Forest Mapping and Classification with Compact PolInSAR Data

Ningxiao Sun, Yuejin Zhao, Lin Sun and Qiongzhi Wu,

(1.School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China;2.School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)

Abstract: An unsupervised classification method was applied to compact polarimetric-interferometric SAR(C-PolInSAR) data to investigate its potential for forest mapping and classification. Unsupervised classification requires an initial class as a training set. In this paper, the compact polarimetric entropy H and the optimal coherence spectrum A were computed, and their capabilities for initial classification were analyzed. Based on the H and A, a partition method was proposed to subdivide the H-A plane, and initial classes were hence obtained. Next, unsupervised C-PolInSAR segmentation procedures based on H-A and the complex coherence matrix J4 were investigated. The effectiveness of the unsupervised classification of C-PolInSAR data was demonstrated by using an E-SAR L-band PolInSAR dataset of the Traunstein test site.

Key words: forest mapping; unsupervised classification; Wishart classifier; optimal coherence set; compact polarimetric-interferometric SAR (C-PolInSAR)

In recent years, new SAR modes called compact polarimetric SAR (C-PolSAR) systems have emerged.A C-PolSAR system has three polarimetric modes: the π/4 mode[1], the CL mode[2], and the CC mode[3]. It has advantages over a fully polarimetric SAR system in terms of pulse repetition frequency reduction, data volume, and system power requirements. Compared with a fully PolSAR, a C-PolSAR only has two data channels. Even though the compact polarimetric data are halved (i.e. only two data channels), the polarimetric information is not. Studies have shown that the C-PolSARs have important potentials for target decomposition[4], terrain classification and ocean targets detection[5], and to a certain extent, its capabilities are comparable to the fully SAR. The C-PolSAR interferometric technique[5],which combines the C-PolSAR with the interferometric technique,also plays an important role in forest parameters inversion.

Forests play an important role as a natural resource of biomass storage and in the dynamic carbon cycle. Research of forestry applications have demonstrated their profound significance. For example, the PolSAR technique was widely applied to forest structure analysis, tree heights and biomass estimation[7-8]etc. Classifications based on polarimetric SAR (PolSAR) data have revealed a good relationship between the Wishart[9]classified results and the tree ages of homogeneous forests[10]. However, for large biomass heterogeneous forests with trees of different types, heights and structures, classifications based on PolSAR data alone do not provide sufficient sensitivity for different forest classes. To solve this problem, classification methods were introduced to the interferometric observations. Studies have shown[11]that unsupervised forest mapping techniques based on quad polarimetric-interferometric SAR (quad-PolInSAR) data improve forest mapping and classification performance.

In this paper, the unsupervised classification method was applied to a C-PolInSAR to investigate the potentials of the C-PolInSAR for forest mapping. Unsupervised C-PolInSAR segmentation procedures based on the complex coherence matrix were investigated. The unsupervised classification results for different compact polarimetric modes were analyzed and discussed. The potential of these C-PolInSAR classification methods were demonstrated using DLR E-SAR L-band PolInSAR datasets acquired in 2003 with a 5 m spatial baseline of the Traunstein test site.

1 Compact Polarimetric SAR Interferometry

1.1 C-PolSAR interferometry

There are three compact polarimetry modes: the π/4 mode, the CL mode, and the CC mode. The C-PolSAR scattering vector k can be obtained from the complex scattering matrix S. The scattering vectors of the three compact modes can be expressed as

(1)

A monostatic C-PolInSAR system can measure two target scattering vectors at both ends of the baseline. The compact polarimetric scattering vectors measured at ends 1 and 2 of the baseline can be expressed as kcp1and kcp2, respectively. A four-element complex scattering target vector k4can be formed by stacking kcp1and kcp2, i.e. k4=[kcp1kcp2]T. Then, the 4×4 compact polarimetric interferometric matrix J4can be expressed as

(2)

where the superscript H stands for the matrix conjugate transpose; J11and J22are the Hermitian coherency matrices of the two images, respectively;Ωis a non-Hermitian complex matrix that contains polarimetric and interferometric information of the two target vectors kcp1and kcp2. The compact polarimetric-interferometric matrix J4is Hermitian and positive semi-definite.

1.2 C-PolInSAR optimal coherence

For C-PolInSAR, the complex polarimetric-interferometric coherenceγ(ω1,ω2) can be expressed as

(3)

whereω1andω2represent polarimetric projection vectors, and particular projection vectors can maximize the modulus of the coherenceγ(ω1,ω2). Many previous works[12]have proved that the maximization of the coherence modulus is an eigenvector-resolving problem, i.e.

