In order for augmented reality to be effective, the real and computer generated object of the environment must be accurately positioned relative to each other. Hence, a new and low cost vision system is currently being developed for tracking the orientation and position of the Capture and Display Unit (CDU) with respect to the target coordinate system. Camera calibration is used for this measuring purpose.

Camera calibration is the process of determining and relating the 3D position and orientation of the camera frame with respect to a certain world coordinate. It is applied to track the location of the Capture and Display Unit and determine the transformation from image space of the CCD camera to the marker system in real world space.

Through calibration, both the camera intrinsic parameters and the extrinsic parameters are obtained.

The intrinsic parameters comprise of:

1. effective focal length of the pinhole camera,
2. two radial and two tangential distortion coefficients,
3. coordinates of the center of distortion in the image space,
4. scale factor that accounts for the uncertainty in the framegrabber’s re-sampling of the horizontal scanline.

The extrinsic properties refer to the position and orientation of the camera coordinate frame with respect to the world coordinate frame.

Barrel Effect caused by Lens Aberration

The image obtained by our camera is negatively distorted as compared to the true-scaled duplicate blue lines (see left figure). This type of distortion is known as the barrel effect. Discrepancies can be found at the extreme corner of the screen. Hence, during calibration, two radial and two tangential distortion coefficients are introduced to rectify the lens distortion.

A new calibration target and a camera platform are designed and built to aid the calibration of the cameras (see right figure).

In our application, two black and white Pulnix TM-7AS cameras with focal length of 12mm and two color Pulnix TMC-73M cameras with focal length of 8mm (which produces an image size of 640 by 480 pixels) are used for tracking and registering of real time images respectively. These cameras are auto-calibrated pre-operatively using a calibration target with points of known position. The projection errors of these points are overcome recursively. Using the lens distortion model, a fifth-order polynomial inverse model is obtained. The inverse model is used by the system to find the undistorted image coordinates in real time. Fast computational Direct Linear Transformation is used to track down the markers fixed on the patient. As the position and orientation of the cameras are obtained in the calibration process, the computer model of the organ can be registered accurately on the display.