Robust registration procedures for endoscopic imaging.

This paper presents a robust algorithm for calibration and system registration of endoscopic imaging devices. The system registration allows us to map accurately each point in the world coordinate system into the endoscope image and vice versa to obtain the world line of sight for each image pixel. The key point of our system is a robust linear algorithm based on singular value decomposition (SVD) for estimating simultaneously two unknown coordinate transformations. We show that our algorithm is superior in terms of robustness and computing efficiency to iterative procedures based on Levenberg-Marquardt optimization or on quaternion approaches. The algorithm does not require the calibration pattern to be tracked. Experimental results and simulations verify the robustness and usefulness of our approach. They give an accuracy of less than 0.7 mm and a success rate >99%. We apply the calibrated endoscope to the neurosurgical relevant case of red out, where in spite of the complete loss of vision the surgeon gets visual aids in the endoscope image at the actual position, allowing him/her to manoeuvre a coagulation fibre into the right position. Finally, we outline how our registration algorithm can be used also for standard registration applications (establish the mapping between two sets of points). We propose our algorithm as a linear, non-iterative algorithm also for projective transformations and for 2D-3D-mappings. Thus, it can be seen as a generalization of the well-known Umeyama registration algorithm.