(4)

Consequently, the modulus of the optimum coherence is the square root of the corresponding eigenvalues of Eq.(4), where |γopt1|≥|γopt2|.

2 Unsupervised Classification Method Based on the H-A and C-PolInSAR Matrix

In this section, an unsupervised C-PolInSAR classification procedures based on the compact polarimetric-interferometric coherency matrix J4is described. Since the unsupervised classification method needs the initial classes’ centers. Consequently, the parameters which can be used for initial classification should be found firstly. In this paper, we used DLR E-SAR L-band PolInSAR datasets acquired in 2003 of the Traustein test site to investigate the classification methods by transforming the fully PolInSAR data into C-PolInSAR data based on Eq.(1). The experimental datasets and the ground truth data are described in detail in the next section.

2.1 Compact polarimetric entropy H and optimal coherence spectrum A

Fig.1 Distribution of correlation coefficient

In Section 2, the coherence of C-PolSAR data was introduced. The coherence between different polarization states is an additional, and important, indicator of the underlying scattering mechanism. The coherence is generally composed of different values and is invariant under apolarimetric change of basis. In addition, the optimized coherences which are computed via Eq.(4) preserve the characteristics of the scene properties and is independent of the radar polarimetric measurement basis. The optimal coherences of C-PolInSAR are shown in Fig.2. Fig.2 reveals the enhanced contrast between different optimal coherences, as studied in previous works[9,11,14]. As a result, optimized coherences indicate that the C-PolInSAR properties of vegetation media can be applied to forest classification.

Fig.2 Magnitudes of two optimal coherences of the CL mode C-PolInSAR data

In order to isolate the polarization-dependent part of the optimal coherences, we computed the relative values as

(5)

The relative optimal coherence spectrum can be expressed as[14]

(6)

This parameter indicates relative amplitude variations between the two optimized channels. WhenAis close to one, it indicates a single coherence scattering mechanism, whereasAclose to 0 depicts a low dependence of the scattering coherence to the polarization information.

2.2 Initial classification based on H- A plane

Fig.3 H-A plane zones division and color coded of the CL mode C-PolInSAR data

Based on the entropyHand the optimal coherence spectrumA, we obtained theH-Aplane. To improve the classification accuracy, theH-Aplane was divided into several classes. These classes were used to provide an initial classification of both the Wishart iteration classification. Based on theH,Adistributions in the plane, theH-Aplane can be divided into 6-8 zones. First, based on the entropy, theH-Aplane was divided into three areas, i.e. low entropy (H<0.8), medium entropy (0.80.9) areas. Low entropy areas correspond to bare ground or agricultural areas, medium entropy areas correspond to the sparsely forested areas, and high entropy areas correspond to forested areas. Then, based on the optimal coherence spectrumA, the above three zones were further divided into several subareas to classify different kinds of forests. Note that the boundaries of different zones are not invariant, and depend on the specific data. Taking the CL mode C-PolInSAR data as an example, theH-Adistribution image and the eight-zone discrimination image are shown in Fig.3.

2.3 Classification based on the C-PolInSAR matrix statistics

(7)

The compact polarimetric-interferometric coherency matrix J4is generated fromnindependent realizations of k4. Consequently, J4follows a complex Wishart pdf,Wc(n,Σ4), whose probability is defined as

(8)

(9)

whereΣm=E(J4|m).

2.4 Unsupervised classification procedure summary

In the former section, we used the CL mode C-PolInSAR data as an example to analyze and investigate the classification parameters and the classification method. In this section, we give the general unsupervised classification steps in detail.

① Data preparation and pre-processing. Obtain the compact polarimetric-interferometric matrix J4via Eq.(2), and filter the data to suppress the noise and achieve an adequate equivalent number of looks.

② Compute the compact polarimetric entropyHbased on eigenvalue decomposition with the master or slave C-PolSAR data, and compute the optimal coherence set |γopt1| , |γopt2| via Eq.(4) and the coherence spectrumAvia Eq.(6).

③ Divide theH-Aplane into several zones to obtain the initial classes, and label all the pixels.

④ Compute the cluster centersΣmwith the compact polarimetric-interferometric matrix J4.

⑤ Compute the Wishart distance of each pixel based on Eq.(9). Reclassify all the pixels, and compute the new cluster centersΣm.

