SAR image distortion
As it was explained before, the spaceborne SAR systems send microwave pulses to the Earth’s surface and receive the echoes. This is done in the range direction which is perpendicular to the flight direction of the sensor (and looking right generally). This range direction is oblique considering the Earth’s surface and it is defined by the elevation angle of the antenna, see figure 2.1.8.
Thus, the echoes coming from the ground objects are distinguished between them thanks to this oblique geometry. Therefore, two objects at an identical range distance to the sensor are indistinguishable, even though they are at different places and with a different height on ground. This is the main reason why these kind of radars cannot look directly down to the ground. As the sensor is side-looking, the objects in the ground (defined by its distance to the nadir of the radar, see figure 2.1.8) are arranged as function of their range from the radar.
However, this side-looking geometry has some important disadvantages which arise in case of abrupt terrain. As result, SAR images present geometric distortions which must be perfectly understood. Those geometric artifacts affect their measurements, making them imposible in some cases. They can be classified into three.
It appears in the SAR images when the radar samples a topographic relief. As a result of the oblique geometry of the acquisition system the slopes of the hills oriented towards the satellite (A-B in figure 2.1.9.a) are compressed (A’-B’ in figure 2.1.9.a) while the slopes oriented away from the satellite (B-C in figure 2.1.9.a) are expanded (B’-C’ in figure 2.1.9.a) in SAR geometry, see figure 2.1.9.a. It means, the slopes in the front side of the hills are sampled with less pixels than the one oriented on the back side.
All the ground features thus appear to be tilted towards the satellite. The slopes facing the radar appears compressed and brighter due to the accumulation of ground reflections within the same resolution cell. Any phenomena occuring on this slope will be poorly sampled. In extreme cases, this accumulation of ground reflections from very different areas can result into an aliasing of the signal, making impossible the exploitation of the SAR measurements.
Foreshortening can be corrected under (a visual point of view) with the use of a DEM during the step of geocoding, see chapter 22.214.171.124. The appropiate geometry the slopes can be recovered by means of using interpolation procedures over the SAR amplitude once it has been projected into ground geometry.
It is an extreme case of foreshortening. It appears when the incidence angle is smaller than the angle given by the local slope, especially in case of very steep slopes oriented towards the satellite. In that cases tops of mountains, closer to the radar, are sampled before than their basis, see figure 2.1.9.b. This results in extremely severe image distortion as the slopes in SAR images are inverted. See how the points A and B in ground geometry are sorted in an inverse way in slant-range geometry (B’ and then A’) in figure 2.1.9.b.
Layover cannot be corrected. The signal is completely lost because of the aliasing and the SAR measurements cannot be exploited.
It appear in steep slopes that do not face the satellite. In such cases there are ground areas which are not illuminated by the radar wave, see figure 2.1.9.c. As result, there is no returned signal coming from those ground terrain regions and no measurements are possible. Those areas appear with a very low amplitude level within the radar images since no backscattered signal is received. Thus, the ground regions between the points B and D are not illuminated by the radar wave in figure 2.1.9.c. Hence, the radar samples compressed between B’ and D’ will present a very low amplitude level in SAR image.
The phase of the SAR signal
In general, the phase value detected by a radar imaging system is the measure of the phase difference between the emitted and the received electromagnetic wave. This magnitude is related basically to three main contributions [Arn97]:
• The travel phase : related to the distance between the antenna and the illuminated object
• The reflection phase : related to the electromagnetic interaction between the wave and the object
• The construction phase : related to the accumulated phase that arrives to the radar within every resolution cell and that is treated as a unique and single reflected echo signal
The recorded phase depends directly on the complex backscattering coefficient of the illuminated surface. It characterizes completely the electromagnetic behavior of the observed ground terrain . In consequence, it could be used for example in order to segmentate and to identify different kinds of terrain and/or land use. The capacity of measuring distance by the signal phase is also a very interesting magnitude. The possibility of detecting very small variations of this distance (below the signal wavelength) make this instrument very useful for monitoring changes in the position of the illuminated object. However, this measure is not straightforward for each single object of the ground because the basic unit of measure of the imaging radars (resolution cell ~ pixel) is very large in comparison with the used wavelength. Thus, for every pixel what is measured is the contribution of several single targets. This total signal is obtained based on the coherent addition of the returned echoes coming from every target on the ground and which slant-range position lies within the same resolution cell. The power of every echo is governed by the backscattering coefficient of every single scatterer. Hence, it is defined as the construction phase of the pixel. This principle is the responsible of the radiometric pixel noise or “speckle”.
