of the single pixels in Figure 5.33represent real measurements caused by the interaction between the polarized microwaves and e.g. trees.
5.8 Discussion
In this chapter a new approach for restoring SAR data in the framework of MRF-MAP has been presented. This approach relies on ratio images for algorithm optimization. The optimization techniques under study are Iterated Conditional Modes (ICM) and Simulated Annealing (SA).
The Gaussiana priorimodel and ICM in Section5.3turned out to be well suited for reproducing homogeneous regions in SAR data. However, when it comes to the preservation of discontinuities and mean amplitude levels, the Gaussian prior performs badly. The performance of the LaPlacea priorimodel, as described in Section5.5, is better than the Gaussiana priorimodel in terms of reproducing discontinuities and mean levels of amplitudes. However, the preservation of homogeneous areas is worse.
In a need for modeling the positive skewness of the SAR amplitude data, the exponential a priori model was selected. The exponential a priori model in Section5.4proved to be good in terms of preserving mean levels of amplitudes.
But again discontinuities are not reproduced satisfactorily. The Gamma distri-bution provides a good model for the skewed distributed SAR amplitude data.
This is utilized in the Gamma mean priorin Section 5.6.1and in the Gamma pixel prior in Section 5.6.2 where the energy function is specially designed to preserve discontinuities and homogeneous regions in SAR data. While the per-formance of the Gamma mean priorwas quite similar to the LaPlace a priori model, the Gammapixel priorturned out to be more convincing when it comes to preserving discontinuities and mean amplitude levels.
Unfortunately the price paid for the high speed of the ICM algorithm is that ICM easily gets trapped in local energy minima. As we have demonstrated this makes the use of ICM for preserving homogeneous areas and details in SAR data doubtful. The other optimization technique, which makes successful use of MRF, is SA. It has the advantage, in preference to ICM, that it is capable of escaping these local energy minima. In order to avoid the artifacts created by ICM the Gamma pixel prioris therefore implemented in the SA algorithm.
A characteristic property of SAR amplitude data is that the standard deviation is proportional to the mean amplitude value. This is utilized by introducing a MTA schedule, where the temperature is proportional to the variance of the local energy distribution.
Also the 8 pair-site interactions wherewc =ware implemented in the Gamma pixel prior using the SA algorithm. The corresponding restored examples of the synthetic one grey-level and five grey-levels SAR data are displayed in the FiguresA.3(a)–(b). A comparison of Figure 5.30(b) and FigureA.3(b) shows a small improvement in the preservation of edges and details using wc = w instead of pair-site interactions with different weights. This is supported by the corresponding statistics in Table A.2, which also indicate that, in terms of preserving mean amplitude level, there is no significant improvement in using the selected weights of the cliques.
The synthetic noise in Figure5.1(a) is independent identically-distributed SAR speckle and one therefore could expect the restored equivalent to be a uniform image. However, the restored one grey-level synthetic SAR data in Figure5.30 do not look homogeneous but have a lot of clutter. This clutter is not due to artifacts, but is due to the natural micro-structure in Figure5.1(a), which the SA-MTA algorithm is capable of preserving. In the cases where the clutter is a problem for the restored result one has to e.g. reduce the image by a factor 2 in order to remove the correlation between neighbouring pixels. In this context where the preservation of details in the test sites in Gjern and Mols Bjerge is of paramount importance no reduction or filtering of the EMISAR data is performed prior to the restoration.
The median filter, i.e. the 50% quantile, is known to be better than the mean filter at preserving discontinuities and sharp edges. This is because single un-representative pixels in a neighbourhood configuration do not affect the median significantly. For that reason it could be interesting to see how the median filter performs in terms of preserving features in the speckled SAR data. Research done by Rees and Satchell (1997) has pointed out, that although the median filter does have edge-preserving properties, it can introduce significant bias and is not suited for preserving small details in SAR data [68]. However, the MAP estimate (4.3) of the local neighbourhood configurations, which is used in the presented algorithms, is at the mode of the energy distribution corresponding to the 40% quantile in the Rayleigh distribution. Instead of the median filter it therefore seems more appropriate to use the 40% quantile filter. The filtered result is presented in FigureA.6and the statistics derived from the correspond-ing ratio image are listed in TableA.2. A comparison between the statistics in the TablesA.1andA.2shows, that the MRF-MAP framework is better suited for preserving edges and discontinuities in the impulsive noise environment of SAR speckle than the 40% quantile filter. Note that because the SAR amplitude data are Rayleigh distributed, and thereby positively skewed, the 40% quantile is lower than the mean level. This explains the high z value using the 40%
quantile filter in TableA.2.
In FiguresA.9(a)-(b) are presented the segmented results of the synthetic SAR
5.8 Discussion 115
data in Figures5.1(a) and5.1(b) using the licensed SA programsegann. The segann algorithm was kindly offered at my disposal by Shaun Quegan of the Sheffield Centre for Earth Observation Science (SCEOS). Even though there is a fundamental difference between a restoration and a segmentation, it is pos-sible to compare their qualitative performances through the statistics of the respective ratio images. Given the specific parameter settings in the two algo-rithms, the statistics in Table A.2 suggest the qualitative performances of the segannalgorithm and the Gammapixel priorto be quite similar. That is to say thesegannalgorithm is on the large-scale slightly better in terms of preserving discontinuities and mean amplitude levels whereas the Gamma pixel prior is more convincing in terms of preserving small-scale structures and homogeneous regions in SAR data.
