*Di, K.C.[Kai-Chang]*,
*Ma, R.J.[Rui-Jin]*,
*Li, R.[Ron]*,

**Rational Functions and Potential for Rigorous Sensor Model Recovery**,

*PhEngRS(69)*, No. 1, January 2003, pp. 33-42.
After improving the geopositioning accuracy of Ikonos Geo stereo
imagery with ground control points by either refining the
vendor-provided Ikonos RF coefficients or refining the RF-derived
ground coordinates, the accuracy of 3D ground point determination was
improved to 1 to 2 meters.

WWW Link.
**0304**

BibRef

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,
*Jiang, W.*,

**Photogrammetric exploitation of Ikonos imagery for mapping applications**,

*JRS(25)*, No. 14, 2004, 2833-2853.

PDF File.
BibRef
**0400**

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,

**3D reconstruction methods based on the rational function model**,

*PhEngRS(68)*, No. 7, July 2002, pp. 705-714.

PDF File.
BibRef
**0207**

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,

**Updating solutions of the rational function model using
additional control information**,

*PhEngRS(68)*, No. 7, July 2002, pp. 715-724.

PDF File.
BibRef
**0207**

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,

**Use of the rational function model for imagery rectification**,

*CanRS(27)*, No. 6, 2001, pp. 593-602.

PDF File.
BibRef
**0100**

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,

**The rational function model:
A Tool for Processing High-Resolution Imagery**,

*EOMag(10)*, No. 1, 2001, pp. 13-16.

PDF File.
BibRef
**0100**

*Tao, C.V.[C. Vincent]*,
*Hu, Y.[Yong]*,

**A Comprehensive Study of the Rational Function Model for Photogrammetric
Processing**,

*PhEngRS(67)*, No. 12, December 2001, pp. 1347-1357.
RPC discussion.

PDF File.
BibRef
**0112**

*Grodecki, J.F.[Jacek Franciszek]*,
*Dial, Jr., O.E.[Oliver Eugene]*,
*Grodecki, J.[Jacek]*,
*Dial, G.[Gene]*,

**Block Adjustment of High-Resolution Satellite Images Described by
Rational Functions**,

*PhEngRS(69)*, No. 1, January 2003, pp. 59-70.
For Ikonos satellite imagery, the Rational Polynomial Coefficient (RPC)
block adjustment achieves the same accuracy
as the ground station block adjustment with the full physical camera model.

WWW Link.
**0304**

BibRef

*Fraser, C.S.[Clive S.]*,
*Dial, G.[Gene]*,
*Grodecki, J.[Jacek]*,

**Sensor orientation via RPCs**,

*PandRS(60)*, No. 3, May 2006, pp. 182-194.

Elsevier DOI
**0610**

High resolution; Satellite; Imagery; Orientation
BibRef

*Fraser, C.S.[Clive S.]*,
*Hanley, H.B.[Harry B.]*,

**Bias-compensated RPCs for Sensor Orientation of High-resolution
Satellite Imagery**,

*PhEngRS(71)*, No. 8, August 2005, pp. 909-916.

WWW Link.
**0602**

A bias-compensated RCP bundle adjustment is shown to produce sub-pixel
accuracy geopositioning from Ikonos and Quickbird stereo imagery.
BibRef

*Fraser, C.S.*,
*Yamakawa, T.*,

**Insights into the affine model for high-resolution satellite sensor
orientation**,

*PandRS(58)*, No. 5-6, July 2004, pp. 275-288.

Elsevier DOI
**0411**

BibRef

*Chen, L.C.[Liang-Chien]*,
*Teo, T.A.[Tee-Ann]*,
*Liu, C.L.[Chien-Liang]*,

**The Geometrical Comparisons of RSM and RFM for FORMOSAT-2 Satellite
Images**,

*PhEngRS(72)*, No. 5, May 2006, pp. 573-580.

