Thierry Toutin
8.1 Introduction
Why orthorectify Earth observation (EO) satellite data? Any EO data, regardless of whether they are acquired by a scanner or a frame camera aboard a satellite, or by a photographic system in an aircraft or any other platform/sensor combination, will have various geome-tric distortions, depending on the manner in which the data are acquired� This problem is inherent in remote sensing, as we attempt to accurately represent the three-dimensional (3D) surface of Earth as a two-dimensional (2D) image� Consequently, raw images contain such significant geometric distortions that they cannot be used directly with geographic CONTENTS
8�1 Introduction ������������������������������������������������������������������������������������������������������������������������ 173 8�2 Sources of Geometric Distortions ������������������������������������������������������������������������������������ 175 8�2�1 Distortions Related to the Platform ��������������������������������������������������������������������� 177 8�2�2 Distortions Related to Sensors ����������������������������������������������������������������������������� 180 8�2�3 Distortions Related to the Earth �������������������������������������������������������������������������� 181 8�3 Geometric Modeling of Distortions �������������������������������������������������������������������������������� 182 8�3�1 Two-Dimensional/Three-Dimensional Empirical Models ������������������������������ 182 8�3�1�1 Two-Dimensional Polynomial Functions �������������������������������������������� 183 8�3�1�2 Three-Dimensional Polynomial Functions ����������������������������������������� 184 8�3�1�3 Three-Dimensional Rational Functions ���������������������������������������������� 185 8�3�2 Two-Dimensional/Three-Dimensional Physical Models �������������������������������� 188 8�4 Methods, Processing, and Errors ������������������������������������������������������������������������������������� 191 8�4�1 Acquisition of Images and Metadata ������������������������������������������������������������������ 191 8�4�1�1 Raw Level-1A Images ����������������������������������������������������������������������������� 192 8�4�1�2 Georeferenced Level-1B Images ������������������������������������������������������������ 193 8�4�1�3 Map-Oriented Level-2A Images ����������������������������������������������������������� 194 8�4�1�4 Synthetic Aperture Radar Images �������������������������������������������������������� 195 8�4�2 Acquisition of Ground Control Points ���������������������������������������������������������������� 195 8�4�3 Geometric Model Computation ��������������������������������������������������������������������������� 197 8�4�4 Digital Elevation Model Generation from Stereo Images ��������������������������������200 8�4�5 “Orthorectification” �����������������������������������������������������������������������������������������������204 8�4�5�1 Geometric Operation ������������������������������������������������������������������������������205 8�4�5�2 Radiometric Operation ��������������������������������������������������������������������������� 207 References ������������������������������������������������������������������������������������������������������������������������������������� 210
174 Advances in Environmental Remote Sensing
information system (GIS)–ready products� Thus, multisource data integration (raster and vector) for geomatics applications requires geometric and radiometric processing adapted to the nature and characteristics of the data in order to keep the best information from each image in the composite orthorectified products�
The processing of multisource data can be based on the concept of “terrain-geocoded images,” a term originally invented in Canada for defining value-added products (Guertin and Shaw 1981)� Photogrammetrists, however, prefer the term “orthoimage” when refer-ring to the unit of terrain-geocoded data, where all distortions including those of the relief are corrected� To integrate different data under this concept, each raw image must be sepa-rately converted to an orthoimage so that each component orthoimage of the data set can be registered, compared, combined, and so on, not only pixel-by-pixel but also with carto-graphic vector data in a GIS�
Why does the geometric correction process seem more important today than in the past?
