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Research Article

On the symmetric transformation with geometric constraints

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Received 10 Nov 2023, Accepted 09 Apr 2024, Published online: 05 Jul 2024

References

  • Augustyn, J., M. Kampik, and K. Musioł. 2023. “On Determination of the Complex Voltage Ratio Using the Ellipse-Fitting Algorithm in the Case of an Ill-Conditioned Scattering Matrix.” Measurement 216:112935. https://doi.org/10.1016/j.measurement.2023.112935.
  • Cai, B., Z. Shao, S. Fang, X. Huang, Y. Tang, M. Zheng, and H. Zhang. 2022. “The Evolution of Urban Agglomerations in China and How it Deviates from Zipf’s Law.” Geo-Spatial Information Science 1–11. https://doi.org/10.1080/10095020.2022.2083527.
  • Chang, G., T. Xu, and Q. Wang. 2018. “M-Estimator for the 3D Symmetric Helmert Coordinate Transformation.” Journal of Geodesy 92 (1): 47–58. https://doi.org/10.1007/s00190-017-1043-9.
  • Chen, L., F. Rottensteiner, and C. Heipke. 2021. “Feature Detection and Description for Image Matching: From Hand-Crafted Design to Deep Learning.” Geo-Spatial Information Science 24 (1): 58–74. https://doi.org/10.1080/10095020.2020.1843376.
  • Chen, J., and J. Wang. 2009. “Orbit Fitting Based on Helmert Transformation.” Geo-Spatial Information Science 12 (2): 95–99. https://doi.org/10.1007/s11806-009-0236-7.
  • Coe, D. 2009. “Fisher Matrices and Confidence Ellipses: A Quick-Start Guide and Software.” arXiv Preprint arXiv: 0906.4123.
  • Dong, J., S. Li, L. Huang, J. He, W. Jiang, F. Ren, Y. Wang, J. Sun, and H. Zhang. 2022. “Identification of International Trade Patterns of Agricultural Products: The Evolution of Communities and Their Core Countries.” Geo-Spatial Information Science 1–15. https://doi.org/10.1080/10095020.2022.2122875.
  • Fang, X. 2011. “Weighted Total Least Squares Solutions for Applications in Geodesy.” PhD diss., Hannover: Gottfried Wilhelm Leibniz Universität Hannover.
  • Fang, X. 2013. “Weighted Total Least Squares: Necessary and Sufficient Conditions, Fixed and Random Parameters.” Journal of Geodesy 87 (8): 733–749. https://doi.org/10.1007/s00190-013-0643-2.
  • Fang, X. 2014a. “On Non-Combinatorial Weighted Total Least Squares with Inequality Constraints.” Journal of Geodesy 88:805–816. https://doi.org/10.1007/s00190-014-0723-y.
  • Fang, X. 2014b. “A Structured and Constrained Total Least-Squares Solution with Cross-Covariances.” Studia Geophysica Et Geodaetica 58 (1): 1–16. https://doi.org/10.1007/s11200-012-0671-z.
  • Fang, X. 2015. “Weighted Total Least-Squares with Constraints: A Universal Formula for Geodetic Symmetrical Transformations.” Journal of Geodesy 89 (5): 459–469. https://doi.org/10.1007/s00190-015-0790-8.
  • Fang, X., Y. Hu, W. Zeng, and O. Akyilmaz. 2022. “Weighted Least-Squares Fitting of Circles with Variance Component Estimation.” Measurement 205:112132. https://doi.org/10.1016/j.measurement.2022.112132.
  • Förstner, W., and B. Wrobel. 2016. Photogrammetric Computer Vision. Switzerland: Springer International Publishing.
  • Frahm, J., J. Heinly, E. Zheng, E. Dunn, P. Fite-Georgel, and M. Pollefeys. 2013. “Geo-Registered 3D Models from Crowdsourced Image Collections.” Geo-Spatial Information Science 16 (1): 55–60. https://doi.org/10.1080/10095020.2013.774103.
