JAG l Volume 3 - Issue 4 - 2001

Precision rectification of high resolution satellite imagery without ephemeris data

Saeid Sadeghian 1,2, Mohammad Javad Valadan Zoej3, Mahmoud Reza Delavarl, Ahmad Abootalebiz

1 Surveying Engineering Department, Engineering Faculty, Tehran University, Tehran, Iran

2 National Cartographic Center (NCC), PO Box 13185-1684, Tehran, Iran (e-mail: Sadeghian@ncc.neda.net.ir)

3 Department of Geodesy and Geomatics Engineering, K.N. Toosi University of Technology, No. 1346, PO Box 19697, Tehran, Iran (email: Valadan@edri.net)

KEYWORDS: High resolution satellite imagery, IKONOS,

SPOT, KFA-1000, mathematical models, rational func-

tion, DLT, multiquadric, finite elements, accuracy.

ABSTRACT

The huge capability of high resolution satellite imageries (HRSI),

that includes spatial, spectral, temporal and radiometric resolutions

as well as stereoscopic vision introduces them as a powerful new

source for the Photogrammetry, Remote Sensing and GIS communi-

ties. High resolution data increases the need for higher accuracy of

data modeling. The satellite orbit, position, attitude angles and

interior orientation parameters have to be adjusted in the geometri-

cal model to achieve optimal accuracy with the use of a minimum

number of Ground Control Points (GCPs). But most high resolution

satellite vendors do not intend to publish their sensor models and

ephemeris data. There is consequently a need for a range of alter-

native, practical approaches for extracting accurate 2D and 3D ter-

rain information from HRSI. The flexibility and good accuracy of

the alternative models demonstrated with KFA-1000 and the well-

known SPOT level 1A images. A block of eight KFA-1000 space

photos in two strips with 60% longitudinal overlap and 15% lateral

sidelap and SPOT image with rational function, DLT, 2D projective,

polynomials, affine, conformal, multiquadric and finite element

methods were used in the test. The test areas cover parts of South

and West of Iran. Considering the quality of GCPs, the best result

was found with the DLT method with a RMSE of 8.44 m for the

KFA-1000 space photos.

INTRODUCTION

In spite of many years of updated launch announcement, program delays and five recent failures to deploy a num- ber of high resolution satellites, such as Earlybird-l 1997,

EROS-A 1998, IKONOS-1 1999, QuickBird- 2000, OrbView- 2001, with the successful launch and deploy- ment of IKONOS-2 satellite in September 1999, EROSAI

in December 2000 and QuickBird- in October 2001, the era of commercial high-resolution earth observation satellites for digital mapping began. Several US compa- nies, Russia, France and India scheduled launches of such high-resolution imaging satellites. Therefore the number

of high resolution satellite sensors for mapping applica-

tions is growing fast. The geometry of them is based on

the pushbroom principle which differs significantly from

photogrammetric frame cameras such as KFA-1000

space photos. In contrast to frame cameras which pre-

serves the same orientation of the 3-D bundle of imaging

rays for the whole frame, the spatial position and orien-

tation of the imaging sensor is continually changing along the orbit and the imaging geometry becomes

dynamic and time-dependent.

In the past 15 years many different models for geometric

correction have been developed, for example Gugan

(1986) suggested an orbital parameter model. The model

was successfully adapted by Valadan Zoej (1998) and

applied to SPOT level 1 A and 1 B, MOMS-02 and IRS-l C imagery (Valadan Zoej, 1999). But the ancillary data

(position, velocity vectors and angular rates) of the satel- lite platform have not been provided with IKONOS

images. Therefore alternative ways of camera modeling

should be used. Recently, several approaches have been

reported to tackle this issue. Among them, the Rational

Function Model (RFM) seams to gain popularity, that

does not require parameters of the interior orientation

and ephemeris information. The solution is based only on

ground control point. This is an advantage for processing

the new HRSI. In this paper the possibility by using non-

rigorous sensor model for geometric correction of HRSI

has been explore and tested for KFA-1000 and

images.

