Calibration of time-of-flight cameras for accurate intraoperative surface reconstruction

In image-guided surgery (IGS) intraoperative image acquisition of tissue shape, motion, and morphology is one of the main challenges. Recently, time-of-flight (ToF) cameras have emerged as a new means for fast range image acquisition that can be used for multimodal registration of the patient anatomy during surgery. The major drawbacks of ToF cameras are systematic errors in the image acquisition technique that compromise the quality of the measured range images. In this paper, we propose a calibration concept that, for the first time, accounts for all known systematic errors affecting the quality of ToF range images. Laboratory and in vitro experiments assess its performance in the context of IGS.

For calibration the camera-related error sources depending on the sensor, the sensor temperature and the set integration time are corrected first, followed by the scene-specific errors, which are modeled as function of the measured distance, the amplitude and the radial distance to the principal point of the camera. Accounting for the high accuracy demands in IGS, we use a custom-made calibration device to provide reference distance data, the cameras are calibrated too. To evaluate the mitigation of the error, the remaining residual error after ToF depth calibration was compared with that arising from using the manufacturer routines for several state-of-the-art ToF cameras. The accuracy of reconstructed ToF surfaces was investigated after multimodal registration with computed tomography (CT) data of liver models by assessment of the target registration error (TRE) of markers introduced in the livers.

For the inspected distance range of up to 2 m, our calibration approach yielded a mean residual error to reference data ranging from 1.5±4.3 mm for the best camera to 7.2±11.0 mm. When compared to the data obtained from the manufacturer routines, the residual error was reduced by at least 78% from worst calibration result to most accurate manufacturer data. After registration of the CT data with the ToF data, the mean TRE ranged from 3.7±2.1 mm for point-based and 5.7±1.9 mm for surface-based registration for the best camera to 6.2±3.4 and 11.1±2.8 mm, respectively. Compared to data provided by the manufacturer, the mean TRE decreased by 8%-60% for point-based and by 18%-74% for surface-based registration.

Using the proposed calibration approach improved the measurement accuracy of all investigated ToF cameras. Although evaluated in the context of intraoperative image acquisition, the proposed calibration procedure can easily be applied to other medical applications using ToF cameras, such as patient positioning or respiratory motion tracking in radiotherapy.