Abstract
In optical image registration, the reference control points (RCPs) used as explanatory variables in the polynomial regression model are generally assumed to be error free. However, this most frequently used assumption is often invalid in practice because RCPs always contain errors. In this situation, the extensively applied estimator, the ordinary least squares (LS) estimator, is biased and incapable of handling the errors in RCPs. Therefore, it is necessary to develop new feasible methods to address such a problem. This paper discusses the scaled total least squares (STLS) estimator, which is a generalization of the LS estimator in optical remote sensing image registration. The basic principle and the computational method of the STLS estimator and the relationship among the LS, total least squares (TLS) and STLS estimators are presented. Simulation experiments and real remotely sensed image experiments are carried out to compare LS and STLS approaches and systematically analyze the effect of the number and accuracy of RCPs on the performances in registration. The results show that the STLS estimator is more effective in estimating the model parameters than the LS estimator. Using this estimator based on the error-in-variables model, more accurate registration results can be obtained. Furthermore, the STLS estimator has superior overall performance in the estimation and correction of measurement errors in RCPs, which is beneficial to the study of error propagation in remote sensing data. The larger the RCP number and error, the more obvious are these advantages of the presented estimator.
Similar content being viewed by others
References
Arbia G, Griffith D, Haining R (1999) Error propagation modeling in raster GIS: adding and ratioing operations. Cartogr Geogr Inf Sci 26(4):297–316. doi:10.1559/152304099782294159
Brown DG, Goovaerts P, Burnicki A, Li MY (2002) Stochastic simulation of land-cover change using geostatistics and generalized additive models. Photogramm Eng Rem S 68(10):1051–1061. doi:10.1.1.63.3788
Burnicki AC, Brown DG, Goovaerts P (2007) Simulating error propagation in land-cover change analysis: the implications of temporal dependence. Computers Environment and Urb 31(3):282–302. doi:10.1016/j.compenvurbsys.2006.07.005
Burnicki AC, Brown DG, Goovaerts P (2010) Propagating error in land-cover-change analyses: impact of temporal dependence under increased thematic complexity. Int J Geogr Inf Sci 24(7):1043–1060. doi:10.1080/13658810903279008
Carmel Y, Dean DJ (2004) Performance of a spatio-temporal error model for raster datasets under complex error patterns. Int J Remote Sens 25(23):5283–5296. doi:10.1080/01431160310001654932
Evans FH (1998) Statistical methods in remote sensing. In: Proceedings of the 3rd National Earth Resource Assessment workshop, Brisbane, Australia, 16-18, Nov., pp 1-26
Faber NM, Kowalski BR (1997) Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares. J Chemometrics 11(3):181–238. doi:10.1002/(SICI)1099-128X(199705)11:3<181::AID-CEM459>3.0.CO;2-7
Felus YA (2004) Application of total least squares for spatial point process. J Surv Eng 130(3):126–133. doi:10.1061/(ASCE)0733-9453(2004)130:3(126)
Ge Y, Leung Y, Ma JH, Wang JF (2006) Modeling for registration of remotely sensed imagery when reference control points contain error. Sci China Ser D 49(7):739–746. doi:10.1007/s11430-006-0739-0
Gillard JW (2006) An historical overview of linear regression with errors in both variables. Technical Report, Cardiff School of Mathematics, UK, Available at http://www.cardiff.ac.uk/maths/resources/Gillard_Tech_Report.pdf
Glasbey CA, Mardia KV (1998) A review of image-warping methods. J Appl Stat 25(2):155–171. doi:10.1080/02664769823151
Goodchild MF, Sun GQ, Yang S (1992) Development and test of an error model for categorical-data. Int J Geogr Inf Syst 6(2):87–104. doi:10.1080/02693799208901898
Jensen JR (1996) Introductory Digital Image Processing: a remote sensing perspective. Prentice Hall, New Jersey
Kyriakidis PC, Dungan JL (2001) A geostatistical approach for mapping thematic classification accuracy and evaluating the impact of inaccurate spatial data on ecological model predictions. Environ Ecol Stat 8(4):311–330. doi:10.1023/A:1012778302005
Lunetta RS, Congalton RG, Fenstermaker LK, Jensen JR, McGwire KC, Tinney LR (1991) Remote sensing and geographic information system data integration: error sources and research issues. Photogramm Eng Rem S 57(6):677–687
Markovsky I (2010) Bibliography on total least squares and related methods. Statistics and Its Interface 3(3):329–334
Markovsky I, Van Huffel S (2007) Overview of total least squares methods. J Signal Process 87(10):2283–2302. doi:10.1016/j.sigpro.2007.04.004
Paige CC, Strakoš Z (2002a) Scaled total least squares fundamentals. Numer Math 91(1):117–146. doi:10.1007/s002110100314
Paige CC, Strakoš Z (2002b) Unifying least squares, total least squares and data least squares. In: Van Huffel S, Lemmerling P (eds) Total least squares and errors-in-variables modeling, Kluwer Academic Publishers, pp 25–34
Ramos JA (2007) Applications of TLS and related methods in the environmental sciences. Comput Stat Data An 52(2):1234–1267. doi:10.1016/j.csda.2007.06.009
Rao BD (1997) Unified treatment of LS, TLS and truncated SVD methods using a weighted TLS framework. In: Van Huffel S (ed) Recent advances in total least squares techniques and errors-in-variables modelling, SIAM, pp 11–20
Richards JA, Jia XP (1999) Remote Sensing Digital Image Analysis: an introduction, 3rd edn. Springer, Berlin, New York
Schaffrin B, Felus Y (2008) On the multivariate total least-squares approach to empirical coordinate transformations: three algorithms. J Geodesy 82(6):373–383. doi:10.1007/s00190-007-0186-5
Van de Kassteele J, Stein A (2006) A model for external drift kriging with uncertain covariates applied to air quality measurements and dispersion model output. Environmetrics 17(4):309–322. doi:10.1002/env.771
Van Huffel S (ed) (1997) Recent advances in total least squares techniques and errors-in-variables modeling. SIAM, Philadelphia
Van Huffel S, Cheng CL, Mastronardi N, Paige C, Kukush A (2007) Total least squares and errors-in-variables modeling. Comput Stat Data An 52(2):1076–1079. doi:10.1016/j.csda.2007.07.001
Van Huffel S, Lemmerling P (eds) (2002) Total least squares and errors-in-variables modeling: analysis, algorithms and applications. Kluwer Academic Publishers, Dordrecht
Van Huffel S, Vandewalle J (1989) On the accuracy of total least squares and least squares techniques in the presence of errors on all data. J Automatica 25(5):765–769. doi:10.1016/0005-1098(89)90033-2
Van Huffel S, Vandewalle J (1991) The total least squares problem: computational aspects and analysis. SIAM, Philadelphia
Veregin H (1995) Developing and testing of an error propagation model for GIS overlay operations. Int J Geogr Inf Sci 9(6):595–619. doi:10.1080/02693799508902059
Wansbeek T, Meijer E (2000) Measurement error and latent variables in econometrics. Elsevier, New York
Acknowledgements
This research was supported in part by the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2-EW-QN303) and the National Natural Science Foundation of China (Grant No. 40971222). The authors are grateful to two anonymous referees for their constructive comments, which helped to improve the quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by: H. A. Babaie
Rights and permissions
About this article
Cite this article
Ge, Y., Wu, T., Wang, J. et al. Scaled total-least-squares-based registration for optical remote sensing imagery. Earth Sci Inform 5, 137–152 (2012). https://doi.org/10.1007/s12145-012-0103-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-012-0103-1