georeferencing accuracy assessment of high-resolution satellite images using figure condition method

1256 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 4, APRIL 2009

Georeferencing Accuracy Assessment ofHigh-Resolution Satellite Images Using

Figure Condition MethodHuseyin Topan and Hakan S. Kutoglu

Abstract—In the case of sensor-independent georeferencing,accuracy of the used model is commonly assessed by misfitsseparately obtained from ground control points and independentcheck points. However, applying only this approach has somedisadvantages. This paper proposes using the figure conditionmethod to support the common approach. Applying the figurecondition process, a more rigorous analysis of accuracy for theused models can be conducted, and one can decide whetherthe used model is proper or not. In this contribution, a casestudy is carried out using affine and extended affine models forhigh-resolution IKONOS Geo, OrbView-3 Basic, and QuickBirdOrthoReady Standard images. The results obtained are subjectedto the analysis of figure condition.

Index Terms—Accuracy assessment, affine projection, figurecondition, georeferencing, high-resolution satellite image,IKONOS, OrbView-3, QuickBird.

I. INTRODUCTION

SATELLITE images have to be georeferenced for geospatialapplications such as generation of orthoimage, topographic

map, or digital elevation model (DEM), image fusion, changedetection, etc. [1]. Georeferencing process consists of a kindof coordinate transformation between image and ground co-ordinate systems. Transformation models for this process canbe classified into two groups: sensor-dependent and sensor-independent models. In case of the sensor-independent georef-erencing, which is treated of in this paper, the model parametersare initially not known, so they have to be estimated by a propermethod of parameter estimation using ground control points(GCPs) whose coordinates are present in the relevant groundcoordinate system. To assess the accuracy of the used model,misfits for the image coordinates corresponding to GCPs arecalculated. Then, by using the misfits, the root mean squareerror (rmse) of unit weight, i.e., accuracy of the georeferencing,is obtained. In general, the georeferencing accuracy is alsovalidated by independent check points (ICPs) which are chosenamong GCPs and not included in the parameter estimationprocess.

Manuscript received March 20, 2008; revised August 17, 2008 andSeptember 12, 2008. Current version published March 27, 2009.

H. Topan is with the Department of Geodesy and Photogrammetry Engi-neering, Zonguldak Karaelmas University, Zonguldak 67100, Turkey (e-mail:[email protected]).

H. S. Kutoglu is with the Department of Geodesy and PhotogrammetryEngineering, Zonguldak Karaelmas University, Zonguldak 67100, Turkey(e-mail: [email protected]).

Digital Object Identifier 10.1109/TGRS.2008.2008098

The aforementioned approach to assess the georeferencingaccuracy carries some disadvantages. These can be classified asfollows.

1) It is a common case that a satellite image covers moun-tainous, forest, and/or water surfaces. In such cases, theaccuracy of the georeferencing cannot be validated onthose fields since ICPs may not be produced [2].

2) The more GCPs, the more reliable transformation pa-rameters. Reserving ICPs causes to estimate the modelparameters with a smaller number of GCPs.

3) Misfits at ICPs are pointwise, i.e., misfits for the adjacentpixels might be very different. Therefore, a continuousanalysis of accuracy based on ICPs is not possible.

A more rigorous analysis of georeferencing accuracy, re-ducing those disadvantages, can be conducted by measuringthe capability of the model parameters, estimated for the geo-referencing, at each pixel. This analysis based on the errorpropagation law is called “figure condition analysis” in [2] and[3]. The first application of the figure condition for satelliteimages was carried out in [2], where IRS-1-D, SPOT-5, andLandsat TM images were georeferenced through the 2-D affinetransformation. In this paper, different from the former one, wefurther the figure condition concept to the different images ofIKONOS, OrbView-3, and QuickBird satellites and improvedmodels in comparison to the 2-D affine.

