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Machine Vision

OpenCV calibrateCamera: Acceptable Return Values

By Jan on 03/12/2025

Learn how to evaluate the re-projection error from cv::calibrateCamera in OpenCV and determine if your camera calibration is successful.

OpenCV calibrateCamera: Acceptable Return Values

Table of Contents

Introduction

Camera calibration is a crucial step in computer vision applications, ensuring that your camera's intrinsic and extrinsic parameters are accurately determined. A key metric to assess the quality of your calibration is the Reprojection Error (RPE). This article provides a practical guide to understanding, evaluating, and improving RPE for successful camera calibration.

Step-by-Step Guide

  1. Understand Reprojection Error (RPE): After calibration, points from your calibration pattern are projected onto the image using the calculated camera parameters. RPE is the average difference between these projected points and their actual locations.

    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(...)
print("Reprojection Error:", ret)

  2. Acceptable RPE: There's no magic number. Aim for RPE < 1 pixel for good calibration. However, acceptable RPE depends on your application's accuracy needs.

  3. Iterative Refinement: If RPE is too high:

    • More Images: Capture more images of the calibration pattern, ensuring good coverage of different angles and distances.
    • Image Quality: Use well-lit, sharp images. Blur can reduce accuracy.
    • Pattern Accuracy: Ensure your calibration pattern is flat and accurately measured.
    • Calibration Flags: Experiment with flags in cv2.calibrateCamera (e.g., CALIB_FIX_PRINCIPAL_POINT) to constrain the optimization.

  4. Visual Inspection:

    • Undistort Images: Use cv2.undistort with the obtained camera parameters to remove distortion from images.
    • Check for Straight Lines: Straight lines in the scene should appear straight in the undistorted image.
    • Examine Edges: Pay attention to the image edges, especially if using a fisheye lens. Distortion correction might be less accurate at the periphery.

  5. Consider Application:

    • High-Precision Measurement: Strive for the lowest possible RPE (well below 1 pixel).
    • Object Detection/Tracking: A slightly higher RPE might be acceptable if it doesn't significantly impact object localization.

Remember, camera calibration is an iterative process. Experimentation and careful analysis of results are key to achieving satisfactory accuracy.

Code Example

This Python code performs camera calibration using a chessboard pattern. It first detects the chessboard corners in a set of calibration images and calculates the camera's intrinsic and extrinsic parameters. The code then undistorts a test image using the obtained calibration parameters and displays the result. Finally, it provides an option to save the calibration parameters for future use.

import cv2
import numpy as np
import glob

# Define the chessboard dimensions
CHECKERBOARD = (6, 9)  # Example: 6 rows, 9 columns

# Termination criteria for calibration
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)

# Prepare object points (3D points in real world space)
objp = np.zeros((CHECKERBOARD[0] * CHECKERBOARD[1], 3), np.float32)
objp[:, :2] = np.mgrid[0:CHECKERBOARD[0], 0:CHECKERBOARD[1]].T.reshape(-1, 2)

# Arrays to store object points and image points from all images
objpoints = []  # 3D points in real world space
imgpoints = []  # 2D points in image plane

# Load calibration images
images = glob.glob('calibration_images/*.jpg')  # Adjust path as needed

for fname in images:
    img = cv2.imread(fname)
    gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

    # Find chessboard corners
    ret, corners = cv2.findChessboardCorners(gray, CHECKERBOARD, None)

    # If corners are found, add object points and image points
    if ret == True:
        objpoints.append(objp)
        corners2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), criteria)
        imgpoints.append(corners2)

        # Draw and display the corners (optional for visualization)
        cv2.drawChessboardCorners(img, CHECKERBOARD, corners2, ret)
        cv2.imshow('img', img)
        cv2.waitKey(500)

cv2.destroyAllWindows()

# Perform camera calibration
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)

# Print reprojection error
print("Reprojection Error:", ret)

# ------------------------------------------------------------------------
# Visual Inspection (Undistort an image)
# ------------------------------------------------------------------------
img = cv2.imread('test_image.jpg')  # Load an image to undistort
h, w = img.shape[:2]
newcameramtx, roi = cv2.getOptimalNewCameraMatrix(mtx, dist, (w, h), 1, (w, h))

