Abstract. Oblique-viewing endoscopes (oblique scopes) are widely used medically. It is essential for certain procedures such as laparoscopy, arthroscopy, and sinus endoscopy. In an oblique scope, its 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 been developed yet. 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, and 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 precision of this estimation was demonstrated to have a significant effect on the overall calibration accuracy in the experimental evaluation especially with large rotation angles. The projection error in the image plane was around two pixels. The proposed method was shown to be clinically applicable.

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.

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.

SUMMARYThis paper proposes a camera projection model for an oblique-viewing endoscope, intended for application to an extended virtual reality system. The oblique-viewing endoscope differs from the forward-viewing endoscope by the fact that the view field can be shifted by rotating the scope cylinder. The projection model proposed in this study describes the systematic relation between the rotation angle of the scope cylinder and the external parameters of the camera model. A calibration method is also proposed for estimating the parameters of the projection model, and its accuracy is investigated. The oblique-viewing projection model is derived as an extension of the general pinhole camera model by adding two axes of rotation as parameters and using the angle of rotation of the scope cylinder as the input. In the experiment, an abdominal endoscope is used as the real equipment. A rotary encoder with an angular resolution of 0.25° is used to input the rotation angle of the scope cylinder. The accuracy is examined by the above condition for a scope cylinder rotation angle of 0 to 132°. The average projection error in the proposed model is 2.4 pixels. When the parameters needed in the model are not estimated, the error is increased to 5 to 8 pixels compared to the case in which they are estimated. It is thus shown that the parameters of the proposed model are indispensable in the description of the actual oblique-viewing endoscope. Even if the number of data points for each angle is 2, an accuracy such that the average error is less than 2.8 pixels is obtained.