Comparison Between 2-D and 3-D Transformations for Geometric Correction of IKONOS images

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1 Comparison Between -D and -D Transormations or Geometric Correction o IKONOS images ABSTRACT Mehdi Hosseini Jalal Amini Department o Geomatics Engineering, Faculty o Engineering, Univesity o Tehran, Tel: mhoseini@geomatics.ut.ac.ir jamini@ut.ac.ir Very high-resolution satellite image technology is considered as a basic inormation sources or mapping and dierent applications in geomantics. For using o parametric models in geometric correction o satellite images, we need orbital parameters and calibration data. In Ionos imagery, however, both the camera model and precise satellite ephemeris data are withheld rom the user. Thereore we should use empirical methods. In this paper, dierent non-rigorous mathematical models in -D and -D cases are comprised and applied or geometric corrections over an Ionos geoproduct image in Iran. Multiquadratic,polynomials and DLT models are used or this test area. KEYWORDS: Remote Sensing, High-Resolution, DLT, Polynomial, Multiquadratic. INTRODUCTION The preprocessing o remotely sensed image consists o geometric and radiometric characteristics analysis. By realizing these eatures, it is possible to correct image distortion and improve the image quality and readability. Radiometric analysis reers to mainly the atmosphere eect and its corresponding terrain eature's relection, while geometric analysis reers to the image geometry with respect to sensor system With the launch o various commercial high-resolution earth observation satellites, such as Indian Remote Sensing Satellite IRS-C/D, the Space Imaging IKONOS system, SPOT 5 and Digital Globe QUIKBIRD system, precise digital maps generated by satellite imagery are expected in the spatial inormation industry. For last decades, airborne photography is the primary technique employed in producing national map products due to its high accuracy and lexible schedule (Li, 998). However, it cannot map areas where airplanes cannot reach and its mapping requency is constrained by the limits o light planning (Li, 000). Now with the highresolution satellites era, accuracy required by medium and small-scale maps are achievable, with the possibility to requently map an area without the special light planning and scheduling required using aerial photographs. Successul exploitation o the high accuracy potential o these systems depends on accurate mathematical models or the satellite sensor. In the last decade, many studies and researches are perormed with rigorous and non-rigorous mathematical models to rectiy IKONOS images by Baltsavias et al. (00), Hanley and Fraser (00), Fraser et al. (00a, and b) and Fraser et al. (00a, b, c) respectively. Investigations into D positioning using alternative models have also been reported by Jacobsen (00, 00a,b), Toutin et al. (00), Hu and Tao (00, 00) and Tao and Hu (00a, b). One o the main goals o these researches is to ind an appropriate mathematical model with precise and accurate results. The geometric accuracy o data products is terminated by the nowledge o precise imaging geometry, as well as the capability o the imaging model to use this inormation. The precise imaging geometry in its turn is stablished by nowledge o orbit, precise attitude, precise camera alignments with respect to the spacecrat and precise camera geometry (Srivastava and Alurar, 997). Rigorous mathematical models or geometric corrections o any images can be deined as the models, which can be precisely, present the relationship between the image space and the object space. Perspective geometry and projection perorms the basis o the imaging model rame cameras as well as other sensors. For any point in the space, there is a unique projective point in the image plane, however, or any point in the plane there are ininite number o corresponding points in the space (Mihail et al. 00). Due to this act, an additional constrain is needed to deine the point in the D space. Collinearity equations are the rigorous model, which describe this projection relation between D image space and D object space.unlie ordinary photogrammetric photography, high-resolution satellites are a line sensing imaging systems where every line is imaged at dierent time. That may help to understand the need o a special treatment o the sensor model (Mai, 99). In general, the rigorous time dependent mathematical models are based on the collinearity equations, which relate image coordinates o a point to its corresponding ground coordinates. Published studies reported to date on IKONOS and other satellites ocus in two main aspects,the accuracy attainable in ortho-image generation and DTM extraction concerning D positioning rom stereo