The travel phase
It is directly related to the physical distance between the sensor (which emits the electromagnetic wave) and the target on ground (where the wave impacts). Then, it is a purely geometric measure see figure 2.1.10,.
In case of having a unique target, plus a constant wavelength and invariant atmospheric con-ditions, the measure of the phase will be always the same if the object remains at the same place. In real cases there are a lot of elements reflecting the signal within the resolution cell. It could be said that the measure is related to the mean distance between a large amount of targets and the sensor. The response of the whole target can be understood as only one unique center of phase that falls at some place within the pixel.
However, this phase measure related to the physical distance could be corrupted. During this travel the electromagnetic wave is crossing several layers of the earth’s atmosphere. In function of the wavelength this layers will introduce non-homogeneous delays which will be accumulated during the two way travel distance. Further details will be given regarding the impact of the atmospheric artifact on the SAR phase in future chapters. The main constrain is that it is a non-stationary and an unpredictable effect. Each SAR acquisition will have a different atmospheric artifacts which could be more or less important depending on the particular conditions of the atmospheric layers at the acquisition time, see figure 2.1.11 for an example.
The reflection phase
It is directly related to the dielectric properties of the object which is being illuminated by the wave, known as the backscattering coefficient of the object. This backscattering coefficient mainly de-pends on the nature of the material constituting the object, the local incidence angle, the wave-length, the polarization and the environmental conditions [Sch93].
In practice, it is very difficult to measure the backscattering coefficient of a single object be-cause echoes coming from many different objects on ground are merged within a resolution cell. In addition, the reflection of the wave is not always specular. There could be found reflections at different levels as in function of the wavelength the wave can penetrate into the materials in a different way. In general, signals with large wavelengths can penetrate more than the shorter ones. For example, as it is illustrated in figure 2.1.12, for the same area one can have different backscattering when a L-band, C-band or X-band SAR system is used just because the wave comes from reflection of different layers while the earth’s surface still the same.
In general, the observed surface can be interpreted as the volumetric repartition of the elemen-tary targets with variable backscattering coefficient for each one. The SAR imaging is detecting the coherent addition of each of the targets placed within the same radar resolution cell. Then, the construction phase will disturb the measure of the real coherent backscattering coefficient of single objects presented on the scene.
The construction phase
It could be defined as a mean that describes the geometric distribution of the single targets on ground and the sensor. It is the resulting phase for each slant-range resolution cell due to the coherent addition of the echoes of all the elementary reflecting elements that lies within. It is the responsible of the apparent random behavior of the phase and it is impossible to model and/or to predict. It is important to notice that it is a phase measurement which does not exist physically. It has the origin on the spatial sampling that the radar performs over the ground surface.
This is illustrated in figure 2.1.13 by means of an example. In the presented radar pixel in figure 2.1.13 five single reflectors characterized under an electromagnetic point of view by their backscattering coefficient σi (coherent magnitude ⇒ reflection phase). Under a geometric point of view the phase for every single target is characterized by the physical distance between the sensor and the position of every single reflector on ground Ri. Then, the final measure for this slant-range pixel will be the resulting coherent addition of all the echoes returned by every single elementary reflector, see equation 2.1.7.
The distribution of the single targets within the resolution cell is completely random. Consider-ing that the size of the pixel (in the order of few meters) is larger than the signal wavelength (in the order of few centimeters) there is no way to know if the echoes of each single target are added in a constructive or in a destructive way. It must be considered that the phase signal is wrapped modulus half a wavelength, see figure 2.1.14.
In consequence the echo signal which arrives to the sensor is not directly related with the nature of the terrain. In a extreme situation, there could be found two single targets within the same pixel and presenting a strong backscattering coefficient, but which contributions are added in an opposite way in phase due to geometric reasons leading to a signal loss. This is the origin of the speckle or fluctuation of the amplitude of the SAR images [Bec63]. Due to this effect an homogeneous surface will appear in the SAR amplitude with a textures or with roughness in function of the random addition of the elementary single reflectors that are contained within every pixel, see figure 2.1.15 for an example of speckle perturbation on SAR images.
