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### How to find the location of a point in an image in millimeters using camera matrix?

I am using a standard 640x480 webcam. I have done Camera calibration in OpenCV in Python 3. This the Code I am using. The code is working and giving me the Camera Matrix and Distortion Coefficients successfully. Now, How can I find how many millimeters are there in 640 pixels in my scene image. I have attached the webcam above a table horizontally and on the table, a Robotic arm is placed. Using the camera I am finding the centroid of an object. Using Camera Matrix my goal is to convert the location of that object (e.g. 300x200 pixels) to the millimeter units so that I can give the millimeters to the robotic arm to pick that object. I have searched but not find any relevant information. Please tell me that is there any equation or method for that. Thanks a lot!

### How to find the location of a point in an image in millimeters using camera matrix?

I am using a standard 640x480 webcam. I have done Camera calibration in OpenCV in Python 3. This the Code I am using. The code is working and giving me the Camera Matrix and Distortion Coefficients successfully. Now, How can I find how many millimeters are there in 640 pixels in my scene image. I have attached the webcam above a table horizontally and on the table, a Robotic arm is placed. Using the camera I am finding the centroid of an object. Using Camera Matrix my goal is to convert the location of that object (e.g. 300x200 pixels) to the millimeter units so that I can give the millimeters to the robotic arm to pick that object. I have searched but not find any relevant information. Please tell me that is there any equation or method for that. Thanks a lot!

This is my Code:

import numpy as np
import cv2
import yaml
import os

# Parameters
n_row=4  #Checkerboard Rows
n_col=6  #Checkerboard Columns
n_min_img = 10 # number of images needed for calibration
square_size = 40  # size of each individual box on Checkerboard in mm
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001) # termination criteria
corner_accuracy = (11,11)
result_file = "./calibration.yaml"  # Output file having camera matrix

# prepare object points, like (0,0,0), (1,0,0), (2,0,0) ....,(n_row-1,n_col-1,0)
objp = np.zeros((n_row*n_col,3), np.float32)
objp[:,:2] = np.mgrid[0:n_row,0:n_col].T.reshape(-1,2) * square_size

# Intialize camera and window
camera = cv2.VideoCapture(0) #Supposed to be the only camera
if not camera.isOpened():
quit()
width = int(camera.get(cv2.CAP_PROP_FRAME_WIDTH))
height = int(camera.get(cv2.CAP_PROP_FRAME_HEIGHT))
cv2.namedWindow("Calibration")

# Usage
def usage():
print("Press on displayed window : \n")
print("[space]     : take picture")
print("[c]         : compute calibration")
print("[r]         : reset program")
print("[ESC]    : quit")

usage()
Initialization = True

while True:
if Initialization:
print("Initialize data structures ..")
objpoints = [] # 3d point in real world space
imgpoints = [] # 2d points in image plane.
n_img = 0
Initialization = False
tot_error=0

# Read from camera and display on windows
cv2.imshow("Calibration", img)
if not ret:
print("Cannot read camera frame, exit from program!")
camera.release()
cv2.destroyAllWindows()
break

# Wait for instruction
k = cv2.waitKey(50)

# SPACE pressed to take picture
if k%256 == 32:
imgGray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)

# Find the chess board corners
ret, corners = cv2.findChessboardCorners(imgGray, (n_row,n_col),None)

# If found, add object points, image points (after refining them)
if not ret:

else:
print("Chessboard corners successfully found.")
objpoints.append(objp)
n_img +=1
corners2 = cv2.cornerSubPix(imgGray,corners,corner_accuracy,(-1,-1),criteria)
imgpoints.append(corners2)

# Draw and display the corners
imgAugmnt = cv2.drawChessboardCorners(img, (n_row,n_col), corners2,ret)
cv2.imshow('Calibration',imgAugmnt)
cv2.waitKey(500)

# "c" pressed to compute calibration
elif k%256 == 99:
if n_img <= n_min_img:
print("Only ", n_img , " captured, ",  " at least ", n_min_img , " images are needed")

else:
print("Computing calibration ...")
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, (width,height),None,None)

if not ret:
print("Cannot compute calibration!")

else:
print("Camera calibration successfully computed")
# Compute reprojection errors
for i in range(len(objpoints)):
imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(imgpoints[i],imgpoints2, cv2.NORM_L2)/len(imgpoints2)
tot_error += error
print("Camera matrix: ", mtx)
print("Distortion coeffs: ", dist)
print("Total error: ", tot_error)
print("Mean error: ", np.mean(error))

# Saving calibration matrix
try:
os.remove(result_file)  #Delete old file first
except Exception as e:
#print(e)
pass
print("Saving camera matrix .. in ",result_file)
data={"camera_matrix": mtx.tolist(), "dist_coeff": dist.tolist()}
with open(result_file, "w") as f:
yaml.dump(data, f, default_flow_style=False)

# ESC pressed to quit
elif k%256 == 27:
print("Escape hit, closing...")
camera.release()
cv2.destroyAllWindows()
break
# "r" pressed to reset
elif k%256 ==114:
print("Reset program...")
Initialization = True


This the Camera Matrix:

818.6   0     324.4
0      819.1  237.9
0       0      1


Distortion coeffs:

0.34  -5.7  0  0  33.45