TEXTURE ANALYSIS OF POLARIMETRIC SAR Gianfranco De Grandi(1), Richard M. Lucas(2), Attilio Gambardella(3), and Maurizio Migliaccio(3) (1) European Commission, DG Joint Research Centre, Via Enrico Fermi, 21027, Ispra (VA), Italy, frank.de-grandi’at’jrc.it (2) Aberystwyth University, Institute of Geography and Earth Sciences, SY23 3DB Aberystwyth, U.K. rml’at’aber.ac.uk (3) Università degli Studi di Napoli Parthenope, Centro Direzionale, Isola C4, 80143 Napoli, Italy, {attilio.gambardella; maurizio.migliaccio}’at’uniparthenope.it ABSTRACT The Wavelet Polarization Signature (WASP) is a recently introduced formalism for analyzing the dependences of texture measures, in SAR imagery, afforded by wavelet frames on scale and polarization state. Based on a previously published theoretical approach, two experiments are reported where wavelet WASP analysis is applied to SAR observations of natural targets, both in the land and marine domains. The objective is to assess the potential usefulness of the technique in different thematic contexts and to validate experimentally the effects predicted by theory. Analysis conducted so far indicates that texture measures based on wavelet frames can be an effective vehicle to characterize the spatial statistics of SAR observations in the combined space-scale-polarization domain. 1. INTRODUCTION Spatial variations of Synthetic Aperture Radar (SAR) backscatter bear information on structural and geometric properties of natural targets, and therefore can be potentially useful for deriving biophysical parameters, or for classification problems. These variations and their relationships are visually perceived as image texture, and can be measured by the statistics of some underlying random process. A method for retrieving local texture measures in SAR imagery using wavelet frames was proposed in [1] from the theoretical point of view. In particular the concept of polarimetric texture was revisited, by investigating the dependences of these measures on the antenna polarization states. The method provides estimates of a two-point statistics (a proxy of the structure function) in the combined space-scalepolarization domain. To analyze from the observational standpoint these dependences, suitable analytical tools are introduced to represent these dependences through signatures that condense information in graphical form. In particular, the Wavelet Scaling Signature (WASS) for single polarization detected data, and the Wavelet Polarization Signature (WASP) for fully polarimetric data are used to characterize the textural properties of extended homogeneous areas of interest. Moreover, textural separability of two regions is studied by means of a criterion function of the Fischer discriminant. Based on this theoretical background, two experiments are reported where wavelet frame texture measures and signature analysis are applied to SAR observations of natural targets, both in the land and marine domains. The objective is to assess the potential usefulness of the technique in different thematic contexts and to validate experimentally the effects predicted by theory. The first experiment is thematically oriented to tropical forest mapping in the Congo River floodplain, and illustrates how spatial properties of the classes of interest (swamp forest, lowland rain forest and secondary forest) are reflected in WASP analysis in a mixture of texture strength and polarimetric diversity. Fully polarimetric single look complex ALOS PALSAR data are used in this analysis. The second experiment is in the marine domain, and concerns the characterization through WASP analysis of oil spills, look-alikes and sea clutter. In this case, SIR-C fully polarimetric C-band data, are considered. 2. TEXTURE MEASURES The method of retrieving texture measures using wavelet frames is extensively documented in [1]. Texture measures are afforded by the variance of the wavelet frame coefficients in a discrete transform, implemented using an à trous algorithm in the oversampled version. The variance is estimated locally at several dyadic scales by convolution with a smoothing kernel. The considered wavelet frame is the first derivative of a B-spline of order 3, which acts as a differential operator [2]. Finally, the following feature vector is achieved: � = [ ] [ ] ,� = [ ] [ ] ,� = [ ] [ ] , (1) where aj[n] is the discrete image at the output of the à trous low-pass filter (smooth image), n=(n1, n2) is a running index of the image and xcj[n] and ycj[n] are the wavelet coefficients in the row and column directions, respectively, at scale 2j (output of the à trous high-pass filters). _____________________________________________________ Proc. of ‘4th Int. Workshop on Science and Applications of SAR Polarimetry and Polarimetric Interferometry – PolInSAR 2009’, 26–30 January 2009, Frascati, Italy (ESA SP-668, April 2009) The wavelet coefficients variance is a proxy of the twopoint spatial statistics, also known in geosciences, as “structure function”. The structure function is effective in characterizing the signal regularity in discontinuities, such as edges and point targets, correlations in stationary random processes, and the scaling properties (e.g., fractal dimension) in non-stationary processes with stationary increments, such as fractional Brownian motion. configurations. The LDA finds a linear mapping of two n-dimensional feature vectors, which maximizes a measure of separability between the regions. The separability criterion is given by the ratio of the “distance” between regions over the overall spread of the projected data. For each case, a figure of the sensitivity to the estimator configuration is given. This analysis is referred to as wavelet separability by Fischer criterion (WASEF). 