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O. A. Chesnokova, E. Erten chesnokova@mfb-geo.com ANALYSIS ON THE RELATION BETWEEN STATISTICAL SIMILARITY MEASURES AND AGRICULTURAL PARAMETERS: A CASE STUDY Swiss Federal Institute of Technology ETH Zurich ABSTRACT Polarimetric Synthetic Aperture Radar (PolSAR) images are widely used for agricultural fields monitoring and change detection applications due to their all-weather acquisition possibilities and inherent properties including phase and amplitude information. The techniques used for such temporal applications can be cast in two groups: polarimetric (incoherent) and polarimetricinterferometric (coherent) being represented in this work by the KL-distance and the Mutual Information, respectively. The goal of this work is to characterize these two kinds of different information sources in terms of ground measurement parameters of the agricultural fields, and to figure out the relationship between temporal trends of the similarity measures versus temporal trends of the physical parameters without dealing with inverse problems. For this purpose multitemporal fully polarimetric SAR images, acquired in the frame of the AgriSAR 2006 campaign with synchronous ground surface measurements over a whole vegetation period are analyzed. INTRODUCTION Information retrieved from remote sensing data connects cropping activities to different landscape factors such as soils and similar, which was investigated in several studies in the respect to Synthetic Aperture Radar (SAR) images in terms of crop inventory and crop yield estimation [1, 2]. Moreover, due to their orbiting nature, remote sensing satellites lend themselves well to on going monitoring initiatives, making a characterization of a scene change in terms of statistical dependencies among a set of temporal variables a common task in remote sensing image processing, including change detection [3] and target tracking [4]. In case of change detection, the aim is to define a scalar identifying regions of high activity in the temporal scene. Here, this scalar is defined by a similarity measure of probability density functions of temporal scenes. One of the similarity measures from the information theory for multivariate populations is a Kullback-Leibler divergence (KL-divergence), and its implementations to SAR images can be seen in recent publications, such as [3, 5]. In [7] and [8], instead of the incoherent KL-divergence, its special case - a coherent measure - called the Mutual Information (MI) has been used for change detection applications for single and multichannel channel SAR images, respectively. However, the interactions between these different kinds of similarity measures and the physical parameters of crop inventories are complex and yet poorly understood. Thus, the objective of this work is an investigation on the differences/similarities between the incoherent and the coherent techniques in terms of temporal scene characterization hence change detection, over agricultural fields. To demonstrate and investigate the potential of these recent similarity measures, multi-temporal polarimetric SAR acquisition series with synchronous ground surface measurements over a whole vegetation period have been used. It was examined which measure correctly characterizes temporal physical parameters in agricultural fields, such as height, wet biomass and soil moisture. STATISTICAL SIMILARITY MEASURES For change detection applications multiple observations of the same territory are necessary. When there is an observation at time 2, a temporal acquisition vector is obtained, being a complex


vector k

, distributed as a multi-component circular Gaussian N C (0, ) . It consists of two target vectors: k1 N C (0, 11 ) and k2 N C (0, 22 ) obtained from temporal multi-channel SAR images at time 1 and time 2, respectively, with the number of elements in one of the target vectors ki at time i being represented by m [8]. The true covariance matrix Sigma contains enough statistics to characterize the acquisition vector k , and it is estimated using a maximum likelihood method by n-sample (n-look) spatial coherent averaging: A (1 / n) nj 1 k j k j .
2

k1 k

T

The matrices A11 and A22 are the standard n-look and m x m dimensional polarimetric covariance matrices of separate temporal images, following Wishart distribution [9]. Discriminating between those temporal acquisitions A11 and A22 , affected by the changes of the scene of interest, is the aim of the change detection and crop monitoring applications. One of the similarity measures between temporal covariance matrices is the KL-distance, which is the symmetrised KLdivergence. Whereas A12 and A21 are cross correlation matrices between the acquisition vectors k1 and k 2 , characterizing the interferometric and polarimetric information [9]. KL-Distance: In probability and information theory, the KL-distance is a symmetric measure of the difference between two probability distributions. The KL-distance between temporal polarimetric matrices A11 and A22 and its analytically derived form are in the following [4]:

DKL ( A11; A22 ) n tr (
1 22 11

lo g

p( A11 ) p( A11 )dA11 p( A22 )
1 11 22

lo g

p( A22 ) p( A22 )dA22 p( A11 ) (1)

I m ) n tr (

Im )

