J. Traub, S. Wiesner, M. Feuerstein, H. Feußner, N. Navab Evaluation of Calibration Methods for Laparoscope Augmentation 4. Jahrestagung der Deutschen Gesellschaft für Computer-und Roboter-Assistierte Chirurgie (CURAC 2005), Berlin, Germany, September 2005 (bib)
	Introduction: Laparoscopic surgery is an operation technique that enables minimally invasive procedures by inserting a laparoscopic camera and surgical tools through ports into the patient. The view of the operating area is limited to the images provided by the laparoscope. Recently, the enhancement of these images by applying distortion correction and filters as well as virtual endoscopy has been investigated intensively. Systems have been developed for the augmentation of laparoscopic images with three dimensional medical imaging data (e.g. CT data) for precise navigation to a target region. Our previous work on laparoscope augmentation for gated augmented reality was accepted for CARS 05 and describes in detail the system setup. The challenges for precise overlay are camera calibration, model registration, and tracking accuracy. In this work we analyze different methods of camera calibration using an optical tracking system. Method: Our experimental setup uses an optical tracking system and markers mounted onto the camera of the laparoscope (cf. 1). For calibration and its evaluation we use a pattern with attached markers. In all applied methods, we first compute the distortion model of the laparoscope image and undistort it. Furthermore, the intrinsic parameters of the camera are computed. Then we apply three different methods to estimate the rigid transformation between the tracking target coordinate system and the camera center. We used the direct linear transformation (DLT), the iterative pose estimation, and two different implementations of hand-eye-calibration, the techniques by Daniilidis and Tsai-Lenz. The entire chain of estimated transformations is visualized in figure 2, where the transformation between the camera target and the camera center is the subject of this evaluation methods. Experiments and Results: The first experiment was a comparative study of the different methods. We used all calibration images to compute the projection matrix. As a distance measurement we used the difference between the original pixel in the image and its backprojected 3D point onto the image. The DLT performs best (9.7px – approx. < 2mm). However, the difference to the iterative pose estimation (10.1px), the Daniilidis method (10.9px), and the Tsai Lenz method (10.8px) are not significant. For further improvement of the augmentation accuracy, we computed the projection matrix only with a subsample of the calibration frames. We generate clusters, that are subsample of frames, which have a backprojection error below a threshold when using a projection matrix estimated by only a single calibration frame. The clusters are then used to estimate the rigid transformation between the tracking target and the camera center. We compare the backprojection errors using a projection matrix computed by all frames, by a cluster, and by single frame (cf. 3). The mean error is minimal for the projection matrix estimated only with a single frame (< 1px). However, this is not of practical use since we can not establish a calibration pattern in every view of the laparoscope during a laparoscopic intervention. The projection computed by a cluster of frames show reasonable reprojection errors (1.8px). We visualized the reprojection accuracy of all described methods in every single frame used for the calibration. One example is shown in figure 4. Conclusion: The augmentation error introduced by the tracking system and the camera calibration is reduced by using a clustering algorithm for the estimation of the projection matrix. In future work, a function has to be defined that maps the estimated pose of the tracking target to its closest cluster. Further improvements have to be made to ensure smooth transition between different clusters. Acknowledgments: Thanks to Dr. Marc Schneberger from ART Tracking GmbH? for his discussions on the design of the tracking target and optimal placement of the tracking system.
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