WWW Link.
**0610**

A comparison of the geometric performances between the
RSM (rigorous sensor model) and RFM (rational function model) for
FORMOSAT-2 satellite images. RFM well behaved, similar positioning errors.o
BibRef

*Chen, L.C.[Liang-Chien]*,
*Chang, W.C.[Wen-Chi]*,
*Teo, T.A.[Tee-Ann]*,

**Geometric Integration of Heterogeneous Models for Multisatellite Image
Positioning**,

*GeoRS(50)*, No. 7, July 2012, pp. 2802-2809.

IEEE DOI
**1208**

BibRef

*Chen, L.C.[Liang-Chien]*,
*Teo, T.A.[Tee-Ann]*,
*Lo, C.Y.[Chao-Yuan]*,

**Elevation-Controlled Block Adjustment for Weakly Convergent Satellite
Images**,

*ISPRS08*(B1: 761 ff).

PDF File.
**0807**

BibRef

*Aguilar, M.A.[Manuel A.]*,
*Aguilar, F.J.[Fernando J.]*,
*Agüera, F.[Francisco]*,
*Sánchez, J.A.[Jaime A.]*,

**Geometric Accuracy Assessment of QuickBird Basic Imagery Using
Different Operational Approaches**,

*PhEngRS(73)*, No. 12, December 2007, pp. 1321-1332.

WWW Link.
**0712**

Geometric correction using rational functions and rigorous sensor
models, and orthorectification with different DEMs of the QuickBird
basic imagery for mapping applications.
BibRef

*Xiong, Z.[Zhen]*,
*Zhang, Y.[Yun]*,

**A Generic Method for RPC Refinement Using Ground Control Information**,

*PhEngRS(75)*, No. 9, September 2009, pp. 1083-1092.

WWW Link.
**0910**

A newly developed Generic method for Rational Polynomial Coefficient
refinement focusing on a comparison between the Bias Compensation
method.
BibRef

*Tong, X.H.[Xiao-Hua]*,
*Liu, S.J.[Shi-Jie]*,
*Weng, Q.H.[Qi-Hao]*,

**Bias-corrected rational polynomial coefficients for high accuracy
geo-positioning of QuickBird stereo imagery**,

*PandRS(65)*, No. 2, March 2010, pp. 218-226.

Elsevier DOI
**1003**

QuickBird; Rational polynomial coefficient; Bias correction;
Geo-positioning accuracy
BibRef

*Xiong, Z.*,
*Zhang, Y.*,

**Bundle Adjustment With Rational Polynomial Camera Models Based on
Generic Method**,

*GeoRS(49)*, No. 1, January 2011, pp. 190-202.

IEEE DOI
**1101**

BibRef

*Zhang, L.[Lu]*,
*Balz, T.[Timo]*,
*Liao, M.S.[Ming-Sheng]*,

**Satellite SAR geocoding with refined RPC model**,

*PandRS(69)*, No. 1, April 2012, pp. 37-49.

Elsevier DOI
**1202**

SAR geocoding; Range-Doppler; Rational Polynomial Camera; SAR
simulation; Image matching
BibRef

*Oh, J.[Jaehong]*,
*Lee, C.[Changno]*,

**Automated bias-compensation of rational polynomial coefficients of
high resolution satellite imagery based on topographic maps**,

*PandRS(100)*, No. 1, 2015, pp. 14-22.

Elsevier DOI
**1502**

High-resolution satellite imagery
RPC descriptions.
BibRef

*Jiang, Y.*,
*Zhang, G.*,
*Chen, P.*,
*Li, D.*,
*Tang, X.*,
*Huang, W.*,

**Systematic Error Compensation Based on a Rational Function Model for
Ziyuan1-02C**,

*GeoRS(53)*, No. 7, July 2015, pp. 3985-3995.

