2015•Engineering of Surveying and MappingRequires access

Independent relative orientation based on unit quaternion

Jianfeng Liu

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Abstract

The main method of describing spatial rotation with unit quaternion is rotation matrix,without considering property of unit quaternion.Unit quaternion can intuitively and succinctly describe rotation of vectors.Based on this,an innovative method in the independent relative orientation based on unit quaternion is proposed.The algorithm describes corresponding image rays as vectors,then uses unit quaternion to describe the rotational relationship of corresponding image rays.Coplanarity condition equation is linearized by the eight elements of two unit quaternion and elements of relative orientation and calculated using an iterative method according to indirect adjustment with constraints.The relative orientation of RC30 aerial images and UAV images are realized with method unit quaternion and method Euler angles.The results show that the relative orientation accuracy of the method unit quaternion is better than method Euler angle.It provides more options to solve the problems of coordinate transformation in photogrammetry.

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What this paper is about

The main method of describing spatial rotation with unit quaternion is rotation matrix,without considering property of unit quaternion.Unit quaternion can intuitively and succinctly describe rotation of vectors.Based on this,an innovative method in the independent relative orientation based on unit quaternion is proposed.The algorithm describes corresponding image rays as vectors,then uses unit quaternion to describe the rotational relationship of corresponding image rays.Coplanarity condition equation is linearized by the eight elements of two unit quaternion and elements of relative orientation and calculated using an iterative method according to indirect adjustment with constraints.The relative orientation of RC30 aerial images and UAV images are realized with method unit quaternion and method Euler angles.The results show that the relative orientation accuracy of the method unit quaternion is better than method Euler angle.It provides more options to solve the problems of coordinate transformation in photogrammetry.

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Available abstract

The main method of describing spatial rotation with unit quaternion is rotation matrix,without considering property of unit quaternion.Unit quaternion can intuitively and succinctly describe rotation of vectors.Based on this,an innovative method in the independent relative orientation based on unit quaternion is proposed.The algorithm describes corresponding image rays as vectors,then uses unit quaternion to describe the rotational relationship of corresponding image rays.Coplanarity condition equation is linearized by the eight elements of two unit quaternion and elements of relative orientation and calculated using an iterative method according to indirect adjustment with constraints.The relative orientation of RC30 aerial images and UAV images are realized with method unit quaternion and method Euler angles.The results show that the relative orientation accuracy of the method unit quaternion is better than method Euler angle.It provides more options to solve the problems of coordinate transformation in photogrammetry.

Key concepts: Quaternion, Euler angles, Rotation (mathematics), Orientation (vector space), Rotation matrix, Euler's rotation theorem, Mathematics, Unit vector

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