Development of a camera model and calibration procedure for oblique-viewing endoscopes.

Oblique-viewing endoscopes (oblique scopes) are widely used in medical practice. They are essential for certain procedures such as laparoscopy, arthroscopy and sinus endoscopy. In an oblique scope the viewing directions are changeable by rotating the scope cylinder. Although a camera calibration method is necessary to apply augmented reality technologies to oblique endoscopic procedures, no method for oblique scope calibration has yet been developed. In the present paper, we formulate a camera model and a calibration procedure for oblique scopes. In the calibration procedure, Tsai's calibration is performed at zero rotation of the scope cylinder, then the variation of the external camera parameters corresponding to the rotation of the scope cylinder is modeled and estimated as a function of the rotation angle. Accurate estimation of the rotational axis is included in the procedure. The accuracy of this estimation was demonstrated to have a significant effect on overall calibration accuracy in the experimental evaluation, especially with large rotation angles. The projection error in the image plane was approximately two pixels. The proposed method was shown to be clinically applicable.