scholarly journals Extended WTLS iterative algorithm of 3D similarity transformation based on Gibbs vector

2021 ◽  
Author(s):  
Huaien Zeng ◽  
Hongwei He ◽  
Legeng Chen ◽  
Guobin Chang ◽  
Haiqing He
Keyword(s):  
Iterative Algorithm ◽  
Similarity Transformation ◽  
Gibbs Vector ◽  
3D Similarity

Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions

2020 ◽  
pp. 1-18
Author(s):  
Süreyya Özgür Uygur ◽  
Cuneyt Aydin ◽  
Orhan Akyilmaz
Keyword(s):  
Similarity Transformation ◽  
3D Similarity

scholarly journals PERFORMING 3D SIMILARITY TRANSFORMATION WITH LARGE ROTATION ANGLES USING CONSTRAINED MULTIVARIATE TOTAL LEAST SQUARES

2020 ◽  
Vol 26 (4) ◽  
Author(s):  
Wuyong Tao ◽  
Xianghong Hua ◽  
Shaoquan Feng
Keyword(s):  
Least Squares ◽  
Similarity Transformation ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Translation Vector ◽  
Large Rotation ◽  
Parameter Matrix ◽  
Transformation Parameters ◽  
Least Squares Algorithm ◽  
3D Similarity

Abstract: 3D similarity transformation is frequently encountered operation in the field of geodetic data processing, and there are many applications that involve large rotation angles. In previous studies, the errors of the coefficient matrix were usually neglected and a least squares algorithm was applied to calculate the transformation parameters. However, the coefficient matrix is composed of the point coordinates in source coordinate system, i.e., the coefficient matrix is also contaminated by errors. Therefore, a total least squares algorithm should be applied. In this paper, a new method is proposed to address the 3D similarity transformation problem with large rotation angles. Firstly, the scale factor and rotation matrix are put together as the parameter matrix to avoid the rank-defect problem. Then, the translation vector is removed and the multivariate model is constructed. Finally, the constraints are introduced according to the properties of the parameter matrix and the constrained multivariate total least squares algorithm is derived to obtain the transformation parameters. The experimental results show that the proposed method has a high computational efficiency.

Data snooping algorithm for universal 3D similarity transformation based on generalized EIV model

Measurement ◽  
2018 ◽  
Vol 119 ◽  
pp. 56-62 ◽  
Author(s):  
Bin Wang ◽  
Jie Yu ◽  
Chao Liu ◽  
Mingfeng Li ◽  
Bangyan Zhu
Keyword(s):  
Similarity Transformation ◽  
Data Snooping ◽  
3D Similarity

scholarly journals WTLS iterative algorithm of 3D similarity coordinate transformation based on Gibbs vectors

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Huaien Zeng ◽  
Guobin Chang ◽  
Haiqing He ◽  
Kezhao Li
Keyword(s):  
Iterative Algorithm ◽  
Coordinate Transformation ◽  
3D Similarity
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