College of Civil Engineering and Architecture, China Three Gorges University, Yichang, China

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Abstract—Three-dimensional coordinate transformation problem is the most frequent problem in photogrammetry, geodesy, mapping, geographical information science (GIS), and computer vision. To overcome the drawback that traditional solution of the problem based on rotation angles depends strongly on initial value of parameter, which makes the method ineffective in the case of super-large rotation angle, the paper adopts an unit quaternion to represent three-dimensional rotation matrix, then puts forward a quaternion-based iterative solution of the problem. The cases study shows that the quaternion-based solution has no dependence on the initial value of parameter and desirable result with fast speed. Thus it is valid for three-dimensional coordinate transformation of any rotation angle.

Index Terms—Three-dimensional coordinate transformation, quaternion, rotation matrix, initial value of parameter, parameter adjustment with constraint, improved Gauss- Newton method

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Cite: Huaien Zeng and Qinglin Yi, "Quaternion-Based Iterative Solution of Three- Dimensional Coordinate Transformation Problem," Journal of Computers vol. 6, no. 7, pp. 1361-1368, 2011.