A comparison between the test statistics in the TablesA.1andA.2shows that the Gamma pixel prior implemented in the SA algorithm is superior in terms of preserving discontinuities as well as homogeneous regions in SAR data. It is therefore concluded that thea priorimodel and optimization technique that best fulfills the objective of this study is the Gammapixel priorand the SA-MTA schedule.
Chapter 6
Gjern
In this chapter fieldwork performed within the semi-natural wetland environ-ment at Ladegaards Enge in the river valley of Gjern is presented. The collected in situdata are used in Chapter8where a possible correlation between the phys-ical properties of the wetland and the restored EMISAR data is investigated.
The fieldwork was initiated at the date of the EMISAR acquisitions 3 and 4 June 1997. In order to support the investigation, supplementary fieldwork was carried out in the autumn of 1998 and in July 1999. The fieldwork comprises a description of vegetation cover, estimation of biomass, soil samples and TDR-measurements. In Sections 3.1.1, 3.1.2and3.1.3is given a brief description of sampling methodologies ofin situdata.
The area in Ladegaards Enge has been subject to a vast amount of research due to its unique properties for studying e.g. ground-water flow and seepage to surface-water in a catchment. For a thorough investigation within these areas refer to Rasmussen (1996) [16] and Andersen E. (2001) [2].
Figure 6.1: Map displaying the geographical placement of the Gjern area. The blue arrow shows the flightline of the EMISAR where the acquisitions are made within the start and end points on 3 June 1997. The EMISAR is looking to the left and the red spot indicates the test site at Ladegaards Enge. (Map material from the Danish Kort- og Matrikelstyrelsen (KMS) is reproduced according to agreement G18/1997 between NERI and KMS.)
6.1 Description of test site
The test site at Ladegaards Enge is located in the river valley of Gjern, which is a part of the Gjern catchment in Eastern Jutland in Denmark. The catchment area for the test site is 114 km2and the land use is 77% cultivated, 14% forest, 4.5% wetland and riparian meadows and 3% urban areas and roads [16]. The geological history of the catchment starts in the late Oligocene and since then several geological events such as glacial activities have formed the landscape.
For a geographical placement of the area refer to Figure 6.1, where the red spot indicates the test site. In Figure6.2the test area is marked within the red crosses on an aerial ortho-photo covering Ladegaards Enge. The ortho-photos in the succeeding are from 1995 and are originally geometrically rectified according to system 34 for Jutland. However, the coordinate system used in the following is Universal Transverse Mercator (UTM), zone 32, datum ED50.
6.1 Description of test site 119
Figure 6.2: An orthophoto from 1995 displaying an aerial view of the test site at Ladegaards Enge. The test area is located within the red crosses. (Ortho-photos are copyright Kampsax 1995.)
The test site is a riparian wet meadow due to a high level of ground-water and during the winter the area is flooded by a stream and in the summer period the conditions are less humid [53]. This particular site has been selected because of its homogeneity. The area can be divided into the three sub-areas I, II and III and within each sub-area the vegetation cover and soil moisture are relatively homogeneous. The wettest part of the test site is sub-area I, which is a swampy area with standing water. This area is numbered 1, 2, 4, 5, 6, 10, 16 in Figure6.3.
Sub-area II, which is intermediate in terms of soil moisture, constitutes number 14 and the third and driest sub-area III is represented by the numbers 3 and 13.
The water table generally follows, with a more subdued form, the contours of the surface topography. In the case of Ladegaards Enge the ground water is near the surface and the ’outcrops’ of the water table are typically the river bed. This implies that the soil moisture of the upper layers in the floodplain during periods of low precipitation mainly is a function of the discharge in the river and the local topography.
The sediment in the test area, or floodplain, is sand and silt which is deposited as the river meanders back and forth. As the river overflows its banks, it rapidly decreases in velocity away from the channel and drops most of its sediment. The
Figure 6.3: Vegetation map illustrating the distribution of the dominant species within the test site at Ladegaards Enge June 1997. (1) Phalaris arundinacea, (2) Carex acuta, (3) vegetation at the cliff of the river which is a mixture of Glyc-eria maxima, Deschampsia caespitosa and Phalaris arundinacea, (4) GlycGlyc-eria maxima and Rumex hydrolapathum, (5) Glyceria maxima and Typha angus-tifolia, (6) Potentilla palustris, (7) mixture of Phalaris arundinacea, Glyceria maxima and Deschampsia caespitosa, (8) Glyceria fluitans, (9) Filipendula ul-maria, (10) Glyceria maxima and Filipendula ulul-maria, (11) Poa trivialis and Carex elata All., (12) mixture of Alopecurus pratensis and Deschampsia cae-spitosa, (13) Alopecurus pratensis , (14) Deschampsia caecae-spitosa, (15) Juncus effusus, (16) mixture of Glyceria maxima and Carex acuta
coarser fraction of sediments is deposited at the levee or near the channel and the finer fraction of sediments such as silt, clay and organic matter, is layered over most of the floodplain. In this way successive floods have build up natural levees and the plain gradually falls away from the levees for about 100 m [2], [64].
The levee is at the surface a sandy loam and the whole levee profile is classified a Gleyic Fluvisol. The central part of the floodplain is in the upper 8 cm a fibric to hemic peat which is overlaying a clay loam. The wettest part of the test site is a marsh which is a hemic peat at the surface and the classification is Histic/Fibric Histosol [2].