3. ANALYSIS TOOLS 3.3. WASP and WASPSEF For polarimetric data, an extension of the a-trous algorithm is considered, where polarimetric power synthesis is performed in the wavelet domain [1]. The tool is referred to as the wavelet polarimetric signature (WASP). An area extensive version of the WASP is used here, which is computationally implemented on the assumption that fully polarimetric data are in covariance matrix form. The process is based on the commutativity of the wavelet and power synthesis operators (both linear). Each element of the polarimetric covariance matrix is decomposed in the frame representation. The wavelet transform of the power image for a given polarization state is then obtained by applying the polarimetric synthesis operator to the frame representation of the covariance matrix. This procedure results in a fast computation of the wavelet transform of the power image for a number of polarization states. The signature consists of a family of graphs, each mapping the normalized wavelet variance against the orientation angle at a given dyadic scale. It is also proposed [3] an extension of the WASEF class-separability analysis. For fully polarimetric data, the Fischer criterion is computed for backscatter power synthesized at a number of polarization states. This signature gives information on the (eventual) dependence of the region textural separability on the polarization state. Accordingly, the signature is dubbed wavelet signature of polarimetric separability by Fischer criterion (WASPSEF). The results of this process are condensed in a family of graphs, which maps the Fischer separability versus polarization state, and are parameterized by the decomposition scale. This signature therefore highlights those polarimetric states that are optimal with respect to the textural separability of two regions. Texture measures afforded by the wavelet variance depend on a number of parameters, including position in space, scale, and polarization states. Thus, the experimental analysis of the wavelet variance therefore requires a meaningful reduction of the representation space to provide information that could be readily linked to some characteristics of the underlying texturegenerating random process. For this purpose, a number of analytical tools, whose description is extensively detailed in [3], are introduced to capture these salient features of the observations and condense them in either a graphical or numerical form. 3.1. WASS This wavelet scaling signature (WASS) captures the scaling behavior of the wavelet variance for power detected data and for a single polarization state. The WASS is computed by averaging the normalized wavelet variance at a number of dyadic scales within an area of interest identified in the backscatter data set. The wavelet coefficients corresponding to two orthogonal directions (rows and columns) of the 2-D filter bank decomposition are considered. If the data set is in the radar geometry (slant or ground range), the two directions correspond to range and cross-range. The WASS signature is based on a two-point statistics estimated over an area. In the case of a texturally homogeneous extended target, this measure provides a good characterization of the textural properties in the neighborhood of the region of interest. This signature highlights the strength of texture and at which scale texture develops. Moreover, the approach provides clues about the type of stationary or non-stationary regime if the underlying random process is scale invariant. 3.2. Measures of Separability The WASS analysis does not give information on the separability of two texturally homogeneous regions, a fact which makes it less suitable for bridging over to a segmentation or classification problem. Therefore, a version of the signatures is proposed in [3] where, given two regions defined using a supervised approach, once the respective feature vectors, as defined in (1), are computed for a number of scales and different dilation factors of the smoothing spline filter, the criterion function of the Fischer’s linear discriminant analysis (LDA) [4] is then evaluated for the different 4. EXPERIMENTS In this section, the spatial statistics relevant to fully polarimetric SAR data are investigated, by WASP analysis, for tropical forest and marine domain mapping purposes. 4.1. The Congo River floodplain The Congo River floodplain in Central Africa hosts the world’s largest formations of swamp forests. This ecosystem is important because occurring biochemical processes influence emissions of greenhouse gases, particularly methane [5]. The canopies of the swamp forests are structurally different from the adjoining lowland rainforest, and these differences are reflected in the spatial statistics generated using radar data. In particular, the upper canopy of the swamp forest, which can be 45 m in height, is composed of a small number of species and is structurally homogeneous compared with the lowland forests. In this experiment, a fine beam fully polarimetric slantrange ALOS PALSAR data set, provided by JAXA in the framework of the ALOS principal investigator (PI) program, is used. The original scattering matrix data set was converted to covariance matrix representation and multi-looked by four. Therefore, the spatial sampling in range and cross-range is approximately 9.36 × 13.47 m. A Pauli decomposition of the data set over the area of interest in the Congo floodplain is shown in Fig. 1 as a color composite, where the green, red, and blue channels are assigned to volume scattering, double bounce scattering and single bounce scattering mechanisms respectively. WASP signatures are computed for (A) swamp forest, (B) primary RF, (C) flooded swamp forest, and (D) secondary degraded forest. The WASP signatures for the four classes at scale 2 are shown in Fig. 2. The (blue) swamp forest features a very homogeneous canopy, which is reflected in low texture and with no dependence on the polarization state in the signature. The (red) degraded forest, on the other hand, presents quite a distinctive signature, with higher texture and polarimetric textural diversity. It is to be noted that the absolute maximum is shifted toward the orientation angle Ψ=45°. We can speculate, based on the model proposed in [1], that this sensitivity to polarization state is due to the mixture of different scattering mechanisms in the fragmented forest and within the estimation window. The (black) primary forest presents an intermediate case between the more homogeneous swamp forest and the rugged secondary forest, in terms of texture strength and polarimetric diversity. Notice how the maximum now occurs near Ψ=0° (HV), which indicates that spatial statistics are dictated primarily by volume scattering. Finally, the flooded swamp forest (green) presents a signature similar to the swamp forest (low texture) but with a more marked dependence on polarization and maxima tending to HV. The WASPSEF signature related to the two classes swamp and primary RFs is shown in Fig. 3. The wavelet variance was estimated at scales 2 and 4 using a smoothing filter with dilation factor of 16. The absolute value of the Fischer discriminant is rather low, an indication that textural information is weak in this type of data set, which may be attributed to the steep incidence angle. However, a clear dependence on the polarization state is observed, with a maximum near the orientation angle Ψ=0° (HV) and a minimum at Ψ=45°. Considering that only the co-polarized channels contribute to power synthesis at Ψ=45°, the HV configuration is likely to allow for better discrimination Figure 1. Pauli decomposition color composite image of a fully polarimetric PALSAR data set acquired over the Congo floodplain on March 2007 (courtesy of the JAXA ALOS PI program). Figure 2. WASP signatures at scale 2 related to the areas of interest marked in Fig. 8. (Blue line) swamp forest area A. (Black line) Primary RF area B. (Red line) Degraded forest area D. (Green line) swamp forest area C. Figure 3. WASPSEF analysis for PALSAR full polarization data. Fischer criterion for wavelet coefficients’ (red line) variance at scale 2 and (black line) filtered wavelet variance. of the two classes compared with the HH or VV channels alone. 4.2. Sea clutter and oil spills In this experiment a set of meaningful experiments performed using multi-look complex (MLC) C-band SAR data, in which oil spills and oil look-alikes are present, are presented and discussed. The data sets were acquired during the SRL-2 SIR-C/X-SAR mission. The incidence angle varied between 20-55 degrees and the SAR swath width on the ground varied between 15 Km and 90 Km. The noise floor at C-band was -28dB [6]. In Fig. 4 is shown the SAR data acquired on October 08, 1994 in the English Channel (p.n. 49939). This case concerns a SAR acquisition characterized by low wind conditions. A typical oil spill pattern due to a ship is present. No information about the type of oil is reported in literature [7]. A subset of the total power SAR image acquired over the area of the experiment is shown in Fig. 4. WASP analysis has been performed over a three area corresponding to the oil spill (OIL), a free sea surface (SEA) and a dark area probably due to an atmospheric wave (AW). The analysis results for OIL, SEA and AW are shown in Fig. 5. In detail, a family of curves corresponding to the wavelet variance of the intensity in the cross-polarized channel at the first four dyadic scales is shown (black 21, red 22, green 23, blue 24). In all cases the scale 2 is the most useful, as a rapid response damping and insensitivity to polarization at longer scales is experienced. Signature relevant to both SEA and AW show a low texture and a weak dependence on the polarization state. On the contrary, the OIL presents quite a distinctive signature, with higher texture and polarimetric textural diversity. It is to be noted that the absolute maximum is near the orientation angle Ψ=45°. This is an indication that unbalance in the correlation properties in the crosspolarized and co-polarized channels come into play and can be exploited for differentiating a true oil slick. The underpinning physical mechanism needs still to be investigated at this stage. Figure 4. Total power image of the area of interest relevant to the SIR-C C-band image acquired on October 08, 1994 in the English Channel (p.n. 49939). WASP analysis was performed for OIL, SEA and AW transects, respectively (courtesy of the JPL and USGS). a 5. CONCLUSIONS Analysis of the spatial statistics in SAR observations of forested areas has been performed in a number of experiments using a method based on a wavelet frame representation. The analysis served the purpose to validate, on a purely observational basis, the principles and the computational aspects of the method, which were exposed on a theoretical ground in [1]. Analysis conducted so far indicates that texture measures based on wavelet frames can be an effective vehicle to characterize the spatial statistics of SAR observations in the combined space-scale-polarization domain. In particular, preliminary observations confirm that polarimetric texture could be potentially useful in connection with specific thematic contexts such as oil spill detection, and forest mapping. b 6. ACKNOLEDGMENT The authors would like to thank Japan Aerospace Exploration Agency (JAXA) for providing PALSAR data through the ALOS PI program, the NASA’s Jet Propulsion Laboratory (JPL), and United States Geological Services (USGS) for providing the SIR-C/XSAR data used in this study. c Figure 5. WASP signatures at scale 2 related to the areas of interest marked in Fig. 4. oil spill (OIL), free sea surface (SEA) and a dark area probably due to an atmospheric wave (AW). 7. REFERENCES 1. De Grandi G., J.-S. Lee, & D. Schuler, (2007). 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