SPOT

HIGH RESOLUTION SATELLITE IMAGERY (HRSI) Fritz (1999) classified five categories of spatial resolution with break points at 0.5, 3, 30 and 300 m, that O.S

Rectification of high resolution satellite imagery JAG l Volume 3 - Issue 4 - 2001

erating cross track stereo a base-height

(sensor height) ratio of 0.6 and

(Li, R, 1998). The high resolution systems that scheduled

worlds first high resolution commercial satellite,

Imaging in September

4-meter 1 l-bit multispectral sensor. IKONOS in a sun-synchro-

through the use of implemented

digital star trackers to establish precise camera

position and attitude (Zhou, 2000). The KFA-1000 cam-

era system is originally planned for interpretation

mapping of a good

resolving

objects like paths narrower than three

meters can be seen on these images when there is suffi-

cient contrast on the The KFA-1000 photo has 5

fiducial marks, 4 in the center of each side and 1 in the

photo center, So, the transformation to the calibrated

fiducial mark coordinates is not a problem. The fiducials

are superimposed onto the film and if there is not suffi-

cient contrast, observation of them can be difficult. The

KFA-1000 imaging system has the advantage of being an

optical frame sensor and is not made of a linear array

sensor such as IKONOS and SPOT. They do not have

problems like shifts or variations between successive sen- sor orientations. However, they have problems like pho-

tographic processing and storage. The vertical accuracy

on the other side is limited by mapping with space pho-

tos. For map revision the vertical component is unimpor-

tant. The height accuracy is mainly determined by the

base to height ratio (B/H). The KFA-1000 has not been

designed for optimal height accuracy. B/H for SPOT4 is

better but the difference in time between the recording

of the same area by SPOT4 can cause some problems. For

example, the reflectance of the ground may be changed.

For KFA-1000 and IKONOS images such a problem with

the stereo effect do not exist. Comparison of technical

data for operational earth observation sensors show in

Table 2.

Due to technical limitation there is still a linear relation

between spatial resolution and swath width. Using high

resolution systems the number of scenes would have to

be increased quadratically for a certain application which

causes additional time and costs for buying, storing and

processing the data. But the sensor in the medium range like SPOT or KFA-1000 has large swath width.

3 ALTERNATIVE MODELS

TABLE 1. High resolution commercial earth observing satellites that scheduled for future

System

Rectification of high resolution satellite imagery

make an orbital resection unstable, and even if many

ground control points and several images are used, a

solution may not be possible. The rigorous sensor model

usually has some disadvantages (Madani, 1999):

- Usually, sensor models and their physical parameters

are not known. Satellite vendors may not publish their

sensor models.

- The rigorous model is usually complex, requiring spe-

cialized software.

- The real-time mathematical model of analytical plot-

ters or softcopy systems must be changed for each dif-

ferent image sensor.

- Selecting proper software for multi-sensor triangula-

tion and using its mathematical model in the real-time

loop can be difficult.

There is consequently a need for a range of alternative,

practical approaches for extracting accurate 2D and 3D

terrain information from high resolution satellite imagery

(Fraser, 2000; Hanley, 2001).

3.1 RATIONAL FUNCTION MODEL (RFM)

The concept of RFM was developed by Gyer, and has

been used extensively by the US Defense Mapping

Agency in their Digital Production System for example

PEGASUS (Greve, 1992). The RFM is widely used is US

intelligence community. An image coordinate is deter-

mined from a ratio of two polynomial functions (OGC,

1999). The RFM maps three-dimensional ground coordinates to

image space on any differentially perspective imagery to

include panoramic, IKONOS, SPOT, MOMS, Landsat, strip and frame imageries like KFA-1000. The Rational

Polynomial Camera (RPC) IKONOS model is expressed sim-

ply as a ratio of two cubic polynomials. It is generic

enough to be easily interfaced with most softcopy pho-

togrammetric packages. Furthermore, it contains enough

degrees of freedom to maintain full accuracy of the phys-

ical IKONOS sensor. RPC IKONOS model differs by no more

than 0.04 pixel from the physical model, with the RMS

error below 0.01 pixel (Grodecki, 2001). DLT, 2D projec- tive, polynomials, affine, conformal transformation and

also collinearity equations is a simplified form of the RFM.

3.1.1 Direct linear transformation (DLT) Eleven linear orientation parameters defining the rela-

tionship between two dimensional image space and

three-dimensional object space.

3.1.2 Two dimensional projective transformation It is defined by eight parameters, the relationship

between the object and image planes.

3.1.3 Polynomial approach

A frequently used approach to model real-time image geometry uses polynomial functions (instead of rigorous

models).

JAG l Volume 3 - Issue 4 - 2001

3.1.3.1 Affine

The model for 3D analysis of linear array imagery via a 20

affine model is given (Hattoriet al, 2000). High resolution

satellite imaging sensors feature very long focal lengths

and narrow fields of view, for example 0.93 for IKONOS

but 4 for SPOT and 7 for MOMS. Therefore high corre-

lations develops between EO parameters within a per-

spective projection since the narrow bundle of rays effec- tively approaches a parallel projection.

3.1.3.2 Conformal Four parameter similarity model (a rotation, shift and uni-

form scaling).