2 spatial intersection using rigorous and non-rigorous sensor orientation models. Due to some limitations, most o the new High Resolution Satellite Imagery (HRSI) vendors hide the satellite orbit inormation and calibration data rom the customers community such as or IKONOS and QUICKBIRD imagery. This means that other alternative models should be used to solve practically this problem and calculate the imagery parameters. Thereore, these empirical approaches can be applied to determine the ground point coordinates in either D or D. In this paper, the dierent non-rigorous mathematical models in D and D have been used or geometric corrections o Ionos image. Dierent orders o polynomials, projective, aine, conormal, Multiquadratic and DLT model were used with dierent numbers o GCPs. Figure shows the steps o geometric correction in satellite images. Input Image Method Parameters determination Accuracy assesment Geometric corrected Image D Transormation D Transormation Figure. Steps o geometric correction In the rest o the paper,mathematical models are discused in section, exprimental results and accuracy assesment are discribed in the last section.. Mathematical Models During the satellite imaging process, the projection, the tilt angle, the scanner, the atmosphere condition, the earth curvature and the undulation etc., will cause the satellite image distorted. It is necessary to correction these distortions beore one can really use it as a precise measurement in the large scale operations. In this paper, as previously stated, the orbital parameters were unnown. The mathematical model used to compensate the distortion correction is the socalled rubber shiting method. It neglects all the sources o distortions but deal with the present ones with the help o control points. This also maes the correction procedure easier in the circumstance o insuicient parameters. In this paper, some o D and D transormation used with dierent numbers o ground control points. These models are generally available within most o remote sensing image processing systems. These models can be used to provide suicient insight about the ground elevation eects on the metric integrity o the rectiied images. The ollowing sub sections discuss the models characteristics... Polynomial models Polynomial models usually can be used in the transormation between image coordinates and object coordinates. The needed transormation can be expressed in dierent orders o the polynomials based on the distortion o the image, the number o GCPs and terrain type. A st-order transormation is a linear transormation, which can change location, scale, sew, and rotation. In most cases, irst order polynomial used to project raw imagery to a object or data covering small areas. Transormations o the nd-order or higher are nonlinear transormations that can be used to convert Lat/Long data to object or correct nonlinear distortions such as Earth curvature, camera lens distortion. The ollowing equations are used to express the general orm o the polynomial models in D and D cases : Two-dimensional general polynomials Linear polynomial x=a 0 a Xa Y y=b 0 b Xb Y Quadratic polynomial Cubic polynomial x=a 0 a Xa Ya XYa 4 X a 5 Y y=b 0 b Xb Yb XYb 4 X b 5 Y x=a 0 a Xa Ya XYa 4 X a 5 Y a 6 X Ya 7 X Y a 8 X a 9 Y y=b 0 b Xb Yb XYb 4 X b 5 Y b 6 X Yb 7 X Y b 8 X b 9 Y Three-dimensional general polynomials Linear polynomial x=a 0 a Xa Ya Z y=b 0 b Xb Yb Z Quadratic polynomial x=a 0 a Xa Ya Z a 4 XYa 5 XZ a 6 YZ a 7 X a 8 Y a 9 Z y=b 0 b Xb Yb Z b 4 XYb 5 XZ b 6 YZ b 7 X b 8 Y b 9 Z () () () (4) (5)

3 Cubic polynomial 5) Calculate the correction or each image points rom the ollowing equation. x = a 0 X Y Z 4 XY 5 XZ 6 YZ 7 X^ a 8 Y^ 9 Z^ 0 X^Y X^Z Y^X Y^Z a 4 Z^X 5 Z^Y 6 X^ 7 Y^ 8 Z^ 9 XYZ (6) y = b 0 X Y Z 4 XY 5 XZ 6 YZ 7 X^ b 8 Y^ 9 Z^ 0 X^Y X^Z Y^X Y^Z b 4 Z^X 5 Z^Y 6 X^ 7 Y^ 8 Z^ 9 XYZ a a a... a n = dx b b b... b n = dy 6) Calculate the true value or each points x =xdx y =ydy n n (8) (9).. Multiquadratic Model Process in the multiquadric model consists o the ollowing steps: ) Calculate the distance ( x, y ) j between an image point (x,y) and G.C points. ( X j, Y j) ) Calculate the distance ij between ith and jth point in G.C.P.s ( x, y ). And i (, y ). i x j j ) Conirm the interpolation matrix ( ). F = ij ( n, n) 4) Calculate the residual vectors [dx] and [dy] rom step. Solve the ollowing equation to calculate the coeeicent matrix A and B (F*A=dX, F*B=dY). a b a b a... b... n n an= dx bn= dy (7).. DLT model L5X L6Y L7Z L8 y= L9X L0Y LZ LX LY LZ L4 x= L9X L0Y LZ. Experimental results and Accuracy assessments An IKONOS satellite image rom a region o Tehran is used as a test ield area.this image is located near the central part o Tehran. Figure a,b respectivly show the image with ground control and chec points distribution. Table presents the main characteristics o the acquired images. (0) (a) (b) Figure. The test area with a) GCP and b) chec points distribution