II. FIGURE CONDITION FOR GEOREFERENCING

In the georeferencing process, the mathematical relationshipbetween image and ground coordinate systems can be formu-lated by

rimi = Agr

i · x (1)

where x is the vector of the parameters required for the georef-erencing, Agr

i is the design matrix composed of ground coor-dinates (Xi, Yi, Zi), and rim

i is the vector of image coordinates(ui, vi) which correspond to the ground coordinates (i is justa running index, integer). As mentioned in introduction, theelements of the vector x are initially not known and have tobe estimated using GCPs as follows:

x =(AgrT

GCP · AgrGCP

)−1

· AgrTGCP · rim

i (2)

where AgrGCP is the design matrix of adjustment constituted in

the same way as Agri using GCPs.

0196-2892/$25.00 © 2009 IEEE

TOPAN AND KUTOGLU: GEOREFERENCING ACCURACY ASSESSMENT OF HIGH-RESOLUTION SATELLITE IMAGES 1257

The variance–covariance matrix giving the precision estima-tion of the parameters obtained from (2) is

Kxx = m20 ·

(AgrT

GCP · AgrGCP

)−1

(3)

where m0 is the a posteriori rmse of unit weight.The process is completed by replacing the obtained model

parameters into (1) and computing the georeferenced imagecoordinates. In this process, the georeferenced coordinates areburdened with errors propagated both from the estimated pa-rameters and the ground coordinates on the right-hand side of(1). To obtain the amount of the propagated errors, the errorpropagation law must be applied to (1). In the first step ofthe error propagation, (1) is differentiated with respect to theparameters and the ground coordinates

δrimi = Agr

i · δx + B · δrgri . (4)

Then, the square of the differential equation reads the errorestimation of the coordinates georeferenced

Krimi

rimi

= Agri · Kxx · (Agr

i )T + B · Krgri

rgri· BT (5)

where B is the coefficient matrix constituted by the modelparameters. In the variance–covariance matrix Krim

irim

i, the

diagonal elements are the variances m2uim

i

and m2vim

i

of the

coordinate components ui and vi, respectively. By using thesevariances, one can calculate the precision of location for thegeoreferenced coordinates

mpi =√

m2uim

i

+ m2vim

i

. (6)

The final equation gives us the figure condition of the georef-erencing process for the pixel that it is applied.

III. CASE STUDY

A. Test Area and Data Set

The test area covers Zonguldak city located in Western BlackSea Region of Turkey. This area has a rolling topography withsteep and rugged terrain in some parts. Despite being urbanizedalong the sea coast, some agricultural lands and dense forestareas exist inland. Elevations around the city range up to 500 m.This area is subjected to many geospatial, environmental, andforestry researches using satellite images (see [4]–[23]). Inthis paper, we use the panchromatic images of IKONOS,QuickBird, and OrbView-3 sensors for the test area. The char-acteristics of the images used are summarized in Table I.

The ground coordinates of GCPs have been produced by GPSin static mode on the accessible grounds. The postprocessingof GPS observations has been resulted in accuracy of about±3 cm. The number of GCPs, which are usable for eachgeoreferencing process, is 38 for IKONOS, 37 for OrbView-3,and 33 for QuickBird. The ground coordinates required forestimating figure condition values, here called figure conditionpoints, have been obtained from DEM generated from 1 : 2000topographic maps. The accuracies of DEM data are about±40 cm in planimetry and about ±50 cm in height. The heights

TABLE ISUMMARY OF THE IMAGE CHARACTERISTICS

range from sea level to 500 m. Fig. 1 shows the contour plot ofthe DEM.

The X and Y components of the ground coordinates of GCPsused for IKONOS and QuickBird data have been preprocessedfor the sensor azimuth and sensor elevation angles for a precisegeoreferencing. The reason of doing so is that the IKONOS Geoand QuickBird OrthoReady Standard images are geometricallyprecorrected and resampled on a specified reference plane ata constant height from the reference surface (geoid) on whichGCP coordinates are given (Fig. 2).

Corrections in this procedure are calculated by the followingequations in order to project GCPs onto the relevant referenceplane [24]:

ΔX = −(Zgri − Z0) · sin a/ tan e

ΔY = −(Zgri − Z0) · cos a/ tan e (7)

where a is the sensor azimuth, e is the sensor elevation angle,and Z0 is the height of reference plane from the sea level(local geoid).

