Projective Camera Parameters

The image of a projective camera can be described in terms of its 11 intrinsic and extrinsic parameters. The intrinsic parameters affect how the image is seen on the image plane once it has entered the camera. These are unique to individual cameras and include:

• Focal Length - The distance from the camera's center to the image plane. In most digital and film cameras this is the distance from the rear-most lens element to the actual sensor/film
• Principal Point - The origin of the image plane in relation to the center of the image plane. For convenience, typically the lower left corner of the image is considered the origin.
• Skew Coefficients - The pixels in a CCD sensor may not be perfectly square, resulting in a small distortion in the X or Y directions. The skew coefficient is the number of pixels per unit length in each direction on the CCD sensor.
• Distortion - The curved nature of a lens results in radial and tangential distortion. These can be quantified by a number of distortion coefficients.

Even with the manufacturer's specifications in hand, these parameters need to be found experimentally as cameras of the same model often vary slightly. Together these parameters form the camera calibration matrix K.

The extrinsic parameters of a camera, on the other hand, are not unique to any given camera. These relate how a camera's orientation and position within world coordinates:

• Rotation - Roll, Pitch, and Yaw of the camera
• Translation - Position of the camera in regards to the World origin.

The intrinsic and the extrinsic parameters define a camera's projection matrix P:

Resources

[1] Hartley, R., and Zisserman, A. Multiview Geometry in Computer Vision (2nd Ed). Cambridge University Press. 2008.