4 Table.Technical speciication o the Ionos Image Image type Pan, Mono Datum WGS 84 Map Projection UTM Zone Number 9 Acquisition date File Format Geo TIFF The chec points and the ground control points (GCPs) in this research were derived rom a digital /500 topographic map that produced by National Catrographic Center (NCC) o Iran. It provides approximately 0cm planimetric accuracy and 50cm vertical accuracy. In Compare with the ground resolution o the IKONOS image, this digital map provides suicient control data. For Investigation o the results rom the mathematical models in section,irstly the unnown coeicients were determined with 0 control points or each model.then with this determined coeicients,the corrected Image coordinates were calculated or 0 chec points.rms errors were calculated or each model base on the two types o coordinates or chec points.table shows results or each model. Table :RMSE values or IKONOS data over Tehran test ield with G.C.Ps Control Chec _D Methods point σxy point σxy Conormal Aine Second order polynomial rd order polynomial D_Projective Multiquadratic First order Third order Multiquadratic(D_Projective) Table :RMSE values or IKONOS data over Tehran test ield with 6 G.C.Ps Control Chec _D Methods point σxy point σxy Conormal Aine Second order polynomial rd order polynomial D_Projective Multiquadratic First order Third order Multiquadratic(D_Projective)

5 Table :RMSE values or IKONOS data over Tehran test ield with G.C.Ps Control Chec _D Methods point σx σy point σx σy Second order polynomial rd order polynomial DLT First Multiquadratic order Third order Multiquadratic(DLT) Table 4:RMSE values or IKONOS data over Tehran test ield with 6 G.C.Ps Control Chec _D Methods point σx σy point σx σy Second order polynomial DLT Multiquadratic First order Multiquadratic(DLT) As we see in above tables,multiquadratic with third order polynomial is the best model in _D case and Multiquadratic with DLT model is the best model in _D case. Also we see in comparison between _D and _D cases, the accuracy is nearly similar because the test area is lat. 4. Conclusion The preprocessing o remotely sensed image consists o geometric and radiometric characteristics analysis. By realizing these eatures, it is possible to correct image distortion and improve the image quality and readability. Radiometric analysis reers to mainly the atmosphere eect and its corresponding terrain eature's relection, while geometric analysis reers to the image geometry with respect to sensor system. In this paper, some o _D and _D transormation models were used with dierent ground control points distribution. These models are generally available within most o remote sensing image processing systems. Comparison between the applied models showed that the multiquadratic with DLT model was the best model or the test area. The accuracy.5 m was be achived with this model. Acnowledjments The autors would lie to thans rom University o Tehran or support this project and Remote Sensing Center (RSC) and Cadaster Organization or the Ionos image and the map. Reerences : Fraser,C.S.,Baltsavias, E.,Gruen, A.,00.Processing o Ionos imagery or submetre D positioning and building extraction,isprs Journal o photogrammetry & Remote Sensing 56 (00) Fraser,C., Hanley, H.,Yamaawa, T.00.sub-Metre Geopositioning with Ionos Geo imagery, ISPRS Joint Worshop on High Resolution Mapping rom Space, Hanover,Germany,00. Fritz,L.,995.Recent Developments or Optical Earth Observation in the United states,photogrammetric Wee,pp75-84,Stuttgart,995. Hanley,H.B. and Fraser,C.S.,00.Geopositioning accuracy o Ionos imagery : indications rom D transormations,photogrammetric Record,7(98) : 7-9. Hattori,S.,one,T., Fraser, C.S. and Hasegawa,H.,000. Orientation o high-resolution satellite images based on aine Projection,International Archires o photogrammetry & Remote Sensing, Amsterdam,(B):59-66(on CD ROM).

6 Li, R., Zhou, G., Yang, S., Tuell, G., Schmidt, N. J. and Flower, C, 000, Astudy o the potential attainable geometric accuracy o IKONOS satellite images, IAPRS, (B4), Mihail, E.M., Bethel, J.S. and McGlone, J.C., 000, Itroduction to modern photogrammetry, John Wiley&sons, New Yor.