IEEE DOI
**1503**

RFM analysis for a particular sensor.
Accuracy
BibRef

*Long, T.F.[Teng-Fei]*,
*Jiao, W.[Weili]*,
*He, G.J.[Guo-Jin]*,

**RPC Estimation via L_1-Norm-Regularized Least Squares (L1LS)**,

*GeoRS(53)*, No. 8, August 2015, pp. 4554-4567.

IEEE DOI
**1506**

least squares approximations
BibRef

*Huang, W.C.*,
*Zhang, G.*,
*Li, D.*,

**Robust Approach for Recovery of Rigorous Sensor Model Using Rational
Function Model**,

*GeoRS(54)*, No. 7, July 2016, pp. 4355-4361.

IEEE DOI
**1606**

Charge coupled devices
BibRef

*Shen, X.[Xiang]*,
*Liu, B.[Bin]*,
*Li, Q.Q.[Qing-Quan]*,

**Correcting bias in the rational polynomial coefficients of satellite
imagery using thin-plate smoothing splines**,

*PandRS(125)*, No. 1, 2017, pp. 125-131.

Elsevier DOI
**1703**

Rational function model
BibRef

*Shen, X.[Xiang]*,
*Li, Q.Q.[Qing-Quan]*,
*Wu, G.F.[Guo-Feng]*,
*Zhu, J.S.[Jia-Song]*,

**Bias Compensation for Rational Polynomial Coefficients of
High-Resolution Satellite Imagery by Local Polynomial Modeling**,

*RS(9)*, No. 3, 2017, pp. xx-yy.

DOI Link
**1704**

BibRef

*Jannati, M.[Mojtaba]*,
*Zoej, M.J.V.[Mohammad Javad Valadan]*,
*Mokhtarzade, M.[Mehdi]*,

**A Knowledge-Based Search Strategy for Optimally Structuring the
Terrain Dependent Rational Function Models**,

*RS(9)*, No. 4, 2017, pp. xx-yy.

DOI Link
**1705**

BibRef

*Li, P.F.[Peng-Fei]*,
*Sun, K.[Kaimin]*,
*Li, D.R.[De-Ren]*,
*Sui, H.G.[Hai-Gang]*,
*Zhang, Y.[Yong]*,

**An Emergency Georeferencing Framework for GF-4 Imagery Based on GCP
Prediction and Dynamic RPC Refinement**,

*RS(9)*, No. 10, 2017, pp. xx-yy.

DOI Link
**1711**

BibRef

*Noh, M.J.[Myoung-Jong]*,
*Howat, I.M.[Ian M.]*,

**Automatic relative RPC image model bias compensation through
hierarchical image matching for improving DEM quality**,

*PandRS(136)*, 2018, pp. 120-133.

Elsevier DOI
**1802**

RPCs bias, Compensation, Image matching, Arctic and Antarctic
BibRef

*Xu, K.[Kai]*,
*Zhang, G.[Guo]*,
*Zhang, Q.J.[Qing-Jun]*,
*Li, D.R.[De-Ren]*,

**Calculating Viewing Angles Pixel by Pixel in Optical Remote Sensing
Satellite Imagery Using the Rational Function Model**,

*RS(10)*, No. 3, 2018, pp. xx-yy.

DOI Link
**1804**

BibRef

*Moghaddam, S.H.A.[Sayyed Hamed Alizadeh]*,
*Mokhtarzade, M.[Mehdi]*,
*Naeini, A.A.[Amin Alizadeh]*,
*Amiri-Simkooei, A.[Ali_Reza]*,

**A Statistical Variable Selection Solution for RFM Ill-Posedness and
Overparameterization Problems**,

*GeoRS(56)*, No. 7, July 2018, pp. 3990-4001.

IEEE DOI
**1807**

geophysical image processing, geophysical techniques,
particle swarm optimisation, polynomials, rational functions,
statistical solution
BibRef

*Gholinejad, S.[Saeid]*,
*Amiri-Simkooei, A.[Alireza]*,
*Alizadeh Moghaddam, S.H.[Sayyed Hamed]*,
*Alizadeh Naeini, A.[Amin]*,

**An automated PCA-based approach towards optimization of the rational
function model**,

*PandRS(165)*, 2020, pp. 133-139.

