Single channel filtering is commonly employed for the reduction of speckle in SAR imagery. While these filters improve the appearance of the image for visual interpretation and result in smoother classification maps, statistical variability in measured backscatter caused by speckle still remains at the pixel level. Thus, in order to compensate for this variability, neighborhood, or contextual, information is often incorporated into the classifier methodology. Markov Random Fields (MRF) are frequently employed to model neighborhood and class label structure for the classification of remotely sensed data. In particular, [3] and [4] have used MRF models in the classification of SAR data and obtained better results than classification methods which do not utilize contextual information.

In analysis of SAR data from coastal environments, variation due to changes in angle of incidence [5] may cause otherwise separable classes, namely water and land, to overlap statistically. In order to compensate for this variation in measured backscatter, a hierarchical classifier is proposed. At each level of the classifier, the data can be class-corrected using models for the variation in backscatter with angle given in [5]. By employing a hierarchical structure, conflicts in class separability can potentially be alleviated.

The following sections contain descriptions of the classification of a coastal environment using polarimetric airborne SAR data acquired by the NASA JPL AIRSAR system. Results are shown for both the MRF-based classifier and a non-contextual classifier utilizing a radial basis function (RBF) neural network. Finally, a hierarchical architecture is presented, and the results of the three classifiers are compared.

A. Test Site Description
Bolivar Peninsula is part of the low relief barrier islands of the Texas coast located at the mouth of Galveston Bay. The test site chosen for this study consists of a salt marsh located at a washover fan on southern Bolivar Peninsula, shown in Figure 1. This salt marsh is adjacent to uplands, agricultural, and urban areas. For classification purposes, the marsh area is further characterized in terms of sub-environments defined by wetland maps [6]. The land cover types which occur in these environments include low and high proximal marsh, high distal marsh, and spoil/barren flats, as well as areas consisting of water and isolated trees.

Figure 1. Test Site on Bolivar Peninsula, TX.

The effects of speckle in the imagery are still readily visible in the grainy texture of Figure 2. In addition, brightness is reduced in the range direction (horizontal direction; near range at left), which is most apparent over the water. The influence of both of these factors can be shown in the classification results.

Figure 2. Measured AIRSAR Data.

Figure 3. RBF Classified Map.

(1)
where s is a given pixel, X_s is the measured data vector for that pixel, L_s is its label, N_s^o is the neighborhood surrounding, but not including, the pixel. The energy function U₁^s corresponds to the ML estimate

(2)
while the energy function U₂^s corresponds to the MRF model
(3)
where the parameter [beta] governs the degree neighboring pixels influence the pixel's label.

Figure 4. MRF Classified Map.

For the resulting classified image shown in Figure 4, the MRF model was defined over a 3x3 neighborhood. The iterative conditional modes (ICM) algorithm was used to minimize the MAP estimate; five iterations were required using a [beta]=1.4. The accuracy of the MRF-based classifier is shown in Table 1. In comparison to the RBF classifier from [2], the MRF model produces a higher rate of correct classification and less "noisy" land cover map. As such, it handles the effects of speckle on backscatter statistics better than the non-contextual classifier.

By employing a hierarchical classifier, different inputs can be used at each level of the overall classification process depending on the classes to be discriminated. This then allows for a possible reduction in the number of inputs, or for the use of class specific data such as topography, at a given level. The described benefits of a hierarchical architecture generally lead to an increase in classification accuracy. An example of a successful hierarchical classifier in remote sensing, based on knowledge-based sequential decision rules, can be found in [1].

A hierarchical version of the above MRF-based classifier was developed to account for the class dependent variation in backscatter associated with changes in incidence angle. A methodology for "correcting" SAR data according to class-specific models is described and is then presented as the first level in the architecture of the hierarchical classifier.

A. Water Correction
To account for the variation in radar backscatter due to changes in angle of incidence of SAR data for a given land cover class, a hierarchical classifier is developed. Because this variation is known to be different for each land cover class, frequency, and polarizations [5], at each level of the classifier, the input vector can be "corrected" using a class-specific model applied to the original SAR data. This will compensate for the variation in backscatter statistics for the given class and produce ideally constant data for that class.

The particular model chosen to account for this variation is taken from [5] and given by
(4)

where is the scattering coefficient, is the maximum value for the scattering coefficient (usually measured at vertical incidence), is the angle of incidence, and is a constant dependent on terrain type, frequency, and polarization.
When the backscatter is analyzed in units of dB, the model simplifies to a linear equation given by
(4)
Thus, a linear correction is applied at each frequency and polarization to generate uniform backscatter statistics for a given class.

Figure 5. "Water-Corrected" AIRSAR Data.

In the SAR data collected over the coastal test site, the greatest variation occurs over the open water, as can be seen in Figure 2. To correct for this variation, water pixels were isolated in a supervised manner, and linear fits were calculated for each of the six bands. An example image depicting the "water-corrected" AIRSAR data is shown in Figure 5.

Now, while the "corrected" class would be easily identifiable as an individual class, the other land cover classes would have had their statistics altered (incorrectly) and would not be reliably separable from one another. This leads directly to the proposed the hierarchical structure whereby the classification process is broken into simpler tasks based upon ease of class separability.

B. Hierarchical Classifier Architecture
For this test site, the two level hierarchical classifier shown in Figure 6 was used. The Level-1 classifier is designed to separate the image into water and land by using the "water-corrected" data as the input, while the Level-2 classifier then discriminates between the land classes consisting of wetlands and uplands using the original SAR data as the input.

At each level, the MRF model is utilized to account for the presence of speckle in the imagery. By incorporating a MRF model in the hierarchical architecture, improved classification accuracy should be obtained.

A. Hierarchical MRF
The MRF-based classifier from Section II.D, along with the two-level hierarchical architecture shown in Figure 6 were used jointly to classify the test site on Bolivar Peninsula. As before, all six channels of AIRSAR data were used as inputs. The same training sites were used, yielding the same six output classes.

For the resulting classified image shown in Figure 7, the MRF model was again defined over a 3x3 neighborhood. At each level of the classifier, the iterative conditional modes (ICM) algorithm was used to minimize the MAP estimate; five iterations were required using a [beta] of 1.9. The accuracy of the hierarchical MRF-based classifier is shown in Table 1.

Figure 7. Hierarchical MRF Classified Map.

B. Hierarchical MRF - Rough/Smooth Water
Some misclassification was attributed to differing backscatter from rough and smooth water, so the water class was divided into "rough water" and "smooth water". The classification process was identical to that in Part A, except that "water" was replaced by "rough water" in Level-1 and "smooth water" was added to Level-2. (The model for water-correction used to generate Figure 5 was actually applied only to "rough water".) After performing the hierarchical MRF-based classification, the two water classes were recombined. The resulting classified image is shown in Figure 8, and the classification accuracy is shown in Table 1.

Figure 8. Hierarchical MRF Classified Map.
(Rough and Smooth Water)

While the hierarchical classifier yielded only slight improvements in classification accuracy, the technique does show promise. In particular, significant improvements would be expected if the test site were chose to include more classes with high returns such as upland and urban classes. The distributions of backscatter for these classes tend to overlap with the near-range returns for the water class, thereby obtaining more benefit from using the "water-correction" model in Level-1. In addition, a hierarchical classifier architecture would be useful in situations where different inputs or data sets were used to discriminate classes at different levels. For example, multisensor classification of this coastal environment using both polarimetric and interferometric SAR data should be investigated. In this case, the bulk of the classification would be performed using polarimetric SAR data, while the terrain would be introduced at Level-2 to separate the land classes into environmental groupings that are affected by elevation.

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