The ArthroNav Project

Computer Assisted Navigation in Orthopedic Surgery using Endoscopic Images

Endoscopic Camera Calibration

The geometric calibration of medical endoscope can not be avoided in the context of image based computer aided surgery. However, developing an effective method for geometric calibration of a medical endoscope is a very challenging task: (i) in general the calibration result must be extremely accurate, because many medical procedures require positioning accuracies of the order of tenth of millimeter; (ii) the endoscope optics introduces strong radial distortion that must be considered in the projection model; and (iii) the calibration procedure has to be performed by a non-expert in the Operation Room (OR), which requires the method to be simple, fast and robust.

Camera calibration is a well studied topic and there are several methods and softwares for accomplishing the task. An example is the Bouguet toolbox that uses images of a planar checkerboard pattern acquired from arbitrary viewpoints (see figure above). Unfortunately, the calibration procedure does not meet the usability requirements specified above. The Bouguet calibration typically implies acquiring several grid images and selecting the corner points. This selection is usually problematic in the presence of strong lens distortion, with the user being asked to provide a rough initialization of the relevant parameters. We can hardly imagine a medical doctor being eager to acquire 10 to 20 grid images during his regular clinical practice, and then struggle to manually select points. Not solving this usability issue can potentially condemn to failure any kind of assistive technology relying on endoscopic video processing. We propose a method for endoscope calibration that overcomes the usability issues without compromising the final accuracy. The approach is fully automatic and, to the best of our knowledge, it is the first algorithm able to calibrate a camera with radial distortion from a single image of a planar grid. We build on recent developments in using lifted coordinates to model the projection in central catadioptric systems [J4,D4]. This theory is extended to the case of medical endoscopes by exploring the similarities between the division model for radial distortion and the para-catadioptric projection [C5] . The graphics below show results for 10 calibration images. They compare the calibration achieved with the Bouguet toolbox, that uses in simultaneous the 10 images, against our Single Image Calibration (SIC) that is run independently for each image.

The top image concerns the relative difference in the intrinsic parameters, the middle refers to the pose of the checkerboard pattern, and the bottom shows the relative orientation of the calibration plane (0 is fronto-parallel). It can be seen that the SIC calibration is repeatable and the estimation results are close to the Bouguet outcome (for further details see [C5,J3]). The algorithm can be used for calibrating any camera with significant lens distortion. If you are interested in using the software please go the the EasyCamCalib page.
The presented work was partially/totally funded by The Portuguese Agency for Innovation (ADI) through the QREN co-promotion project n 2009/003512 sponsored by the Operational Program "Factores de Competitividade" and the 10 European Fund for Regional Development.