  • Houshiar, H., J. Elseberg, D. Borrmann, and A. Nüchter. 2015. “A Study of Projections for Key Point Based Registration of Panoramic Terrestrial 3D Laser Scan.” Geo-Spatial Information Science 18 (1): 11–31. https://doi.org/10.1080/10095020.2015.1017913.
  • Hu, Y., and X. Fang. 2023. “Linear Estimation Under the Gauss–Helmert Model: Geometrical Interpretation and General Solution.” Journal of Geodesy 97 (5): 44. https://doi.org/10.1007/s00190-023-01737-x.
  • Hu, Y., X. Fang, and H. Kutterer. 2023. “Center Strategies for Universal Transformations: Modified Iteration Policy and Two Alternative Models.” GPS Solutions 27 (2): 92. https://doi.org/10.1007/s10291-023-01419-3.
  • Hu, Y., X. Fang, Y. Qin, and O. Akyilmaz. 2022. “Weighted Geometric Circle Fitting for the Brogar Ring: Parameter-Free Approach and Bias Analysis.” Measurement 192:110832. https://doi.org/10.1016/j.measurement.2022.110832.
  • Hu, Y., X. Fang, W. Zeng, and H. Kutterer. 2023. “Multi-Frame Transformation with Variance Component Estimation.” IEEE Transactions on Geoscience & Remote Sensing 61:1–10. https://doi.org/10.1109/TGRS.2023.3302322.
  • Kanatani, K. 1994. “Analysis of 3-D Rotation Fitting.” IEEE Transactions on Pattern Analysis & Machine Intelligence 16 (5): 543–549. https://doi.org/10.1109/34.291441.
  • Kotsakis, C., A. Vatalis, and F. Sansò. 2014. “On the Importance of Intra-Frame and Inter-Frame Covariances in Frame Transformation Theory.” Journal of Geodesy 88 (12): 1187–1201. https://doi.org/10.1007/s00190-014-0753-5.
  • Leick, A., L. Rapoport, and D. Tatarnikov. 2015. GPS satellite surveying. Hoboken, New Jersey: John Wiley & Sons, Inc.
  • Li, B., Y. Shen, X. Zhang, C. Li, and L. Lou. 2013. “Seamless Multivariate Affine Error-In-Variables Transformation and Its Application to Map Rectification.” International Journal of Geographical Information Science 27 (8): 1572–1592. https://doi.org/10.1080/13658816.2012.760202.
  • Mercan, H., O. Akyilmaz, and C. Aydin. 2018. “Solution of the Weighted Symmetric Similarity Transformations Based on Quaternions.” Journal of Geodesy 92 (10): 1113–1130. https://doi.org/10.1007/s00190-017-1104-0.
  • Ning, E., C. Wang, H. Zhang, X. Ning, and P. Tiwari. 2023. “Occluded Person Re-Identification with Deep Learning: A Survey and Perspectives.” Expert Systems with Applications 122419. https://doi.org/10.1016/j.eswa.2023.122419.
  • Ramos, P., F. Janeiro, and T. Radil. 2009. “Comparison of Impedance Measurements in a DSP Using Ellipse-Fit and Seven-Parameter Sine-Fit Algorithms.” Measurement 42 (9): 1370–1379. https://doi.org/10.1016/j.measurement.2009.05.005.
  • Rao, C. R., H. Toutenburg, and C. Heumann. 2008. Linear Models and Generalizations: Least Squares and Alternatives. Berlin, Heidelberg: Springer.
  • Schaffrin, B., and Y. A. Felus. 2008. “On the Multivariate Total Least-Squares Approach to Empirical Coordinate Transformations. Three Algorithms.” Journal of Geodesy 82 (6): 373–383. https://doi.org/10.1007/s00190-007-0186-5.
  • Tao, L., R. Xia, J. Zhao, T. Zhang, Y. Li, Y. Chen, and S. Fu. 2023. “A High-Accuracy Circular Hole Measurement Method Based on Multi-Camera System.” Measurement 207:112361. https://doi.org/10.1016/j.measurement.2022.112361.
