Quaternion: An alternate approach to medical navigation

Abstract

Quaternion algebra provides a strong base for the representation of orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose, numerically more stable, more efficient and avoid the problem of gimbal lock. This paper addresses the instruments tracking of medical navigation by using rotation matrices and quaternion. The calculation of the instrument's tip of the video-optical localizer for the complete spatial plane plays a decisive role. A comparison is made between the two methods to find the solution of the gimbal lock problem. The calculation in the two methods is presented for the instrument's tip of a video-optical localizer. The results are compared, and it is concluded that method based on quaternions are more efficient and fail-safe than traditional methods with rotation matrices. For same spatial rotations, e.g. two rotations axes overlap in the gimbal lock, rotation matrices may provide wrong results.