Camera Models and Calibration
Camera models describe how points in the 3D world project onto an image, and calibration estimates the parameters of that projection for a real camera.
Definition
A camera model is a mathematical mapping from 3D scene points to 2D image points, and calibration is the estimation of the model's intrinsic and extrinsic parameters for a specific camera.
Scope
This topic covers the pinhole camera model and its projection matrix, intrinsic parameters such as focal length and principal point, extrinsic parameters giving the camera's pose, models of radial and tangential lens distortion, and calibration procedures that recover these from images of known targets.
Core questions
- How does a camera project a 3D point onto the image plane?
- What internal parameters characterize a camera?
- How is lens distortion modeled and corrected?
- How are these parameters estimated in practice?
Key concepts
- Pinhole camera model
- Projection matrix
- Intrinsic parameters
- Extrinsic parameters
- Lens distortion
- Calibration targets
Key theories
- Pinhole projection model
- An ideal camera projects 3D points through a center onto an image plane, expressed in homogeneous coordinates as a 3-by-4 projection matrix factoring into intrinsic and extrinsic parts, the foundation of geometric computer vision.
- Plane-based calibration
- Capturing several views of a planar pattern lets the intrinsic and extrinsic parameters and distortion be recovered by closed-form initialization followed by nonlinear refinement, a flexible and widely used calibration technique.
Clinical relevance
Camera calibration is a prerequisite for accurate 3D reconstruction, robot and vehicle navigation, augmented reality, photogrammetry, and any metric measurement from images.
History
Photogrammetric calibration methods predate computer vision; Hartley and Zisserman systematized the projective camera in the 1990s, and Zhang's 2000 plane-based method made calibration simple and accessible, becoming a de facto standard.
Key figures
- Richard Hartley
- Andrew Zisserman
- Zhengyou Zhang
Related topics
Seminal works
- hartley2004
- zhang2000
Frequently asked questions
- What does it mean to calibrate a camera?
- It means measuring how the camera maps the 3D world to pixels, including its focal length, the image center, and lens distortion, so that image measurements can be related back to real-world geometry.
- Why does lens distortion need correcting?
- Real lenses bend straight lines, especially near image edges; modeling and removing this distortion restores the straight-line geometry assumed by the pinhole model, which is needed for accurate reconstruction.