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Augmented Reality (AR) applications typically involve a real space and a virtual space which should be co-registered. Both spaces have an observer usually in the form of some camera system. In the real space our camera is typically the surgical microscope's optical system or an endoscope's optical element. The virtual space is a computer graphics space - e.g. implemented in C++ with OpenGL - with a virtual camera.
The calibration step aims to align the real camera and the virtual camera. This alignment requires the knowledge of:
Six extrinsic parameters
Five intrinsic parameters
The extrinsic parameters are the six spatial degrees of freedom (dof's), i.e. three for position (translational dof's) and three for orientation (rotational dof's). The intrinsic parameters are the effective focal length, the optical center (2 parameters in x,y), the scale factor and the first order radial distortion factor (second order radial distortion can be ignored in most practical cases).
Several calibration algorithms have been designed for this purpose. We used a modified version of the well-established Tsai's calibration algorithm. To perform calibration, a mouthpiece (VBH - Vogele Bale Hohner) with calibration pattern is inserted in the patient's mouth (see left image).