Where I m is an m dimensional identity matrix, and n indicates the number of samples used for sample covariance matrix estimation. If the temporal random variables A11 and A22 are equal, the KL-distance makes its minimum and equals to zero. For more details one can take a look at [4, 5]. An alternative approach to discriminate between A11 and A22 is to form their mutual information. Mutual Information: The MI between polarimetric covariance matrices due to the temporal Wishart process in time can be written as [7]:

DMI ( A11; A22 )

lo g

p( A11 , A22 ) p( A11 , A22 )dA p( A22 ) p( A22 ) 2nP2 Im P
1 22

~ E{log(0 F1 (n, T ))}
T
1 11 / 22 1 22

2

n log( I
1 11 / 22

m

P2 )

(2)
1 22

12

A11 A22

21

;

11 / 22

11

12

21

,

~ Where (0 F1 (n, T ) is the complex hypergeometric function of matrix T. This function can be calculated with the help of the positive eigenvalues of the m x m Hermitian matrix T, which is described in detail in [7]. To make clear the differences between the KL-distance (1) and the MI (2) it may be highlighted that the KL-divergence is a difference between temporal probability distributions, and the MI is a difference between the joint distribution and marginal distributions of temporal probability distributions. The MI, additionally, takes into account interferometric matrices A12 and A21 , if compared with the KL-distance, meaning that the MI makes use of not only polarimetric but also of interferometric information. Therefore, the main question is to figure out i f the interferometric phase provides additional information.


EXPERIMENTAL RESULTS The incoherent (1) and coherent (2) similarity measures are applied to fully polarimetric images at L-band acquired by the airborne E-SAR system of German Aerospace Center (DLR) in the frame of the AgriSAR 2006 project. PolInSAR data sets were collected over the Goermin test site, located in northern Germany, during a whole vegetation growth period from soil cultivation to harvesting, starting on the 19th of April and ending on the 2nd of August. For the study, three fields with different crop types, such as winter rape, winter wheat and maize have been chosen based on their differences in harvest/sowing time, crop volume and crop structure. The ground measurements acquired simultaneously with PolSAR acquisitions were: wet biomass in kg/mІ, height of the plants in cm and soil moisture in Vol.% on the two depths of 0-5 cm and 5-10 cm. Moreover, the photographs of the observations during the acquisition are available. After applying the coherent coregistration processor as expounded in [10], the transformation of the fully polarimetric image to the covariance matrix was performed. Then, the temporal evolution of the similarity measures with biophysical parameters that were measured during the campaign was examined. In order to see the temporal trend of the change detectors with applied techniques, the fixed master image was chosen and compared pairwise with the following acquisitions. The resulting plots and conclusions of the studied crops are described below. Winter rape: Analyzing Fig. 1, it can be seen that crops have a height of more than one meter

Fig. 1 on the second date of the acquisition period. In June, the plants are already fully developed but in the beginning of July wet biomass starts to decrease significantly since the plants are getting dry, whereas the height of the crop remains the same. As highlighted in Fig. 2(a), a high temporal correlation between the MI and wet biomass was observed. Entirely covering soil, winter ra pe plants were developing together with wet biomass until the end of June. Afterwards, winter rape was getting dry making the MI between the master image and following images higher. Fig. 1(b) yield temporal trend of the KL-distance shown in Fig. 2(b) only in the presence of bare soils and/or when the signal is fairly transparent due to the dryness of the vegetation.


Fig. 2

Fig. 3 Winter Wheat: From the field work data, it was observed that winter wheat reaches a height of


only 80 cm (Fig. 3(a)), and has much lower wet biomass comparing with the winter rape field. However, a strong similarity between temporal behavior of the coherent techniques and wet biomass was observed; see Fig. 3(c). It is important to highlight that winter wheat dries significantly at the end of the observation period, starting to be transparent to the L-band signal and causing not only a drop in the MI but also a high increase in the KL-distance value (Fig. 3(d)), hence - in both cases - strong unsimilarity with the master image. Maize Field: Analyzing the plot of crop parameters in Fig. 4(a), it can be seen that maizestarts to grow late comparing with the other crop types. Wet biomass is very low and stable