  • Tran, D., J. Nocquet, N. Luong, and D. Nguyen. 2023. “Determination of Helmert Transformation Parameters for Continuous GNSS Networks: A Case Study of the Géoazur GNSS Network.” Geo-Spatial Information Science 26 (1): 125–138. https://doi.org/10.1080/10095020.2022.2138569.
  • Umeyama, S. 1991. “Least-Squares Estimation of Transformation Parameters Between Two Point Patterns.” IEEE Transactions on Pattern Analysis & Machine Intelligence 13 (4): 376–380. https://doi.org/10.1109/34.88573.
  • Wang, C., X. Ning, W. Li, X. Bai, and X. Gao. 2023. “3D Person Re-Identification Based on Global Semantic Guidance and Local Feature Aggregation.” IEEE Transactions on Circuits and Systems for Video Technology 1–1. https://doi.org/10.1109/TCSVT.2023.3328712.
  • Wang, C., X. Ning, L. Sun, L. Zhang, W. Li, and X. Bai. 2022. “Learning Discriminative Features by Covering Local Geometric Space for Point Cloud Analysis.” IEEE Transactions on Geoscience & Remote Sensing 60:1–15. https://doi.org/10.1109/TGRS.2022.3170493.
  • Wang, C., C. Wang, W. Li, and H. Wang. 2021. “A Brief Survey on RGB-D Semantic Segmentation Using Deep Learning.” Displays 70:102080. https://doi.org/10.1016/j.displa.2021.102080.
  • Wang, C., H. Wang, X. Ning, S. Tian, and W. Li. 2022. “3D Point Cloud Classification Method Based on Dynamic Coverage of Local Area.” Journal of Software 34 (4): 1962–1976. (in Chinese with English abstract).
  • Wang, Y., M. Wang, Y. Zhu, and X. Long. 2024. “Low Frequency Error Analysis and Calibration for Multiple Star Sensors System of GaoFen7 Satellite.” Geo-Spatial Information Science 27 (1): 82–94. https://doi.org/10.1080/10095020.2022.2100284.
  • Wang, B., Z. Zhao, Y. Chen, and J. Yu. 2023. “A Novel Robust Point Cloud Fitting Algorithm Based on Nonlinear Gauss–Helmert Model.” IEEE Transactions on Instrumentation and Measurement 72:1–12. https://doi.org/10.1109/TIM.2023.3239630.
  • Xu, P., J. Liu, W. Zeng, and Y. Shen. 2014. “Effects of Errors-In-Variables on Weighted Least Squares Estimation.” Journal of Geodesy 88 (7): 705–716. https://doi.org/10.1007/s00190-014-0716-x.
  • Yoshimura, R., H. Date, S. Kanai, R. Honma, K. Oda, and T. Ikeda. 2016. “Automatic Registration of MLS Point Clouds and SfM Meshes of Urban Area.” Geo-Spatial Information Science 19 (3): 171–181. https://doi.org/10.1080/10095020.2016.1212517.
  • Zaminpardaz, S., and P. Teunissen. 2022. “On the Computation of Confidence Regions and Error Ellipses: A Critical Appraisal.” Journal of Geodesy 96 (2): 10. https://doi.org/10.1007/s00190-022-01596-y.
  • Zhang, H., C. Wang, S. Tian, B. Lu, L. Zhang, X. Ning, and X. Bai. 2023. “Deep Learning-Based 3D Point Cloud Classification: A Systematic Survey and Outlook.” Displays 79:102456. https://doi.org/10.1016/j.displa.2023.102456.
  • Zhu, Q., X. Guo, Z. Li, and D. Li. 2022. “A Review of Multi-Class Change Detection for Satellite Remote Sensing Imagery.” Geo-Spatial Information Science 1–15. https://doi.org/10.1080/10095020.2022.2128902.