⑥ Return to the above steps for iterative classification until the termination criterion is met.

This iterative procedure is convergent[15]. In this paper, when the number of pixels switched classes to the pre-specified number (5%), the iteration ended[16]. In addition, during classification, two classes will be merged if their center distances were very close.

3 Unsupervised Classification Results and Discussion

3.1 Experimental data and ground truth data description

The PolInSAR data used in this research are the DLR-SAR L-band PolInSAR datasets acquired in 2003 of the southwestern part of the city of Routh, Germany (Traunstein). The spatial baseline is 5 m and the temporal baseline is 20 min. The flight height was 3 000 m. The range resolution is 1.5 m and azimuth resolution is 3.0 m. The original SLC image has 10 260×1 414 pixels. To suppress specked pixels and increase the SNR, we first performed 4×4 multi-look processing in the azimuthal direction. The resultant test data had a dimension of 2 565×1 414 pixels, where the RGB coded image is shown in Fig.4. Note that 4×4 multi-look is insufficient to obtain an unbiased coherence estimation and the polarimetric entropy. Therefore, 7×7 multi-look processing is further used to obtain anunbiased and stable coherence and entropy estimation. These heterogeneous forests have different heights and biomasses. The different experimental areas and species description are shown in Fig.4 and Tab.1.

Fig.4 Experimental sites distribution and labels based on different biomass

Tab.1 Mean biomass of each experimental site (t/ha)

Fig.5 Unsupervised classification results of the C-PolInSAR data

3.2 Unsupervised classification results

Following the unsupervised classification steps in Section 4, the final classification results are achieved, as shown in Fig.5. To better evaluate forests classification results, we remove the bare ground and agriculture areas. In addition, the classification results are reclassified into 3 board categories: the low biomass class (light gray), the medium biomass (medium gray) and the high biomass class (dark gray) as shown in Fig.5. The low, medium biomass and high biomass classes are corresponding tob<200 t/ha, 200 t/ha300 t/ha, respectively, wherebstand for the biomass. The producer accuracy, user accuracy and the final accuracy based on the known biomass data of each forest area can be retrieved.

From Fig.5, the unsupervised classification with three compact modes of the C-PolInSAR data show clear and correct results. Different biomass classes are clearly distinguishable. We compared the classification results with ground truth data in detail. We know the class level of each pixel. Based on the ground truth data (Fig.4), 30 455 pixels belong to the low biomass class, 84 038 pixels belong to the medium biomass class, and 111 566 pixels belong to the high biomass class. These pixels were used as the validation set. We computed the producer and user accuracies of the classification results, which are listed in Tab.2-Tab.4.

We find that the high biomass class (coded in dark gray color) is easily discriminated from the medium (medium gray) and low biomass (light gray) classes, and the producer accuracy of the high biomass classification is greater than 91%. The user accuracy of the high biomass class is greater than 88%. For the π/4 and CC modes, the accuracy reached 90%. In addition, the producer accuracy of the low biomass and medium biomass classes are both greater than 74%. The user accuracy of the medium biomass class is greater than 83%, while the user accuracy of low biomass is about 60%. Even though the classification accuracy of the low biomass class is low, the final accuracy of the classification with the three compact polarimetric modes PolInSAR data was more than 83%, which validates the effectiveness of our proposed methods. We also find that the three compact modes of the PolInSAR data have similar classification results, which also means that any C-PolInSAR mode has great potential in forest classification and mapping.

Tab.2 Classification results of π/4 mode PolInSAR

Tab.3 Classification results of CL mode PolInSAR

Tab.4 Classification results of CC mode PolInSAR

4 Conclusion

In this paper, unsupervised classification methods based on the Wishart classifier were introduced to the C-PolInSAR to investigate the potential for C-PolInSAR forest mapping and classification. The compact polarimetric entropyHand the optimal coherence spectrumAwere first computed and analyzed. Based on theH-Aplane, a partition method was proposed and applied to subdivide theH-Aplane, and initial classes were obtained. Unsupervised C-PolInSAR segmentation procedures based onH-Aand the complex coherence matrix J4were investigated. The unsupervised classification results for different compact polarimetric modes were analyzed and discussed via the actual E-SAR airborne PolInSAR data. Classification results of the three compact modes C-PolInSAR data showed clear and highly accurate classification results, and to some extent, the classification results matched those obtained from quad PolInSAR classification results. This demonstrates that supervised classification with C-PolInSAR data has a significant potential for forest mapping and classification.