3.1.3.3 Multiquadric approach

A polynomial is first used to model the general geomet-

ric transformation. An interpolating function is then used

to separately fit the vectors of residuals in X and Y at

each control point. Weights explaining the effect of local

distortions measured at each control point are calculated

using an interpolating matrix developed from distance

between control points. Details are given by Ehlers

(1997).

3.2 FINITE ELEMENT METHOD

The finite element method provids a systematic proce-

dure for the derivation of the approximation functions

over subregions of the domain. The method is endowed

with three basic features that account for its superiority

over other competing methods. First, a geometrically

complex domain of the problem is represented as a col-

lection of geometrically simple subdomains, called finite

elements. Second, over each finite element, the approxi-

mation functions are derived using the basic idea that

any continuous function can be represented by a linear

combination of algebraic polynomials. Third, algebraic

relations among the undetermined coefficients (i.e.,

nodal values) are obtained by satisfying the governing

equations, often in a weighted-integral sense, over each

element.

Linear triangular elements were used in this investiga-

tion.

4 TEST DATA 4.1 TEST AREA AND DATA OF THE KFA-1000 PHOTOS

A block of eight KFA-1000 photos in two strips with 60% longitudinal overlap and 15% lateral sidelap was used in the test. The adjacent photo strips had been

exposed simultaneously with the KFA-1000 double cam- era system where the rotational angle between the cam- era unit is 16 degrees. The flying height was 276 km and the image size on the ground was 80*80 km. The focal length of the camera was 1009 mm, and the original image scale was about 1:272000. The photos had been taken in 1990 of the South of Iran and the test area is

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Rectification of high resolution satellite imagery

flat. There were not remarkable differences in contrast

and sharpness between photos. The radial distortions of

the camera lenses were given in 8 different directions with the last digit of 10 microns. The values were given

only to the radius length of 140 and 184 mm from the

origin of coordinates and the distortion was strongly

asymmetric. At the same distance along different radius,

the difference in distortion values could be up to 50

microns.

The main problem of handling space photos and images is the availability of GCPs. In this test GCPs have been

measured on the model at a scale of I:40000 aerial

photos in DSR14 analytical plotter after completion of

inner, relative and absolute orientation. The two color

films of the KFA-1000 supported the object identifica-

tion. The accuracy of the GCPs was estimated to be bet-

ter than 1 m.

There was no available photogrammetric instrument in

Iran of sufficient accuracy that could be used because of

the large format of the photos (30*30cm). Ways of over-

coming the problems can be as follows: 1) Making a pho-

tographic reproduction of the image in suitable pieces,

measuring with traditional instruments and pining the

pieces together before calculation. 2) Shipping the image to a foreign institution which has image carriers of suffi-

cient size. 3) Reproducing the image photographically from the original 30*30cm size to 23*23 cm to be mea-

surable in a mono comparator. 4) Using overlapping

copies (23*30) in Planicomp Pl, analytical plotter. 5)

Scanning the space photos and use the digital pho- togrammetric and image processing systems. At first

method 3 was used. For determination of geometric dis-

tortion of camera a grid was used and then the grid and

its photo were measured. After computation, it was real-

ized that geometric distortion due to photography is high

(for example 150 micron) and the root mean square

errors of residuals was 530 micron because of large lens

JAG . Volume 3 - Issue 4 - 2001

distortion of camera, therefore, method 1 was employed.

Point selection, numbering and pugging were prepared.

Artificial points (tie points) drilled into emulsion with

PUG V Wild. After calibration, photo coordinates of the

18 pieces of 8 KFA-1000 photos were measured with a

monocomparator.

After making a photographic reproduction of the image

in suitable pieces and measuring with traditional instru-

ments, the pieces are then joined together before calcu-

lation. The pieces of one KFA-1000 photo pinned with

conformal transformation using at least four common points. The results were better than 3 micron.

4.2 TEST AREA AND DATA ACQUISITION OF THE SPOT

IMAGE

The SPOT level IA image that was used covers the

Kermanshah area in the west of Iran. It was acquired in

September 1999. Height range of the terrain is 1300 m

to 3500 m. A GPS survey to provide the test field of

ground control and check points was carried out by staff

from N.C.C. in 2001. Their positions and heights were

measured using GPS employing differential GPS tech-

niques. The position of the GCPs on image were mea-

sured monoscopically using the PCI EASYPACE package,

who knew the positions of these points on the ground.

The image measurements were then presented and input

to the adjustment program.

