Tsai Camera Calibration

This software package contains routines for calibrating Roger Tsai's perspective projection camera model. Routines are provided for two levels of calibration. The first level is a direct implementation of Tsai's algorithm in which only three (f, Tz, and kappa1) of the 11 calculated model parameters are numerically optimized. The second level is an extension of Tsai's algorithm in which the full 11 parameter model is numerically optimized. Full optimization is slower but provides the most accurate calibration. This software also contains routines for using the camera model and for gauging the model's accuracy.

The current (October 28, 95) software release is contained in the files

Tsai-method-v3.0b3.tar.Z  (205K bytes)

and

tsai30b3.zip  (151K bytes)

The software can be extracted using the Unix commands

uncompress Tsai-method-v3.0b3.tar.Z

tar -xvf Tsai-method-v3.0b3.tar

or the PKWARE MS-DOS command

pkunzip -d tsai30b3.zip

Release 3.0 features include:

• 100% C source code (including MINPACK non-linear optimization),
• Unix and MS-DOS (Borland C 4.5) compatibility, and
• a Frequently Asked Questions (FAQ) file.

A detailed list of the changes in this release can be obtained by clicking here.

 

Tsai's Camera Model

Tsai's camera model is based on the pin hole model of perspective projection. Given the position of a point in 3D world coordinates the model predicts the position of the point's image in 2D pixel coordinates. Tsai's model has 11 parameters: five internal (also called intrinsic or interior) parameters,

• f - effective focal length of the pin hole camera,
• kappa1 - 1st order radial lens distortion coefficient,
• Cx, Cy - coordinates of center of radial lens distortion -and- the piercing point of the camera coordinate frame's Z axis with the camera's sensor plane,
• sx - scale factor to account for any uncertainty due to framegrabber horizontal scanline resampling,

and six external (also called extrinsic or exterior) parameters,

• Rx, Ry, Rz - rotation angles for the transform between the world and camera coordinate frames, and
• Tx, Ty, Tz - translational components for the transform between the world and camera coordinate frames.

The internal parameters describe how the camera forms an image while the external parameters describe the camera's pose (i.e. position and orientation) in the world coordinate frame. Calibration data for the model consists of 3D (x,y,z) world coordinates of a feature point (in mm for example) and corresponding 2D coordinates (Xf,Yf) (typically in pixels) of the feature point in the image. Two forms of calibration are possible:

coplanar - the calibration points lie in a single plane in 3D, and

non-coplanar - the calibration points occupy a 3D volume.

An explanation of the basic calibration algorithms and descriptions of the variables can be found in several publications, including:

"An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision", Roger Y. Tsai, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, Miami Beach, FL, 1986, pages 364-374,

and

"A versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses", Roger Y. Tsai, IEEE Journal of Robotics and Automation, Vol. RA-3, No. 4, August 1987, pages 323-344.

Reprints can be ordered through the Ask*IEEE document delivery service.