# Undistort the image
dst = cv2.undistort(img, mtx, dist, None, newcameramtx)

# Crop the image (optional, if there's black border after undistortion)
x, y, w, h = roi
dst = dst[y:y+h, x:x+w]

cv2.imshow('Undistorted Image', dst)
cv2.waitKey(0)
cv2.destroyAllWindows()

# Save calibration parameters (optional)
np.savez("calibration_params.npz", mtx=mtx, dist=dist, rvecs=rvecs, tvecs=tvecs)

Explanation:

  1. Setup: Import libraries, define chessboard size, and set calibration criteria.
  2. Prepare Object Points: Create an array representing the 3D coordinates of the chessboard corners in the real world (assuming a flat pattern).
  3. Image Loading and Processing:
    • Load calibration images from a directory.
    • Convert images to grayscale.
    • Find chessboard corners using cv2.findChessboardCorners.
    • Refine corner locations for accuracy using cv2.cornerSubPix.
    • Store object points and corresponding image points.
  4. Calibration: Use cv2.calibrateCamera to calculate camera matrix, distortion coefficients, rotation and translation vectors.
  5. Reprojection Error: Print the reprojection error (ret) as a measure of calibration quality.
  6. Visual Inspection:
    • Load a test image.
    • Undistort the image using cv2.undistort and the calculated camera parameters.
    • Display the undistorted image to visually assess the correction.
  7. Saving Parameters (Optional): Save the calibration parameters for later use.

Key Points:

  • Image Quality: Use high-quality, well-lit images for calibration.
  • Pattern Coverage: Capture images with the chessboard at various angles and distances to cover a wide range of the camera's field of view.
  • Iterative Refinement: If the reprojection error is high, capture more images, adjust calibration flags, or re-evaluate the accuracy of your calibration pattern.
  • Application-Specific Needs: The acceptable reprojection error depends on your application's accuracy requirements.

Additional Notes

Understanding RPE:

  • Think of it visually: Imagine the calibrated camera projecting the ideal chessboard pattern onto the image. RPE is how far, on average, those projected points land from the actual detected corners in your image.
  • Units: RPE is typically measured in pixels.
  • Not the whole story: While crucial, a low RPE doesn't guarantee perfect calibration. Visual inspection remains essential.

Acceptable RPE:

  • Rule of thumb: RPE < 0.5 pixels is excellent, < 1 pixel is generally good.
  • Application context matters: For applications like measuring distances in the scene, even lower RPE might be necessary.
  • Trade-offs: Sometimes, achieving extremely low RPE might require sacrificing other factors like field of view due to aggressive distortion correction.

Iterative Refinement:

  • Systematic approach: Start with a decent number of images (20-30), then gradually add more if RPE is unsatisfactory.
  • Pattern size and type: Larger chessboards with more squares can improve accuracy. Asymmetric patterns can help determine orientation.
  • Lens distortion: Fisheye lenses generally require more images and careful attention to edge behavior during visual inspection.

Visual Inspection:

  • Real-world objects: Instead of just chessboards, undistort images containing known straight lines (e.g., buildings, tables) for a more practical assessment.
  • Zoom in: Examine areas of the image, especially edges, closely for any remaining distortion artifacts.
  • Quantitative metrics: While visual inspection is crucial, consider using metrics like lens distortion profiles for a more objective evaluation.

Beyond the Basics:

  • Subpixel accuracy: For very high precision, explore techniques to refine corner detection beyond pixel accuracy.
  • Calibration software: Consider using dedicated camera calibration software or libraries that offer advanced features and analysis tools.
  • Rectification: For stereo vision applications, calibrate two cameras together to rectify images, making them appear as if taken from the same viewpoint.

Summary

This table summarizes key aspects of evaluating and refining camera calibration results:

| Aspect | Description

Conclusion

By understanding the factors influencing RPE and employing a combination of quantitative analysis and visual inspection, you can achieve accurate camera calibration for your computer vision tasks. Remember that the acceptable RPE threshold is application-dependent, and achieving a very low RPE might involve trade-offs. This iterative process requires careful planning, execution, and analysis of results, ultimately leading to more reliable and precise computer vision applications.

References

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