Comparative study of hand-eye calibration methods for augmented reality using an endoscope

We performed a comprehensive study of hand-eye calibration approaches for augmented reality (AR) using endoscopes, aiming to find the approaches that yield the best performance and to reveal the mechanism that makes these approaches successful. The two unknown values in this calibration problem are the hand-eye transformation between an endoscope and the endoscope-attached optotracked marker and the transformation between a calibration board with a checker pattern and the board-attached marker. We classify possible approaches to solving hand-eye transformation as direct, simultaneous, and sequential. The effect of the translation components of transformations on an approach's accuracy is theoretically analyzed using error equations derived from the approaches and demonstrated using both synthetic and real data. We found that sequential approaches performed the best when the magnitude of the translation of hand-eye transformation was larger than that between the board and its marker, which is the general case in implementing AR using endoscopes. In addition, this approach is less sensitive to noise and the number of calibration poses than others. Our results and analyses provide guidance for choosing an optimal hand-eye calibration solution for AR using endoscopes.