Fig. 4 till the middle of the observation period. It increases significantly from the end of June to the beginning of July and stays stable afterwards. Both height and wet biomass follow the same trend making it impossible to separate them in the interpretation phase. The changes in soil moisture would have much more influence on the maize field monitoring, due to the fact that maize field stays bare for a half of the observation period. Thus, it becomes important to select the most suited master image for characterizing the beginning of flowering growth. To emphasize on the problem of selecting the master image in change detection application, and to make the dependence on soil moisture easier to see, temporal analysis were done based on three different master images. This


analysis made it possible to observe the opposite behaviour of the temporal trends with the applied KL-distance and MI, depending on the acquisition of the master image during relatively high and relatively low soil moisture conditions, which are plotted by blue and red curves on Fig. 4(c-d), respectively. Maize was neither flowering nor seeding until the beginning of June. Afterwards plants within rows were fully developed, and have reached the maximum height of 250 cm to the end of July. Thus, maize inventory analysis, as shown by black curves on Fig. 4(c-d), was done between the acquisitions on the 13th of June and 26th of July. However, with the master image acquired on the 13th of June, a high similarity was observed on temporal trend of the MI and wet biomass/height of plants, as in the other agricultural fields. The same temporal trend was observed for the KL-distance, which was not the case for the other fields. Reasons for this might be connected to the well developed maize crop condition with no gaps between plants in the late period of its inventory, which has decreased the effect of soil moisture in incoherent change detector. The main outcomes of the temporal analysis for the three crop types are the observation of a significant temporal correlation between wet crop biomass and the MI technique (representing coherent techniques), and a correlation between KL-distance and soil moisture in cases where the vegetation volume is short. CONCLUSIONS Polarimetric SAR imagery is an important tool in the monitoring of environmental changes, especially in the crop inventory. During the last decade the polarimetric SAR community investigated on the methods for the agricultural biophysical parameters calculation. For the overall accuracy estimation, inverse problems tend to be defined, increasing the complexity of derivation. Despite the apparent complexity introduced with inverse problems, simple statistical multichannel models provide reliable means of describing the temporal information. Due to the fact that such simple models can be used to characterize crop inventory, a lot of chan ge detection algorithms have been recently proposed. However, sensitivity of these change detection algorithms on physical parameters has not been fully investigated. An objective of this work was to understand which temporal trend of the coherent and incoherent techniques correspond to changes in which biophysical parameter of soil and/or vegetation. The results have clearly demonstrated that despite avoiding the definition of the specific change, the coherent methods can be successfully used for the dete rmination of the temporal trend of wet biomass. Although an important role of the incoherent methods in terms of soil moisture temporal trend retrieval was expected, it showed a good performance only for the bare fields regardless the fact that L-band polarimetric SAR data was used. REFERENCES 1. I. Hajnsek, T. Jagdhuber, H. Schon, and K. P. Papathanassiou, "Potential of estimating soil moisture under vegetation cover by means of PolSAR," IEEE Trans. Geosci. Remote Sens., vol. 47, no. 2, pp. 442­454, Feb. 2009. 2. J. M. Lopez-Sanchez, I. Hajnsek, and J. D. Ballester-Berman, "First Demonstration of Agriculture Height RetrievalWith PolInSAR Airborne Data," IEEE Geosci. Remote Sens. Lett., vol. 9, no. 2, pp. 242­246, Mar. 2012. 3. J. Inglada, G. Mercier, and T. Cnes, "A new statistical similarity measure for change detection in multitemporal SAR images and its extension to multiscale change analysis," IEEE Trans. Geosci. Remote Sens., vol. 45, no. 5 Part 2, pp. 1432­1445, Apr. 2007. 4. E. Erten, A. Reigber, O. Hellwich, and P. Prats, "Glacier velocity monitoring by maximum likelihood texture tracking," IEEE Trans. Geosci. Remote Sens., vol. 47, no. 2, pp. 394­405, Feb. 2009. 5. E. Erten, O. Chesnokova, C. Rossi, and I. Hajnsek, "A polarimetric temporal scene parameter and its application to change detection," in Proc. IGARSS, 2011, pp. 1091­1094.


6. F. Chatelain, J. Y. Tourneret, J. Inglada, and A. Ferrari, "Bivariate gamma distributions for image registration and change detection," IEEE Trans. Image Process., vol. 16, no. 7, pp. 1796­ 1806, Jul. 2007. 7. E. Erten, A. Reigber, L. Ferro-Famil, and O. Hellwich, "A new coherent similarity measure for temporal multichannel scene characterization," IEEE Trans. Geosci. Remote Sens., vol. 50, no. 7, 2012. 8. J. Lee and E. Pottier, Polarimetric radar imaging: from basics to applications. CRC, 2009. 9. L. Ferro-Famil, E. Pottier, and J. S. Lee, "Unsupervised classification of multifrequency and fullypolarimetric SAR images based on the H/A/Alpha-Wishart classifier," IEEE Trans. Geosci. Remote Sens., vol. 39, no. 11, pp. 2332­2342, Nov. 2001. 10. I. Hajnsek and P. Prats, "Soil moisture estimation in time with D-InSAR," in Proc. IGARSS, vol. 3, 2008, pp. 546­549.