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Camera calibration with OpenCV
2022-06-27 18:49:00 【51CTO】
List of articles
- What is camera calibration , Why is it important ？
- Why use a chessboard ？
- Use OpenCV Perform camera calibration
- Print chessboard
- Measure the length of the square
- Take pictures of the chessboard from different distances and directions
- Find the corner
- Write a for camera calibration Python Code
- Output
What is camera calibration , Why is it important ？
The job of the camera is to convert the light that shines on its image sensor into an image . An image consists of picture elements called pixels .
In a perfect world , These pixels （ That is, what the camera sees ） It looks exactly like what you see in the real world . However , No camera is perfect . They all contain physical defects , In some cases, it will cause serious distortion .
for example , See the following extreme example of image distortion .
This is the same image after calibrating the camera and correcting the distortion .
Do you see that this can cause problems …… Especially in the precision critical robot technology ？
Imagine , You have a mechanical arm working in the warehouse . Its job is to pick up items from the conveyor belt and put them into the dustbin .
To help the robot determine the exact location of the object , There is a camera at the top . To obtain accurate conversion between camera pixel coordinates and real-world coordinates , You need to calibrate the camera to eliminate any distortion .
The two most important forms of distortion are radial distortion and tangential distortion .
Radial distortion occurs when the line appears to be bent . The following is an example of a radial distortion called barrel distortion . Notice that the bulge in the image makes the line （ In the real world ） It looks bent .
When the camera lens is not completely parallel to the camera sensor , Tangential distortion will occur . Tangential distortion makes the real world look stretched or tilted . It can also make objects look closer than in real life .
In order to accurately represent the real world on the camera , We have to calibrate the camera . We want to know , When we see an object of a certain size in the real world , This size is converted to a known size in the camera pixel coordinates .
for example , By calibrating the camera , We can make the manipulator have better “ Hands and eyes ” The coordinated ability . You can also let autonomous vehicle know pedestrians 、 The position of dogs and other objects relative to cars .
Calibrating the camera is done using a known real-world mode （ For example, chessboard ） To estimate the external parameters of camera lens and image （ Rotation and translation vectors ） And internal parameters （ For example, focal length 、 Optical center, etc ） Process sensors , To reduce distortion errors caused by camera defects .
These parameters include ：
- The focal length
- Images （ Namely optics ） center （ Usually not entirely in （ Width /2, Height /2） It's about ）
- Scaling factor for pixels along rows and columns
- skewness factor
- Lens distortion
Why use a chessboard ？
Checkerboard calibration is a standard technique , Used to perform camera calibration and estimate the values of unknown parameters I mentioned in the previous section .
OpenCV There is a checkerboard calibration Library , It tries to put the real world on the chessboard 3D Points map to 2D Camera coordinates . This information is then used to correct the distortion .
Please note that , You can use any object （ book 、 laptop 、 Automobile, etc ）, But the chessboard has unique characteristics , It is very suitable for correcting camera distortion ：
- It's flat , So you don't have to deal with z Axis （z=0）, Just deal with x and y Axis . All the points on the chessboard are on the same plane .
- There are clear corners and points , It's easy to put 3D Points in the real world coordinate system are mapped to the camera 2D A point in a pixel coordinate system .
- Points and angles appear on a straight line .
Use OpenCV Perform camera calibration
Print chessboard
The first step is to take a chessboard and print it on a regular A4 Size paper . You can learn from OpenCV Download this... From the documentation pdf Official chessboard , Then print it out .
Measure the length of the square
Measure the side length of one of the squares . As far as I'm concerned , I measured 2.3 centimeter （0.023 rice ）.
Take pictures of the chessboard from different distances and directions
We need to shoot at least from different distances and directions 10 A picture of a chessboard . I will shoot 19 A picture , So that my algorithm will have a large number of input images for performing camera calibration .
Tape the chessboard onto a flat solid object .
Taking pictures , Then move them to a directory on your computer .
Here are some examples of photos I took ：
Find the corner
use Python Write the following code . You can copy and paste this code into your favorite IDE in . Select a checkerboard image as the test case . I named the file draw_corners.py. This code will draw a corner on the input chessboard image , Then save the drawing to an image file .
import
cv2
# Import the OpenCV library to enable computer vision
import
numpy
as
np
# Import the NumPy scientific computing library
# Author: Addison Sears-Collins
# https://automaticaddison.com
# Description: Detect corners on a chessboard
filename
=
'chessboard_input1.jpg'
# Chessboard dimensions
number_of_squares_X
=
10
# Number of chessboard squares along the x-axis
number_of_squares_Y
=
7
# Number of chessboard squares along the y-axis
nX
=
number_of_squares_X
-
1
# Number of interior corners along x-axis
nY
=
number_of_squares_Y
-
1
# Number of interior corners along y-axis
def
main():
# Load an image
image
=
cv2.
imread(
filename)
# Convert the image to grayscale
gray
=
cv2.
cvtColor(
image,
cv2.
COLOR_BGR2GRAY)
# Find the corners on the chessboard
success,
corners
=
cv2.
findChessboardCorners(
gray, (
nY,
nX),
None)
# If the corners are found by the algorithm, draw them
if
success
==
True:
# Draw the corners
cv2.
drawChessboardCorners(
image, (
nY,
nX),
corners,
success)
# Create the output file name by removing the '.jpg' part
size
=
len(
filename)
new_filename
=
filename[:
size
-
4]
new_filename
=
new_filename
+
'_drawn_corners.jpg'
# Save the new image in the working directory
cv2.
imwrite(
new_filename,
image)
# Display the image
cv2.
imshow(
"Image",
image)
# Display the window until any key is pressed
cv2.
waitKey(
0)
# Close all windows
cv2.
destroyAllWindows()
main()
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Write a for camera calibration Python Code
Now we know how to recognize the corners on the chessboard , Let's write code to perform camera calibration .