5 EVALUATION OF RESULTS Table 3 and 4 show the summary of the results of poly-

nomials and multiquadrics methods. Using a 11 terms

polynomial transformation, various tests was carried out

on the SPOT level 1 A data. 12 points was used as control

points and the remaining 7 points as check points.

The vector diagram constructed from the residual values

achieved with 12 control points and 7 check points for

TABLE 3. AE , AN RMSE values achieved in terms of UTM coordinates of the SPOT level IA data

Method Control Points (n=l2

Polynomial AE b-t) AN (ml API (m) 3 term (affine) 149.73 25.07 151.81

4 term (xy) 138.62 23.34 140.57

5 term (x2) 14.21 3.04 14.53

6 term (~2) 13.93 3.02 14.25

7 term (x2y) 13.24 2.75 13.52

8 term (xy2) 13.23 2.29 13.43

9 term (~2~2) 10.26 2.24 10.50

10 term (x3) 3.90 0.98 4.02

11 term (~3) 3.71 0.11 3.71

Multiquadric (3 term) 0.00 0.00 0.00

Multiquadric (6 term) 0.00 0.00 0.00

Multiquadric (10 term) 0.00 0.00 0.00

Rational PCI V7.0 13.84 4.77 14.63

AE (m) 185.80

189.02

18.10

18.77

16.90

17.04

20.20

13.56

13.65

185.70

3.85

13.32

18.12

Check Points (n= 7)

AN b-4 API (m) 29.12 188.07 29.67 191.33 3.72 18.47 3.52 19.10 3.02 17.16

2.61 17.24

2.73 20.39

6.69 15.13

9.43 16.59

29.11 187.97

15.08 15.57

6.94 15.02

7.83 19.73

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Rectification of high resolution satellite imagery JAG l Volume 3 - Issue 4 - 2001

the SPOT level IA are included as Fig.1. This diagram

shows that the residual errors at the individual control

and check points are completely random, no systematic

component can be discovered in this plot.

Table 5 shows the summary of the results of 30 projec-

tive (DLT), 20 projective, finite elements and conformal

methods. In finite element method, a linear triangle ele-

ment with six node was used.

CONCLUSIONS AND RECOMMENDATIONS

This project described the interpolative mathematical

models for geometric corrections of space photos and

images. It is important to note that polynomials are

mathematically unconstrained between control points such that higher order polynomials will begin to intro-

duce undesirable oscillations. The application of the mul-

tiquadric method in the image registration and rectifica-

tion is suitable, than using global polynomials or local

piecewice methods. The great advantages of the multi-

quadric algorithm are that : i) it describes a continuous

interpolation function; ii) all GCPs contribute to the

geometric transformation; and iii) the image geometry can be wrapped in any given constraint.

For KFA-1000 photos with 2D and 3D projective for inde-

pendent check points, accuracy is better than IOm. Projective transformation with a priori affine or projective

inner orientation gave better results than without it. The

results of DLT is better than 2D projective transforma-

tion. KFA-1000 photos give better results than SPOT

image. KFA-1000 photos can be used for production of

photomap, planimetric map, thematic map and updating

of topographic map up to scale of 1:50000.

TABLE 4. AE , AN RMSE values achieved in terms of UTM coordinates of the KFA-1000 data

Method Control Points (x21 Check Points (n= 7)

Polynomial AE (ml AN b-n) API (m) AE b-4 AN (ml API (m) 3 term (affine) 92.18 97.86 134.44 89.23 107.85 139.98 4 term (xy) 67.66 16.54 69.65 76.18 20.28 78.83

5 term (x2) 8.65 11.96 14.76 7.82 19.44 20.95

6 term (~2) 7.95 9.57 12.44 7.63 17.90 19.46

7 term (xzy) 6.61 9.28 11.39 9.74 17.26 19.82

8 term (xy2) 4.76 5.67 7.41 9.24 13.11 16.04

9 term (~2~2) 4.74 5.39 7.18 8.63 12.84 15.47

10 term (x3) 4.74 5.37 7.16 8.63 12.98 15.59

11 term (~3) 4.65 5.35 7.09 8.39 12.95 15.43

12 term (xy3) 4.61 4.77 6.64 8.70 12.33 15.09

13 term (x3y) 3.63 2.60 4.47 9.65 12.42 15.73

14 term (~2~3) 3.39 2.59 4.27 9.61 12.46 15.74

15 term (~3~2) 3.35 2.42 4.13 9.71 11.78 15.27

16 term (x5) 2.71 1.64 3.17 70.38 61.80 93.66

Multiquadric (3 term) 0.00 0.00 0.00 89.22 107.85 139.97

Multiquadric (6 term) 0.00 0.00 0.00 12.21 11.22 16.58

Multiquadric (10 term) 0.00 0.00 0.00 11.70 12.38 17.03

TABLE 5. BE, AN RMSE values of check points achieved in terms of UTM coordinates of the KFA-1000 data

