STATISTICAL SEGMENTATION OF POLARIMETRIC SAR DATA L. Ferro-Famil (1), E. Pottier (1),D. Corr (2), A. Rodrigues (2) (1) IETR Laboratory, UMR CNRS 6164, University of Rennes 1, Campus de Beaulieu, Bât. 11D, 35042 Rennes, France. E-mail: laurent.ferro-fami@luniv-renne1.fr, eric.pottier@univ-rennes1.fr (2) QinetiQ Ltd, Room 1058, A8 Building, QinetiQ, Cody Technology Park, Farnborough, Hants. UK. GU14 0LX, E-mail: afrodrigues@qinetiq.com, DCORR@qinetiq.com ABSTRACT This paper introduces an approach to the classification and interpretation of SAR data using complementary polarimetric and interferometric information. Strictly polarimetric and polarimetric interferometric data are first analyzed and classified separately. An unsupervised polarimetric segmentation, based on multivariate Wishart statistics, is applied to one of the separate polarimetric datasets. Pertinent polarimetric indicators permit to classify the observed scene into three canonical scattering types. The interpretation and the segmentation of an optimized interferometric coherency set leads to the discrimination of different natural media that cannot be achieved with polarimetric data only. Each type of scattering mechanism is processed through an unsupervised statistical interferometric classification procedure. The resulting classes show an enhanced description and understanding of the observed scene. 1. INTRODUCTION Polarimetric SAR data classification has been widely addressed in the last decade [1]. The tight relation between natural media physical properties and their polarimetric features leads to highly descriptive classifications results that can be interpreted by analyzing underlying scattering mechanisms[2][3]. Interferometric data provide information concerning the coherence of the scattering mechanisms and can be used to retrieve observed media structures and complexity[4] [5]. An example of the complementary aspect of polarimetric and interferometric information is given with polarimetric interferometric data acquired by the DLR E-SAR sensor at L band in repeat-pass mode with a baseline of 10m. Fig. 1: Optical image (left), polarimetric color coded image (center) and interferometric coherence (right) over Oberpfaffenhofen The Oberpfaffenhofen scene (Germany) is composed of various agricultural areas, forests and urban zones. A polarimetric color-coded image and a coherence image give different descriptions of the observed scene. It can be observed in Fig. 1 that, in general, forests have a uniform polarimetric behavior while the interferometric coherence shows large variations. On the opposite some surface have similarly high coherences while the polarimetric image depicts different scattering mechanisms. This paper introduces an unsupervised classification process gathering the complementary information contained in polarimetric and interferometric data. The second section is dedicated to the unsupervised classification of polarimetric SAR data based on Cloude and Pottier [3] decomposition theorem and on the multivariate Wishart [6][7]density function. An efficient identification of the resulting clusters to three canonical scattering mechanisms is introduced. In the third part is presented a joint polarimetric interferometric classification procedure based on the polarimetric interferometric optimization procedure developed by Papathanassiou and Cloude [4][5]. Finally polarimetric and interferometric results are merged into a statistical classification procedure. 2. UNSUPERVISED CLASSIFICATION OF POLARIMETRIC SAR DATA 2.1. Unsupervised H-α classification This classification procedure is based on the polarimetric decomposition theorem introduced by Cloude and Pottier[2][3]. They propose to identify in an unsupervised way polarimetric scattering mechanisms in the H- α plane sub- divided into 8 basic zones characteristic of different scattering behaviors. The different class boundaries, in the H- α plane, have been determined so as to discriminate surface reflection (SR), volume diffusion (VD) and double bounce reflection (DB) along the α axis and low, medium and high degree of randomness along the entropy axis. Detailed explanations, examples and comments concerning the different classes can be found in [2][3]. This unsupervised estimation of the type of scattering mechanisms may reach some limitations due to the arbitrarily fixed linear decision boundaries in the H- α plane which may not fit data distribution, leading to noisy classification results. The use of other indicators such as the span or specific correlations coefficients may improve the classification results in a significant way. 2.2. Combined Wishart H-A- α Unsupervised Classification Schemes 2.2.1. Wishart H- α Unsupervised Segmentation of Polarimetric SAR data Lee et al. [1][6] introduced an unsupervised ML segmentation procedure based on the Wishart statistics of multilook coherency matrix. A k-mean iterative clustering algorithm is used to assign, at each iteration, a sample coherency to the nearest class according to a ML decision rule. Clusters centers are initialized with the results of the unsupervised identification of a scattering mechanism. This initialization provides 8 classes relating to the underlying physical scattering mechanism and giving a stable initial approximation of the segmentation. Results obtained using Wishart H- α segmentation are displayed in Fig. 2. The main kinds of natural media are clearly discriminated by the Wishart H- α segmentation scheme. This unsupervised classification algorithm modifies the decision boundaries in an adaptive way to better fit the data distribution and takes into account information related to the back-scattered power. 