In 1972, the impact of geometric distortions was quite negligible for different reasons:
The images, such as those from a Landsat multispectral scanner (Landsat-MSS),
•
were nadir viewing, and the resolution was coarse (around 80–100 m)�
The products resulting from the image processing were analog on paper�
•
The interpretation of the final products was performed visually�
•
The fusion and integration of multisource and multiformat data did not exist at
•
that time�
Today, the impacts of geometric distortions, although they are similar to the ones in the past, are less negligible because of the following factors:
The images are off-nadir viewing, and the resolution is fine (submeter level)�
•
The products resulting from image processing are fully digital products�
•
The interpretation of the final products is realized on the computer�
•
The fusion of multisource images (different platforms and sensors) is in general use�
•
The integration of multiformat data (raster/vector) is a general tendency in geomatics�
•
One must admit that the new EO data, their method and processing, the resulting pro-cessed data, and their analysis and interpretation introduced new needs and requirements for geometric corrections, due to a drastic evolution accompanied by large scientific and technology improvements between the two periods� Even if the literature is quite abun-dant mainly in terms of books and peer-reviewed articles (an exhaustive list is given in the references section), it is important to update the problems and the solutions recently adopted for geometrically correcting remote sensing images with the latest developments and research studies from around the world� This chapter will then address the following concepts:
The sources of geometric distortions and deformations with different
categoriza-•
tions (Section 8�2)
The modeling of these distortions with different 2D/3D physical/empirical
mod-•
els and mathematical functions (Section 8�3)
The 3D geometric correction method and algorithms with their processing steps
•
and errors (Section 8�4)
Three-Dimensional Geometric Correction of Earth Observation Satellite Data 175
Comparisons between the models and mathematical functions, their applicability, and their performance on different types of images (frame camera, visible and infrared [VIR]
oscillating or pushbroom scanners, and side-looking antenna radar [SLAR] or synthetic aperture radar [SAR] sensors at high, medium, or low resolutions) are also addressed� The errors with their propagation from the input data to the final results are also evaluated through the full processing steps�
8.2 Sources of Geometric Distortions
Each EO image acquisition system produces unique geometric distortions in its raw images and consequently the geometry of these images in its own local coordinate system does not correspond to the terrain and to the user’s specific map projection� Obviously, the geo-metric distortions vary considerably with different factors, such as the platform (airborne and satellite), the sensor (VIR and SAR; total field of view [FOV], low to high resolution), and the associated scanner (whiskbroom, pushbroom, frame, etc�)� However, it is possible to make general categorizations of these distortions�
The sources of distortions (Table 8�1) can be grouped into two broad categories: (1) the
“observer” or the acquisition system (platform, imaging sensor, and other measuring instruments, such as gyroscope and stellar sensors) and (2) the “observed” (atmosphere and Earth)� In addition to these distortions, deformations related to map projections have to be taken into account because the terrain and most GIS end-user applications are generally represented and performed respectively in a topographic map space and not in a referenced ellipsoid� Figures 8�1 and 8�2 illustrate the geometry of acquisition and the quasi-polar elliptical orbit approximation of remote sensing satellites around the Earth, respectively� The map deformations are logically included in the distortions of the observed�
Previous studies made a second-level categorization into low-, medium-, and high-fre-quency distortions (Friedmann et al� 1983), where frehigh-fre-quency is determined or compared
Table 8.1
Description of Error Sources for the Two Categories, the Observer and the Observed, with Different Subcategories
Category Subcategory Description of Error Sources
The observer or the acquisition
system Platform (spaceborne or airborne) Variation of the movement; variation in platform attitude (low to high frequencies)
Sensor (VIR, SAR, or HR images) Variation in sensor mechanics (scan rate, scanning velocity, etc�); lens distortions, viewing/look angles;
panoramic effect with the FOV Measuring instruments Time variations or drift; clock
synchronicity
The observed Atmosphere Refraction and turbulence