This is the code. . I put the distorted image in my working directory named “ Distortion ” In the folder of . This folder is where the output is saved undistorted .
Don't be afraid of how long the code is . To make it easier for everyone to understand each line , I put a lot of notes here . Just copy and paste the code into your favorite text editor or IDE Then you can . I named the file camera_calibration.py.
# Author: Addison Sears-Collins
# https://automaticaddison.com
# Description: Perform camera calibration using a chessboard.
import
cv2
# Import the OpenCV library to enable computer vision
import
numpy
as
np
# Import the NumPy scientific computing library
import
glob
# Used to get retrieve files that have a specified pattern
# Path to the image that you want to undistort
distorted_img_filename
=
'distorted/chessboard_input12.jpg'
# Chessboard dimensions
number_of_squares_X
=
10
# Number of chessboard squares along the x-axis
number_of_squares_Y
=
7
# Number of chessboard squares along the y-axis
nX
=
number_of_squares_X
-
1
# Number of interior corners along x-axis
nY
=
number_of_squares_Y
-
1
# Number of interior corners along y-axis
# Store vectors of 3D points for all chessboard images (world coordinate frame)
object_points
= []
# Store vectors of 2D points for all chessboard images (camera coordinate frame)
image_points
= []
# Set termination criteria. We stop either when an accuracy is reached or when
# we have finished a certain number of iterations.
criteria
= (
cv2.
TERM_CRITERIA_EPS
+
cv2.
TERM_CRITERIA_MAX_ITER,
30,
0.001)
# Define real world coordinates for points in the 3D coordinate frame
# Object points are (0,0,0), (1,0,0), (2,0,0) ...., (5,8,0)
object_points_3D
=
np.
zeros((
nX
*
nY,
3),
np.
float32)
# These are the x and y coordinates
object_points_3D[:,:
2]
=
np.
mgrid[
0:
nY,
0:
nX].
T.
reshape(
-
1,
2)
def
main():
# Get the file path for images in the current directory
images
=
glob.
glob(
'*.jpg')
# Go through each chessboard image, one by one
for
image_file
in
images:
# Load the image
image
=
cv2.
imread(
image_file)
# Convert the image to grayscale
gray
=
cv2.
cvtColor(
image,
cv2.
COLOR_BGR2GRAY)
# Find the corners on the chessboard
success,
corners
=
cv2.
findChessboardCorners(
gray, (
nY,
nX),
None)
# If the corners are found by the algorithm, draw them
if
success
==
True:
# Append object points
object_points.
append(
object_points_3D)
# Find more exact corner pixels
corners_2
=
cv2.
cornerSubPix(
gray,
corners, (
11,
11), (
-
1,
-
1),
criteria)
# Append image points
image_points.
append(
corners)
# Draw the corners
cv2.
drawChessboardCorners(
image, (
nY,
nX),
corners_2,
success)
# Display the image. Used for testing.
#cv2.imshow("Image", image)
# Display the window for a short period. Used for testing.
#cv2.waitKey(200)
# Now take a distorted image and undistort it
distorted_image
=
cv2.
imread(
distorted_img_filename)
# Perform camera calibration to return the camera matrix, distortion coefficients, rotation and translation vectors etc
ret,
mtx,
dist,
rvecs,
tvecs
=
cv2.
calibrateCamera(
object_points,
image_points,
gray.
shape[::
-
1],
None,
None)
# Get the dimensions of the image
height,
width
=
distorted_image.
shape[:
2]
# Refine camera matrix
# Returns optimal camera matrix and a rectangular region of interest
optimal_camera_matrix,
roi
=
cv2.
getOptimalNewCameraMatrix(
mtx,
dist,
(
width,
height),
1,
(
width,
height))
# Undistort the image
undistorted_image
=
cv2.
undistort(
distorted_image,
mtx,
dist,
None,
optimal_camera_matrix)
# Crop the image. Uncomment these two lines to remove black lines
# on the edge of the undistorted image.
#x, y, w, h = roi
#undistorted_image = undistorted_image[y:y+h, x:x+w]
# Display key parameter outputs of the camera calibration process
print(
"Optimal Camera matrix:")
print(
optimal_camera_matrix)
print(
"\n Distortion coefficient:")
print(
dist)
print(
"\n Rotation Vectors:")
print(
rvecs)
print(
"\n Translation Vectors:")
print(
tvecs)
# Create the output file name by removing the '.jpg' part
size
=
len(
distorted_img_filename)
new_filename
=
distorted_img_filename[:
size
-
4]
new_filename
=
new_filename
+
'_undistorted.jpg'
# Save the undistorted image
cv2.
imwrite(
new_filename,
undistorted_image)
# Close all windows
cv2.
destroyAllWindows()
main()
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Output
This is the original distorted image .
This is an undistorted image , The output . Please note that , The distorted image has the same size as the undistorted image . Both images are 600 x 450 Pixels .
The correction is very subtle , So it may be difficult to see （ My camera must be very good ！）. As you see below gif As seen in , When I flip back and forth between two images , The effect will be more obvious .
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