2.2.2. Wishart H-A- α Unsupervised Segmentation of Polarimetric SAR data Pottier and Lee [8] further improved the ML Wishart unsupervised segmentation by explicitly including the anisotropy information during the segmentation procedure. This polarimetric indicator is particularly useful to discriminate scattering mechanisms with different eigenvalue distributions but with similar intermediate entropy values. In such cases, a high anisotropy value indicates two dominant scattering mechanisms with equal probability and a less significant third mechanism, while a low anisotropy value corresponds to a dominant first scattering mechanism and two non-negligible secondary mechanisms with equal importance. Polarimetric data are first segmented according to the algorithm presented in the former paragraph. Once this procedure has converged, the 8 resulting clusters are split into 16 ones by comparing the anisotropy of each pixel to a threshold fixed to 0.5. The 16 segments are then used to initialize a second Wishart ML segmentation procedure. The segmentation results presented in Fig. 2 show an enhanced description of the Oberpfaffenhofen scene. The introduction of the anisotropy in the clustering process permits to split large segments into smaller clusters discriminating small disparities in a refined way. This classification scheme does not provide any information concerning the nature of the scattering mechanism associated to each cluster. C1 C2 C3 C4 C5 C6 C7 C8 C1 C2 C3 C4 C9 C10 C11 C12 C5 C6 C7 C8 C13 C14 C15 C16 Fig. 2 Wishart H- α segmentation results (left), Wishart H-A- α segmentation results (right) 2.3. Unsupervised Identification to Canonical Scattering Mechanisms An efficient estimation of the nature of scattering mechanisms over natural scenes can be achieved by gathering results obtained from the polarimetric decomposition and segmentation procedures presented in the previous paragraphs [8]. Volume diffusion and double bounce scattering were found to be over-estimated during the identification of scattering mechanisms using the H- α segmented plane. One of the reasons of this over-estimation resides in the calculation of the polarimetric decomposition average parameter set, which may lead to an erroneous interpretation of the nature of the scattering mechanism. This phenomenon is illustrated by the following example: 0.4731 T =  −0.3242  0 −0.3242 0 0.2369 0 0 0.29  gives Λ = diag[0.7,0.29,0.1] [α1 ,α 2 ,α 3 ] = [35°, 90°, 55°] ⇒ α = 51.15°, H = 0.6, A = 0.93 (1)  The example depicted in (1) shows that secondary mechanisms may corrupt average parameters and lead to the estimation of double bounce reflection, while the dominant contribution, with 70% of the total power, corresponds to surface scattering. H and A may be used to restrict the polarimetric study to the most significant contributions. High and low entropy respectively correspond to random and almost deterministic scattering. Global scattering with intermediate entropy values are associated to two scattering mechanisms with equal importance or one dominant scattering mechanism perturbed by secondary terms according to the anisotropy value. Specific identification procedures may then be applied to each of the three cases discriminated in the H-A plane [8]: - One dominant mechanism : single and double bounce scatterings are separated by α1 < 45° and α1 > 45° . - Two significant mechanisms: a distributed matrix, Td , is constructed from the first two elements of the eigenvector expansion. The nature of the scattering is determined by comparing its first two Huynen generators, 2A0 and B0 + B . - Three significant mechanisms: the random polarimetric scattering is associated to volume diffusion. A cluster based estimation of the canonical scattering mechanisms prevents an excessive sensitivity of the classification process to the hard-decision limits with respect to the parameters H, A and α . The identification results are shown in Fig. 3. The unsupervised classification results show a good discrimination of the three basic scattering mechanisms over the scene under consideration. It may be noted that the identification assigns some buildings to the volume diffusion class. The polarimetric properties as well as the power related information do not permit to separate these targets from forests. SR A A 1 DR 1stst nd 1stst & 2nd 1stst 1stst 0.5 22ndnd 33rdrd H VD 11stst 0 0.5 0.9 1 H Fig. 3 : Unsupervised identification to canonical scattering mechanisms (left) selection of relevant mechanisms in the H-A plane (right). 