Elsevier DOI
**2006**

Rational function model, Principal component analysis,
Noise reduction, Thresholding ridge ratio
BibRef

*Li, Q.Y.[Qing-Yang]*,
*Zhong, R.[Ruofei]*,
*Yang, C.[Cankun]*,
*Zhao, K.[Ke]*,
*Zhang, C.C.[Chen-Chen]*,
*Li, Y.[Yue]*,

**Geometric Quality Improvement Method of Optical Remote Sensing
Satellite Images Based on Rational Function Model**,

*RS(14)*, No. 18, 2022, pp. xx-yy.

DOI Link
**2209**

BibRef

IEEE DOI

Cameras, Geometry, Orbits, Retina, Visualization BibRef

*Topan, H.*,
*Taskanat, T.*,
*Cam, A.*,

**Georeferencing Accuracy Assessment of Pléiades 1A Images Using Rational
Function Model**,

*SSG13*(251-256).

DOI Link
**1402**

BibRef

*Yavari, S.*,
*Zoej, M.J.V.*,
*Mokhtarzade, M.*,
*Mohammadzadeh, A.*,

**Comparison Of Particle Swarm Optimization And Genetic Algorithm In
Rational Function Model Optimization**,

*ISPRS12*(XXXIX-B1:281-284).

DOI Link
**1209**

BibRef

*Samadzadegan, F.*,
*Ramzi, P.*,
*Abootalebi, A.*,

**Capability Assessment of High Resolution Satellite Imagery for 3D
Reconstruction Using RPC Parameters**,

*ISPRS08*(B1: 889 ff).

PDF File.
**0807**

BibRef

*Liu, S.J.*,
*Tong, X.H.*,

**Transformation between Rational Function Model and Rigorous Sensor
Model for High Resolution Satellite Imagery**,

*ISPRS08*(B1: 873 ff).

PDF File.
**0807**

BibRef

*Singh, S.K.[Sanjay K.]*,
*Naidu, S.D.[S. Devakanth]*,
*Srinivasan, T.P.*,
*Krishna, B.G.[B. Gopala]*,
*Srivastava, P.K.*,

**Rational Polynomial Modelling for CARTOSAT-1 data**,

*ISPRS08*(B1: 885 ff).

PDF File.
**0807**

BibRef

*Lin, X.Y.[Xian-Yong]*,
*Yuan, X.X.[Xiu-Xiao]*,

**Improvement of the Stability Solving Rational Polynomial Coefficients**,

*ISPRS08*(B1: 711 ff).

PDF File.
**0807**

BibRef

*Claus, D.[David]*,
*Fitzgibbon, A.W.[Andrew W.]*,

**A Rational Function Lens Distortion Model for General Cameras**,

*CVPR05*(I: 213-219).

IEEE DOI
**0507**

BibRef

And:

**A Plumbline Constraint for the Rational Function Lens Distortion Model**,

*BMVC05*(xx-yy).

HTML Version.
**0509**

BibRef

*Kim, H.J.[Hye Jin]*,
*Kim, D.S.[Dae Sung]*,
*Lee, H.S.[Hyo Sung]*,
*Kim, Y.I.[Yong Il]*,

**A Study on the Generation of the KOMPSAT-1 RPC Model**,

*PCV02*(B: 112).
**0305**

BibRef

*Hartley, R.I.[Richard I.]*,
*Saxena, T.[Tushar]*,

**The Cubic Rational Polynomial Camera Model**,

*DARPA97*(649-654).
BibRef
**9700**

Chapter on Active Vision, Camera Calibration, Mobile Robots, Navigation, Road Following continues in

Camera Calibration, Stereo .

Last update:May 22, 2023 at 22:32:27