Methods AE fm) AN (4 API (ml

DLT 06.07 05.86 08.44

2D Projective 05.46 08.12 09.78

Finite element 26.95 08.30 28.19

Conformal - 78.00

FIGURE I Vector plot of the planimetric errors at the control and check points over the Kermanshah area for SPOT level IA. Blue pluses are check points and red circles are control points

Rectification of high resolution satellite imagery JAG l Volume 3 - Issue 4 - 2001

The flexibility and good accuracy of the solution is

demonstrated with KFA-1000 and SPOT images. These

models can be easily used to process images from high resolution imaging system.

ACKNOWLEDGEMENT

The authors would like to thank Dr. J. Amini for helpful comments on this paper, and National Cartographic

Center (N.C.C.) for SPOT image and GCPs and National

Geographic Organisation (N.G.O.) for KFA-1000 photos.

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RESUME

Lenorme capacite dimageries satellites de haute resolution (HRSI), qui incluent des rPsolutions spatiale, spectrale, temporel- le et radiometrique ainsi que la vision stereoscopique introduit une puissante et nouvelle source de donnees pour les commu- nautes de la Photogrammetrie, de la Telededection et des SIG. Des don&es de haute resolution accroissent le besoin dune meilleure precision de modelisation des donnees. Lorbite du satellite, la position, les angles dattitude et les parametres dorientation interne doivent @tre ajustes dans le modPIe geome- trique pour atteindre une precision optimale avec Iutilisation dun nombre de points de calage (GCPs) minimum. Mais la plu- part des vendeurs dimages satellite de haute resolution nont pas Iintention de publier les modeles de leurs capteurs et les donnees dephemerides. II y a par consequent un besoin pour un &entail dalternatives, des approches pratiques pour extraire une information terrain 2D et 30 a partir des HRSI. La flexibilite et la bonne precision des modPIes alternatifs a et@ demontre avec KFA - 1000 et les images SPOT niveau 1A bien connues. Un bloc de 8 photos spatiales KFA - 1000 dans deux bandes avec un recouvrement longitudinal de 60 % et un recouvrement late- ral de I5 % et des images SPOT avec une fonction rationnelle, DLT, des transformations projective 2D, polynomiale, affine, conforme, multiquadratique et la methode des elements finis ont eteutilises dans ce test. Les zones de test se situent le sud et Iouest de Ilran. Considerant la qualite des points de calage (GCPs), les meilleurs resultats ont et@ obtenus par la methode DLT avec une EMQ de 8.44 m pour les photos spatiales KFA - 1000.

RESUMEN

La enorme capacidad de las imdgenes satelitdrias de alta resolu- ci6n (ISAR), incluyendo resoluci6n espacial, espectral, temporal y radiometrica, asi coma visi6n estereoscbpica, las convierte en una poderosa nueva fuente para las comunidades de cientificos trabajando en Fotogrametria, Teledetecci6n y SIG. La disponibili- dad de datos de alta resoluci6n incrementa la necesidad de mayor precisi6n en la modelizacion de 10s datos. La orbita del satelite, su posici6n, sus dngulos de postura y sus pardmetros de orientaci6n interna tienen que ser ajustados en el modelo geo- metrico, para obtener una precisi6n 6ptima con el use de un ntjmero minim0 de Puntos de Control de Terreno (PCT). Pero, la mayoria de 10s proveedores de satelites de alta resoluci6n no tiene la intenci6n de divulgar sus modelos de sensores y sus datos de efemerides. En consecuencia, se requiere una gama de enfoques alternativos prdcticos para extraer informaci6n de terreno precisa en 2D o 3D a partir de las ISAR. La flexibilidad y la buena precisidn de 10s modelos alternativos quedaron demos- tradas con las imdgenes KFA-I 000 y SPOT tipo IA. En el ensayo, se hizo use de un bloque de echo fotografias espaciales KFA- 1000 en dos fajas con un solapamiento longitudinal del 60% y lateral del I5%, y una imagen SPOT con una funcion rational, DLT, una proyeccion ZD, polinomios, y metodos afines, confor- males, multicuadrdticos y de elementos finitos. Las areas de ensayo cubren partes del Sur y Oeste de Iran. Considerando la calidad de 10s PCT, el mejor resultado se obtuvo con el metodo DLT, con un error residual medio estandar de 8.44 m para las fotograflas espaciales KFA-1000.

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