coordinates for given 2d points.
corners2 = cv2.cornerSubPix(gray, corners, (11,11),(-1,-1), criteria)
imgpoints.append(corners2)
# Draw and display the corners
img = cv2.drawChessboardCorners(img, CHECKERBOARD, corners2, ret)
cv2.imshow('img',img)
cv2.waitKey(0)
cv2.destroyAllWindows()
h,w = img.shape[:2]
"""
Performing camera calibration by
passing the value of known 3D points (objpoints)
and corresponding pixel coordinates of the
detected corners (imgpoints)
"""
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
return [ret, mtx, dist, rvecs, tvecs]
if __name__ == '__main__':
parser = ArgumentParser()
parser.add_argument('--type', dest='type',type=str, default='topview',help='is the image topview or sideview?')
parser.add_argument('--folder', dest='folder',type=str, default='cal_images/checkerboard_topview',help='is the image topview or sideview?')
args = parser.parse_args()
WIDTH = 6
HEIGHT = 9
# Calibrate
ret, mtx, dist, rvecs, tvecs = calibrate_chessboard(args.folder)
print(mtx)
print(dist)
mtx_list = ["calibration matrix:\n", str(mtx),
"\ndistortion matrix:", str(dist)]
txt_file = "matrix_" + camera_orientation +".txt"
with open(txt_file, mode='wt', encoding='utf-8') as myfile:
myfile.write('\n'.join(mtx_list))
and get the calibration matrix as:
M = [[2.86276094e+03 0.00000000e+00 8.23315889e+02]
[0.00000000e+00 2.86846709e+03 5.80987675e+02]
[0.00000000e+00 0.00000000e+00 1.00000000e+00]]
This gives me the focal length (f) in pixel units (M[0][0]) i.e. 2862.
I then calculate size in pixels (X_sizepx) of the checkerboard grid 11 mm (X_sizemm) object at distance Z (in my case 500mm) using formula:
X_sizepx = (f/Z) * X_sizemm
Substituting all the values: f = 2862, Z =500, X_sizemm = 11, I get 62.94. So as per opencv calibration and the formula, 11mm should ~63 pixels.
I then open the checkerboard image in MS paint to see the pixel dimension of the square grid in pixels and it says 41 pixels (image below).
This is a big difference if I were to use camera calibration matrix and the the formula. Is there something I am doing wrong?
Note: Z can never be more than 530 mm if I were to assume that Z might be slightly off.