B. Mathematical Models Used for Georeferencing

Various mathematical models can be applied for the georef-erencing of satellite images. In this paper, we discuss a basicand two different modified affine projections. The basic affinemodel (model 1) is formulated by [25]

uimi = a000 + a100 · Xgr

i + a010 · Y gri + a001 · Zgr

i

vimi = b000 + b100 · Xgr

i + b010 · Y gri + b001 · Zgr

i (8)

and the modified models (model 2 and model 3, respectively)are given by

uimi = a000 + a100 · Xgr

i + a010 · Y gri + a001 · Zgr

i

+ a101 · Xgri · Zgr

i + a011 · Y gri · Zgr

i + a200 · Xgr2

i

vimi = b000 + b100 · Xgr

i + b010 · Y gri + b001 · Zgr

i

+ b101 · Xgri · Zgr

i + b011 · Y gri · Zgr

i

+ b110 · Xgri · Y gr

i (9)

uimi = a000 + a100 · Xgr

i + a010 · Y gri + a001 · Zgr

i

+ a101 · Xgri · Zgr

i + a011 · Y gri · Zgr

i

vimi = b000 + b100 · Xgr

i + b010 · Y gri + b001 · Zgr

i

+ b101 · Xgri · Zgr

i + b011 · Y gri · Zgr

i (10)

where a and b with running index are the coefficients of theaffine models; there, three running indexes below each coeffi-cient are for the coordinate axes of X , Y , and Z, respectively.


Fig. 1. Contour plot of DEM generated from 1:2000 topographic maps. East and north coordinates are with Universal Transfer Mercator projection of EuropeanDatum—1950.

Fig. 2. Discrepancies in X- and Y -axes for the images resampled on areference plane with constant height.

The model 1 is applied for all three images in this paper.The model 2 is applied only for OrbView-3 Basic becausethis image originally has nonparallel boundaries [5]. As forthe model 3, it is arranged for satellite images with largerview angle and in slow-down imaging like IKONOS Geo andQuickBird OrthoReady Standard [26].

C. Georeferencing and Figure Condition Analysis

The test images have been georeferenced by the methodsstated earlier. The results obtained are summarized in Table II,where mu and mv are the rmse values in u and v axes,respectively. As shown from the table, model 2 for OrbView-3yields a better rmse in the axis v than the model 1, but thesame rmse in the axis u. Model 3 for IKONOS provides thesame results as model 1 but, for QuickBird, reduces the rmsevalues more than 30% in both axes u and v. When Fig. 3 isinvestigated, no systematic errors are observed except somelocal characteristics.

TABLE IISUMMARY OF THE RMSE IN u AND v AXES (mu and mv) AND

FIGURE CONDITION (mp) RESULTS

Those georeferencing applications are subjected to the figurecondition analysis. Table II shows the minimum and maximumvalues from those analyses. According to these values, thebest figure conditions are obtained from the IKONOS image,while the worst are obtained from the OrbView-3 image. Theresults for the QuickBird are very close to that of the IKONOS.Model 1 solution for IKONOS is slightly better than model 3;the opposite is valid for the QuickBird. For the OrbView-3,model 2 has been produced remarkably better figure conditionthan model 1.

Fig. 4 shows the detailed representations of the figure con-dition results. In all representations, it is noticeable that theequivalent figure condition lines are elliptically shaped on theareas where the heights are not available or zero. The ellipticallines bulge in direction of the left lowermost and the rightuppermost corners where GCPs are intensified around. Thismeans that the figure conditions are stronger in this direction.

The flatness in direction of the left uppermost and the rightlowermost corners where GCPs are sparse points out that the


Fig. 3. Vector plot of the rmse in u and v axes at the GCPs. (a) IKONOS with model 1. (b) IKONOS with model 3. (c) OrbView-3 with model 1. (d) OrbView-3with model 2. (e) QuickBird with model 1. (f) QuickBird with model 3.

figure condition corrupts faster in this direction. The best resultsof the figure condition are obtained around the geometric centerof the GCP set. As a general characteristic, the results aredegraded with distance from the center for GCPs. Accordingly,the worst results are obtained toward the image corners. There,the most remarkable result is that the figure condition valuesare dramatically disturbed by increasing in height; the lines areoscillating toward inland where the topography rises and attainthe worst values around the right uppermost corner where theheights are the maximum.

