Camera calibration is essential for ensuring that your camera systems can accurately interpret real-world measurements and translate them into digital data. This process corrects lens distortions and aligns the camera's coordinate system with the real world, enabling precise measurements and accurate 3D reconstructions. In this blog post, we will explore the key parameters used in camera calibration, particularly those utilised in our calibration software.
Key Parameters in Camera Calibration
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Camera Matrix (Intrinsic Parameters)
- Focal Length (fx, fy): Represents the distance between the camera lens and the image sensor, measured in pixels. It determines how much the camera magnifies the scene.
- Principal Point (cx, cy): The point where the optical axis intersects the image plane. Ideally, it should be at the center of the image sensor, but minor deviations are common.
- Skew Coefficient (s): Represents the angle between the x and y pixel axes. In most cameras, the skew is negligible and assumed to be zero.
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Distortion Coefficients (Radial and Tangential Distortions)
- Radial Distortion (k1, k2, k3): These coefficients account for the common barrel and pincushion distortions in lenses. Radial distortion causes straight lines to appear curved.
- Tangential Distortion (p1, p2): These coefficients account for the misalignment of the lens and the image sensor. Tangential distortion causes the image to be skewed.
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Extrinsic Parameters
- Rotation Matrix (R): Describes the orientation of the camera in the world coordinate system. It aligns the camera's coordinate system with the real-world coordinate system.
- Translation Vector (t): Describes the position of the camera in the world coordinate system. It represents the translation from the world origin to the camera origin.
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Reprojection Error
- This parameter measures the difference between the observed image points and the projected points obtained from the estimated camera parameters. Lower reprojection errors indicate a more accurate calibration.
Parameters in Our Calibration Software
Our calibration software simplifies the calibration process by automatically calculating these parameters based on the images you provide. Here’s a closer look at how these parameters are used:
- Pattern Selection: Choose between ChArUco and checkerboard patterns for calibration. The software detects the pattern corners and uses them to calculate the intrinsic and extrinsic parameters.
- Image Acquisition: Capture multiple images of the calibration pattern from different angles. The software uses these images to compute an accurate camera model.
- Parameter Estimation: The software estimates the focal length, principal point, skew coefficient, distortion coefficients, rotation matrix, and translation vector.
- Reprojection Error Visualization: View the reprojection error to assess the accuracy of the calibration. The software provides visual feedback to help you understand the quality of the calibration.
How to Achieve Accurate Calibration
- Capture High-Quality Images: Ensure the calibration pattern is well-lit and in focus. Capture images from various angles and distances.
- Use the Entire Image Frame: Cover different areas of the image frame to ensure that the calibration parameters are accurately estimated across the entire sensor. The board should cover as much of the image frame as possible and ideally more than half of the frame.
- Avoid Movement: Keep the camera and calibration pattern steady during image capture to avoid blurring and misalignment.
- Check for Reprojection Error: Use the software’s reprojection error visualization to identify and correct any inaccuracies in the calibration.