3. POLARIMETRIC INTERFEROMETRIC SAR DATA ANALYSIS 3.1. Polarimetric interferometric representations The polarimetric interferometric behavior of a target is fully described by two scattering matrices, S1 and S 2 . A six element complex target vector, k 6 , obtained by stacking target vectors from each interferometric image, gathers the polarimetric interferometric information into a compact representation. The corresponding (6×6) interferometric coherency matrix is given by [3]: T6 = k  T 1 k 6k †6 with k 6 =  1  T6 =  1† ∑ n n k 2  T12 T12  1 with T12 = ∑ k 1k †2  T2  n n (2) The matrices T1 and T2 are the standard n-look (3×3) hermitian sample covariance matrices for separate images. T12 is a (3×3) complex matrix which contains information about the interferometric correlation between k 1 and k 2 . 3.2. Polarimetric interferometric coherence set The sample interferometric correlation matrix, T12 , has complex diagonal elements, from which is computed a three polarimetric complex coherence set as follows: ( γ 1, γ 2 , γ 3 ) with γi = k1i k 2*i k1i k1*i k 2 i k 2*i and γ = γ SNR .γ spatial .γ temporal .γ polar (3) Standard real coherence values are obtained from the modulus of γ i , while its arguments correspond to the interferometric phase difference. It may be noted that such a the coherence is not invariant under a change of polarimetric basis and may be decomposed into multiplicative contributions. Range filtering and topographic phase removal procedures are applied to the interferometric data sets prior to the computation of the polarimetric interferometric coherences. Cloude and Papathanassiou [4][5] introduced the following original formulation of the interferometric coherence: γi = w1†T12 w 2 w1†T1 w1 w †2 T2 w 2 (4) where w1 and w 2 are three elements complex vectors permiting to compute the interferometric coherence of a polarization channel in any emitting-receiving polarization basis. Papathanassiou and Cloude further developed this concept to define an optimal coherence set ( γ opt 1, γ opt 2 , γ opt 3 ) , with γ opt 1 ≥ γ opt 2 ≥ γ opt 3 . The optimal coherence set is obtained by analytically tuning the projection vectors, w1 and w 2 , to maximize the modulus of the coherences. The results of the optimization procedure show an enhanced contrast between the different optimal coherences. The complete optimized coherence set represents highly descriptive indicators and may then be used efficiently in a classification process. 4. UNSUPERVISED CLASSIFICATION OF POLARIMETRIC INTERFEROMETRIC SAR DATA The color-coded image presented in Fig. 4 represents the joint information associated to the optimal coherencies and reveals particular behaviors of different types of natural medium under examination. White areas indicate targets showing high coherence independently of the polarization. Such a behavior is characteristic of point scatterers and bare soils. Green zones reveal the presence of a single dominant coherent mechanism within the resolution cell. Secondary coherences, associated to the red and blue channels have significantly lower values. Such zones correspond to surfaces with low SNR responses and some particular fields. Forested areas, characterized by a dark green color have scattering features dominated by a single mechanism but with a very low coherence. A comparison of the image of Fig. 4 with the polarimetric color-coded image shown in Fig. 1 indicates that the distribution of strictly polarimetric and polarimetric interferometric features over surfaces and agricultural fields are significantly different. Coherence related information permits to discriminate particular buildings that cannot be separated from forested areas using only polarimetric data. Over forested areas, the polarimetric color-coded image shows homogeneous zones, while interferometric data indicate that there exist large variations of the coherent scattering properties corresponding to clear-cuts and low-density forest. Two characteristic indicators, A1 and A2 are defined to characterize the relative optimal coherence spectrum as follows : γ~ − γ~ γ~ − γ~ A1 = opt 1~ opt 2 and A2 = opt 1~ opt 3 with γ~opt i = γ opt i / ∑ γ opt j , γ~opt 1 ≥ γ~opt 2 ≥ γ~opt 3 (5) γ opt 1 γ opt 1 These parameters indicate relative amplitude variations between the different optimized channels. Similarly to the polarimetric case, the indicators A1 and A2 may be used to estimate the number of independent coherent scattering mechanisms from the optimization results. The different optimal coherence set configurations are represented and identified in Fig. 4. A segmentation base on data interferometric properties is performed by projecting pixels in the A1-A2 plane separated in nine regions, as shown in Fig. 4. This unsupervised segmentation was also found to achieve a high degree of descriptivity on other scenes observed with different baselines [8]. This is a consequence of both the coherence optimization and the definition of a relative coherence set. γopt A2 A2 1 1 γopt N/A 0.5 2 γopt 3 N/A N/A A1 0 0.9 1 0.5 A1 Fig. 4 Color-coded image of the optimal coherence set (left). Discrimination of optimal coherence sets in the A1-A2 plane (right). The classification results are used to provide an adequate initialization to a segmentation merging polarimetric and interferometric analysis results. The classification algorithm processes the different canonical scattering mechanisms separately. Pixels belonging to one of the typical scattering type shown in Fig. 3 are first segmented using the results of the