However, for a random position of the single reflectors on ground and for two consecutive ac-quisitions in time this SAR roughness (or speckle) should be maintained (if we consider that no physic modification has occurred on the objects). In other words, the construction phase should be the same as the geometry of acquisition between the sensor and the elementary targets on ground is kept.
Table of contents :
126.96.36.199 Data Model of XML Document
188.8.131.52 Recursion in XML Document
184.108.40.206 Document Depth
220.127.116.11 Stream-querying Process
18.104.22.168 Stream-filtering Process
22.214.171.124 Selectivity Estimation Technique
126.96.36.199 Performance Prediction Model
1.2.1 The Expressiveness of XPath
1.2.2 Structure of XML Data Set
1.2.3 Query Evaluation Strategy
1.2.4 Evolution and Data Set Updating
1.4 Thesis Organisation
1.4.1 The Dependency of Thesis’s Chapters
2 State of the Art
2.2 Selectivity Estimation
2.2.1 Properties of Selectivity Estimation Techniques
2.2.2 Path/Twig Selectivity Estimation Techniques
188.8.131.52 Synopsis-Based Estimation Techniques
184.108.40.206 Histogram-Based Estimation Techniques
2.2.3 Summary – The Choice of the Path tree Synopsis
2.3 Stream-processing Approaches
2.3.1 Stream-filtering Algorithms
2.3.2 Stream-querying Algorithms
2.3.3 Summary – Lazy Stream-querying Algorithm LQ
3 Path tree: Definition, Construction, and Updating
3.1.1 The XML Data Model
3.2 Path tree Definition
3.3 Path tree Construction: Automata Technique
3.3.1 Automaton Definition A
3.3.2 Automata Transformation into a Graph Doc(A)
3.3.3 Automata Minimization AMin
3.3.4 Example of Path tree Construction: Automata Technique 54
3.4 Path tree Construction: Streaming Technique
3.4.1 Path tree Construction
3.4.2 Path tree Updating
4 Selectivity Estimation Techniques
4.2 Lazy Stream-querying Algorithm
4.2.1 Query Preprocessing
4.2.2 LQ – Blocks Extension
4.2.3 Examples of Query Processing Using LQ-Extended
220.127.116.11 Query Processing – Simple Path
18.104.22.168 Query Processing – Twig Path
4.3 Selectivity Estimation Algorithm
4.3.1 Examples of the Selectivity Estimation Process
22.214.171.124 Selectivity Estimation – Simple Path
126.96.36.199 Selectivity Estimation – Twig Path
4.3.2 Accuracy of the Selectivity Estimation Technique
5 Performance Prediction Model
5.2 Performance Prediction Model- Preliminaries
5.2.1 Performance Prediction Model – Motivations
5.2.2 Performance Measurements Towards the Optimization of Stream-processing for XML Data
188.8.131.52 Prototype O-Search
184.108.40.206 Experimental Results
5.2.3 Performance Prediction Model – General Structure
5.3 Performance Prediction Model – Simple Path
5.3.1 Lazy Stream-querying Algorithm (LQ)
5.3.2 Building the Mathematical Model
5.3.3 Building the Prediction Model
220.127.116.11 Prediction Rules
5.3.4 User Protocol
5.3.5 Experimental Results
18.104.22.168 Experimental Setup
22.214.171.124 Quality of Model Prediction
126.96.36.199 Impact of Using Metadata in our Model on the Performance
188.8.131.52 Model Portability on Other Machines
5.4 Performance Prediction Model – Twig Path
5.4.1 Lazy Stream-querying Algorithm (LQ)
5.4.2 Building the Mathematical Model
5.4.3 Building the Prediction Model
184.108.40.206 Example of the Selectivity Estimation Process
5.4.4 Experimental Results
220.127.116.11 Experimental Setup
18.104.22.168 Accuracy of the Selectivity Estimation
22.214.171.124 Efficiency of the Selectivity Estimation Algorithm
126.96.36.199 Comparing our Approach with the other Approaches
5.4.5 Use Case: Online Stream-querying System
188.8.131.52 Online Stream-querying System
5.4.6 Conclusion and Future Work
6 Conclusion and Perspectives
6.2 Future Work
6.2.2 Selectivity Estimation Technique
6.2.3 Parallel Processing