An improved camera model for oblique-viewing laparoscopes: high reprojection accuracy independent of telescope rotation.

Objective
Oblique-viewing laparoscopes are popular in laparoscopic surgeries where the target anatomy is located in narrow areas. Their viewing direction can be shifted by telescope rotation without changing the laparoscope pose. This rotation also changes laparoscope camera parameters that are estimated by camera calibration to be able to reproject an anatomical model onto the laparoscopic view, creating augmented reality (AR). The aim of this study was to develop a camera model that accounts for these changes, achieving high reprojection accuracy for any telescope rotation. 

Approach
Camera parameters were acquired by calibrations encompassing a wide telescope rotation range. For those parameters showing periodic changes upon rotation, interpolation models were created and used to establish an updatable camera model. With this model, corner points of a tracked checkerboard were reprojected onto the checkerboard laparoscopic images, at random rotation angles. Root-mean-square reprojection errors (RMSEs) were calculated between the reprojected and imaged corner points.

Main results
Reprojection RMSEs were low and approximately independent on telescope rotation angle, over a wide rotation range of 320 degrees. The mean reprojection RMSE was 2.8±0.7 pixels for a conventional laparoscope and 3.6±0.7 pixels for a chip-on-the-tip laparoscope, corresponding to 0.3±0.1mm and 0.4±0.1mm in world coordinates respectively. Worst-case reprojection errors were about 9 pixels (0.8mm) for both laparoscopes.

Significance
The camera model developed in this study improves on existing models for oblique-viewing laparoscopes because it provides high reprojection accuracy independent of the telescope rotation angle and is applicable for conventional and chip-on-a-tip oblique-viewing laparoscopes. The work presented here is an important step towards creating accurate AR in image-guided interventions where oblique-viewing laparoscopes are used while simultaneously providing the surgeon the flexibility to rotate the telescope to any desired rotation angle.