IV. DISCUSSIONS

In this paper, different from the former one [2], the figurecondition method has been applied for the high-resolution opti-cal satellite images (IKONOS, QuickBird, and OrbView-3) bymeans of affine and extended affine models using 3-D groundcoordinates. The results obtained showed the following.

1) The most precise georeferencing precision is achievedaround the geometric center of GCP set.

2) Precisions (figure condition) are degraded with distancefrom the geometric center.

3) GCP distribution influences the figure condition; it cor-rupts faster in directions where GCPs are sparse.

This agrees with the findings of Sertel et al. [2]. As a furthercontribution, this paper shows that the figure condition of themodels using 3-D ground coordinates is extremely sensitiveto the change in topographical heights. Consequently, this

contribution reveals that the number and distribution of GCPs,distance from the geometric center of GCP set, and, mostimportantly, changes in topographical heights are the three keyparameters for the precision of georeferencing model.

V. CONCLUSION

The figure condition method is an application of error propa-gation within the used satellite images. It allows a comprehen-sive analysis of georeferencing as done earlier. Employing thefigure condition method, one can survey how the georeferenc-ing accuracy varies on the image and where the accuracies arestrong or weak. The figures show how accuracy dramaticallychanges at adjacent pixels, depending on the change in height;this is a clear proof of inadequacies of values obtained at ICPsto characterize errors at adjacent points.

When the figure condition is employed to support ICP analy-sis, the following advantages can be attained.

1) To control mountainous, forest, and/or water surfaceswhere ICPs do not exist is possible.

2) A continuous analysis of accuracy can be conducted;therefore, accuracies at adjacent pixels to ICPs can beobtained.

3) In case of a few numbers of GCPs, some ICPs can be usedas GCP to obtain more reliable model parameters. In caseof a very limited number of GCPs, even all ICPs can beconsidered to use as GCPs so that accuracy test can becarried out only by the figure condition analysis.


Fig. 4. Contour plot of figure condition results. East and north coordinates are with Universal Transfer Mercator projection of European Datum—1950.(a) IKONOS with model 1. (b) IKONOS with model 3. (c) OrbView-3 with model 1. (d) OrbView-3 with model 2. (e) QuickBird with model 1. (f) QuickBirdwith model 3.

4) Use of a not proper mathematical model for the imagegeoreferencing is one of the main reasons of the secondand third disadvantages, stated in introduction, for theclassical accuracy assessment. Through the figure con-dition method, the limitations of a mathematical modelapplied can be determined and decided whether the modelis proper or not.

ACKNOWLEDGMENT

The authors would like to thank Dr. K. Jacobsen,Dr. Ç. Mekik, and M. Oruç for their important contributions,and TUBITAK and ZKU for providing the images within theresearch projects. The authors would also like to thank theanonymous reviewers for their comments that greatly improvedthis paper.

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Huseyin Topan received the B.Sc. and M.Sc. de-grees in geodesy and photogrammetry engineeringfrom Zonguldak Karaelmas University, Zonguldak,Turkey, in 2001 and 2004, respectively. He is cur-rently Ph.D. student at Istanbul Technical University,Istanbul, Turkey.

Since 2002, he has been a Researcher with theDepartment of Geodesy and Photogrammetry Engi-neering, Zonguldak Karaelmas University. His mainresearch topics include georeferencing and informa-tion content analysis of remote sensing images.

Hakan S. Kutoglu received the B.Sc., M.Sc., andPh.D. degrees in geodesy and photogrammetry engi-neering from Istanbul Technical University, Istanbul,Turkey, in 1994, 1997, and 2001, respectively.

He joined the Zonguldak Karaelmas University,Zonguldak, Turkey, in 1994, as a Research Assistant,where he was an Assistant Professor between 2001and 2006 and obtained the title of Associate Pro-fessor in 2006. Since 2006, he has been holding theVice Dean position with the Faculty of Engineering,Zonguldak Karaelmas University, where he is also

currently with the Department of Geodesy and Photogrammetry Engineering.His research interests include theoretical and practical geodesy, geodetic ap-plications of GPS, geodetic networks, datum transformations, and deformationmonitoring.

georeferencing accuracy assessment of high-resolution satellite images using figure condition method

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