Earth Curvature, rotation, topographic effect
Map Geoid to ellipsoid, ellipsoid to map
176 Advances in Environmental Remote Sensing
with the image acquisition time� Examples of low-, medium-, and high-frequency distor-tions are those arising from orbit variadistor-tions, Earth rotation, and local topographic effects, respectively� Although this categorization was suitable in the 1980s when there were very few remote sensing systems, today, with so many different acquisition systems, it is no longer acceptable because it differs with each acquisition system� For example, attitude
FIgure 8.1
(See color insert following page 426.) Geometry of viewing of a satellite scanner in orbit around the Earth�
(Courtesy and copyright Serge Riazanoff, VisioTerra, 2009�)
n + 1 n n + 2
Satellite n + 3
n + 4 N
Révolution
Mars Fevrier
Janvier
Decembre
Novembre Octobre
Septembre
Equlroxe de printemps
Equlroxe d’automne FIgure 8.2
(See color insert following page 426.) Near-Earth, quasi-circular, quasi-polar, sun-synchronous orbit for EO satellites� The different revolutions around the poles with a constant illumination angle (top) showing the same illumination condition all the year (bottom)� (Courtesy and copyright Serge Riazanoff, VisioTerra, 2009�)
Three-Dimensional Geometric Correction of Earth Observation Satellite Data 177
variations are a high-frequency distortion for QuickBird or airborne pushbroom scanner, a medium-frequency distortion for System Pour l’Observation de la Terre (high resolution in the visible SPOT-HRV) and Landsat Enhanced Thematic Mapper (Landsat-ETM+), and a low-frequency distortion for Landsat-MSS, but not a distortion for a medium resolution imaging spectrometer (MERIS)�
The geometric distortions and their error sources given in Table 8�1 are deterministic and predictable and generally well understood� Some of these distortions, especially those related to instrumentation, are systematic and generally corrected at ground receiving sta-tions or by the image vendors� Other distorsta-tions are not taken into account and corrected because they are specific to each acquisition time and location; further, information on the atmosphere is rarely available� Such distortions are also geometrically negligible for low- to medium-resolution images�
8.2.1 Distortions related to the Platform
Some basic information on satellite orbits and celestial mechanics are useful to better understand platform-related distortions� The EO satellites obey the celestial mechanical laws defined by Newton and Kepler for an unperturbed trajectory (Keplerian orbit) and by Gauss and Lagrange for a perturbed trajectory (osculatory orbit; Escobal 1965; Centre National d’Études Spatiales 1980)� A number of perturbations (due to Earth gravity and surface irregularities, atmospheric drag, etc�) slowly change the Keplerian orbit based on the two-body attraction of Newton’s law into an osculatory orbit (Centre National d’Études Spatiales 1980)� Information on orbits is often needed, and different orbital models can be used depending on their utility and required accuracy (Bakker 2000):
To calculate the satellite location on its osculatory orbit in order to compute the
•
Earth coordinates of scanned pixels, requiring high accuracy (submeters) over a small time frame (seconds)
To predict when the satellite will pass over a specific area, requiring low accuracy
•
(kilometers) but over a long time frame (days)
Many orbital models have been developed since 1960 using the same mechanical laws with Gaussian/Lagrangian equations; the differences between the orbital models are mainly in the number and types of perturbations and the techniques to integrate them�
As defined and adapted by the North American Aerospace Defense Command, sim-plified general perturbations (SGPs), SGP4, and the most accurate SGP8 are the orbital models to be used for low- and near-Earth satellites (orbital period less than 225 minutes and altitude less than 6000 km)� Most, if not all, of the civilian EO spacecrafts have near-Earth, retrograde, quasi-circular, quasi-polar, geosynchronous, and sun-synchronous orbits (Figure 8�2)�
Near-Earth orbits (altitude more than 300 km) are high enough to reduce the atmo-spheric drag� Retrograde orbits with 90°–180° inclination are westward-launched orbits, which require extra fuel to compensate for the Earth’s rotation, but they provide the only solution for obtaining sun-synchronous orbits� Quasi-circular orbits avoiding large changes in altitude enable images with similar scales to be acquired, which is desirable for EO� Quasi-polar orbits with 90°–100° inclination enable sensors to image the entire Earth, including most of the poles� Because geosynchronous orbits have a repeating ground track, they have an orbital period that is an integer multiple of the