interferometric coherence set identification depicted in Fig. 4. The resulting clusters are used to initialize a k-mean unsupervised segmentation procedure based on the Wishart distribution of the (6×6) polarimetric interferometric coherency matrix, T6 [9][10]. In this way, pixels are segmented according to their polarimetric and interferometric features. Results for the Volume Diffusion and Surface Reflection classes are shown in Fig. 5. VD SR DR Fig. 5 Segmentation results over the Volume Diffusion class (left), and all three canonical scattering mechanisms (right) Clusters resulting from the ML segmentation are assigned a color indicating their average coherence, ranging from dark for low coherence to light for high coherence. Globally, polarimetric interferometric characteristics are efficiently segmented into compact clusters corresponding to scatterers with similar polarimetric and interferometric characteristics. The segmentation of the Volume Diffusion class successfully discriminates buildings, dense forest, sparse forest and clear-cuts. Surface Reflection areas are separated into segments according to both polarimetric and interferometric characteristics information. Details of the classification are displayed in Fig. 6 for two particular zones corresponding to the DLR buildings and forest parcels. It may be seen in Fig. 6 a) that the DLR buildings do not have the same polarimetric behavior. The color-coded interferometric coherence image in Fig. 6 b) indicates that scattering mechanisms over the buildings have a high degree of coherence. The classification approach proposed in this paper first assigns the different buildings to the double bounce reflection or volume diffusion classes according to their polarimetric behavior. The introduction of the interferometric information permits then to separate vegetated areas from man-made targets and corrects possible errors in the interpretation of the scattering from strictly polarimetric data only, Fig. 6 c). The classification of the areas dominated by surface reflection, presented in Fig. 6 d) clearly discriminates very smooth surfaces with low SNR, car parks and agricultural fields. The selected forested area presents a uniform polarimetric behavior dominated by volume diffusion, characteristic of dense vegetation observed at L band. The color-coded interferometric image shows some large variations of the polarimetric interferometric coherence set. The joint use of polarimetric and interferometric data permits to segment the corresponding sparsely vegetated zones or clear-cuts and provides a final mapping with significantly increased information content. a) b) c) d) e) Fig. 6 Polarimetric Interferometric classification results over two areas. a) polarimetric color coded image b) optimal coherence set color coded image c) volume diffusion classification results d) surface reflection classification results e) Global classification into three canonical mechanisms including double bounce reflection 5. CONCLUSION Data acquired in polarimetric and interferometric modes have complementary characteristics; their joint use in a classification process provides significantly higher performance. The classification approach resides on separate polarimetric and interferometric data classification and interpretation. Each scatterer is accurately identified to a basic scattering mechanism using efficient polarimetric indicators. The results of this identification are then used to evaluate polarimetric properties of clusters obtained from an unsupervised statistical segmentation based on the multivariate Wishart distribution.A parameterization of an optimal interferometric coherence spectrum is used to segment data according to their interferometric properties. Finally, an unsupervised classification process, gathering polarimetric and interferometric results, is applied to each canonical scattering mechanism. The resulting images show significant improvements compared to the strictly polarimetric case. The parameters used in these studies were chosen so as to reduce the sensitivity of the whole algorithm to changes from one site to the other or for different measurement conditions. Its applications to data acquired over a different site with a different baseline also led to equally satisfying results. 6. REFERENCES [1] J.S. Lee, M.R. Grunes, R. Kwok, " Classification of multi-look polarimetric SAR imagery based on the complex Wishart distribution ", International Journal of Remote Sensing, vol. 15, No. 11, pp 2299-2311, 1994. [2] L. Ferro-Famil, E. Pottier, J. S. Lee, "Unsupervised classification of multifrequency and fully polarimetric SAR images based on the H/A/Alpha-Wishart classifier", IEEE Trans. GRS, vol. 39, n°11, pp 2332-2342, November 2001. [3] S. R. Cloude, E. Pottier " A Review of Target Decomposition Theorems in Radar Polarimetry ", IEEE Trans. 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Lee, "Classification and Interpretation of Polarimetric Interferometric SAR data", Proceedings of IGARSS, June 2002, Toronto, Canada. [10] L. Ferro-Famil, 2000, “Multi-frequency and multi-temporal remote sensing of natural media using polarimetric SAR data”, Ph. D. Thesis, IRESTE, University of Nantes, France, December 2000. View publication stats