ROTATION WITHIN CAMERA PROJECTION MATRIX USING EULER ANGLES, QUATERNIONS, AND ANGLE-AXES

M.E. Ragab∗ and K.H. Wong∗∗

Keywords

Projection, rotation, Euler angles, quaternion, angleaxis, gimbal lock

Abstract

In this paper, we study the rotation model within the camera projection matrix. The rotation models used in the literature are either the camera rotation, R, or its transpose. These two rotation models may be close when rotation magnitudes are small. However, the gap is widened for dynamic applications like longsequence pose estimation, especially when Jacobians are calculated. In contrast, we introduce and validate a third new model based on left-handed rotation representation. We derive the new model for the Euler angles, quaternion, and angle-axis rotation representations. Moreover, we show that there is a gimbal-lock problem associated with the camera projection matrix, and suggest a solution to it.

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