THE K-GENERALIZED MODEL TO CHARACTERIZE MARINE FEATURES IN SAR IMAGES: FIRST RESULTS Maurizio Migliaccio(1), Giuseppe Ferrara(1), Attilio Gambardella(2) and Dario Aiello(1) (1) (2) Dipartimento per le Tecnologie - Università degli Studi di Napoli Parthenope, Via Acton, 38, 80133 Napoli, Italy Dipartimento di Ingegneria Elettrica ed Elettronica - Università degli Studi di Cagliari, Piazza D’Armi, 19, 09123 Cagliari, Italy ABSTRACT The K-generalized distribution is a three parameters probability density function (pdf) which ensures a continuous and physically consistent transition among different scattering scenarios. This speckle model can embody the Rayleigh case (which is descriptor of land scenes), the Rice case (which is descriptor of the presence of a dominant scatterer) and the K case (which is descriptor of marine scenes). Thus, in principle, this speckle model allows a continuous and physically consistent transition among very different scattering scenarios. In this paper, we investigate the sensitivity of the three K-generalized parameters as descriptors of features over marine SAR images with special attention to oil spills and look-alikes. The reference data set has been provided by the ESA under the CAT-1 Project C1P-2769. 1 INTRODUCTION Synthetic Aperture Radar (SAR) is the key sensor for a large set of environmental applications. The enormous quantity of SAR image data to be analyzed calls for automated and skillful geophysical feature extraction procedures. In this paper we investigate the stochastic nature of a SAR image as an additional source of information to be exploited to learn more about the underlying physics to be observed. The classical Rayleigh distribution model for the amplitude of backscattered signal well fits homogeneous land scenes and it represents a reference since it is associated to the so-called fully-developed speckle [1]. Several other distributions have been used to model speckle statistics, i.e. them are the β [2], lognormal [3], and Weibull [2] distributions. The K distribution has been found to be a particularly useful model for sea amplitude statistics [1]. The Kdistribution model has a reasonable justification in terms of physical scattering processes, and it reduces to the Rayleigh distribution model under appropriate circumstances [1], [4-6]. Moreover, the K-distribution model has been generalized to model the amplitude of backscattered signals with a non-uniform distribution of phase by a fluctuating population of objects [6], [7]. The proposed model is based on the K-generalized probability density function (pdf) [7]. The K-generalized pdf which ensures a continuous and physically consistent transition among different scattering scenarios [6]. This speckle model can embody the Rayleigh case (which is descriptor of land scenes), the Rice case (which is descriptor of the presence of a dominant scatterer) and the K case (which is descriptor of marine scenes) [6-8]. In this study we investigate the sensitivity of the three K-generalized parameters as descriptors of marine features over SAR images. In practice, instead of suppressing the speckle by means of appropriate averagings which make the SAR image spatial resolution coarser, we look for the speckle statistics under the unitary K-generalized formulation to assist geophysical image analysis. In particular, the study is focused on the use if the statistical model to improve oil-spill detection. The base idea is to estimate the electromagnetic return of selected regions of interest (ROI) over single-look SAR images by means of the three characteristic parameters of the K-generalized pdf, α η and ν. The working hypothesis is that the three parameters assume values within characteristic intervals in function of the different marine scenes analyzed. The physical interpretation has been carried out considering the typical aspects associated to such analysis, i.e. the influence of the wind and the not-correct time/spatial co-location between SAR and wind data. The reference data set has been provided by the European Space Agency (ESA) under the CAT-1 Project C1P-2769 and the SeaWinds/QuikSCAT wind data have been provided by NASA (PODAAC). The paper is organized as follows: the K-generalized pdf is introduced in section 2. First experimental results are shown in section 3 and, finally, in section 4 the conclusions are drawn. __________________________________________________ Proceedings of SEASAR 2006, 23-26 January 2006, Frascati, Italy, (ESA SP-613, April 2006) 2 THE K-GENERALIZED MODEL In this section, we briefly summarize the speckle model employed in this study. The basic assumption is that the backscattered field received at a linearly polarized receiving antenna can be written as the sum of N elementary fields ∑ N E (r .t ) = ai (r , t )e − jΦ i ( r , t ) (1) i =1 where ai(r,t) is a real form factor governing the ith elementary field scattering, Φi(r,t) is the ith elementary field phase factor depending on the propagation path and N is the number of elementary field scattering contributions. The amplitudes ai(·) and phases Φi(·) are real random variables with corresponding continuous pdfs, and N is a discrete random variable. Mathematically, (1) can be seen as a random walk in a complex plane in which the number of steps is ruled by N and the ith step is ruled by ai and Φi [8]. Since the physical processes governing ai, Φi and N are essentially independent it is possible to consider them consequently [7-9]. Further, since the physical process governing the elementary fields is the same, all ai are characterized by the same pdf f’(a), and all Φi are characterized by the same pdf f’’(Φ) [7]. Moreover, we generally have that the excess propagation path lengths are larger than the electromagnetic wavelength λ, and hence, all Φi are uniformly distributed over radians (rectangular pdf). This is the characteristic of a strongbackscattering regime [6-7]. An effective and physical pdf for N is the negative binomial pdf [7]. Say α the real and nonnegative parameter associated to such a pdf. Note that for α approaching large values the limiting Poisson pdf is found [7]. If we consider the latter assumption, we recover the popular Rayleigh field model [7]. In general, if we relax it, by manipulating (1), we have an intensity total field pdf characterized by a K-pdf [1], [7]. The actual shape of the K-pdf is dictated by α. In other words, we have a field model generalization of the exponential pdf, which is relevant to the intensity distribution in case of the Rayleigh field case [8]. It is actually possible to generalize such a model to the case of weak-backscattering regime, i.e., to the case of nonuniformly distributed phases. Mathematically this corresponds to a directional bias in the random walk and is modeled in [7] in terms of the von Mises pdf. The von Mises pdf measures the departure from the uniform phase distribution by means of a parameter ν, which reduces to the uniform case when is set to zero. In [7], it is shown after some mathematical manipulations, that the pdf of the square magnitude of the total linear field is given by the following analytical expression which is unfortunately not directly viable: ∫ ∞ 1 ⎛⎜ ν h ⎞⎟ f ( h) = I o Ψ ( s) J o ( h s ) sds 2 ⎜⎝ α ⎟⎠ 0 (2) in which we have the Bessel function of the first kind of zeroth-order Jo(·), the modified Bessel function of the first kind of zeroth-order and a function Ψ(·) depending on the mean number of elementary field scattering contributions, α and ν [7]. Equation (2) can be greatly simplified in the case that the mean number of elementary field scattering contributions tends to infinity (but α and ν are left arbitrary) [7]. Hence, we have ⎛ ⎜ α 2 ⋅α f ( h) = ⋅⎜ 2 α +1 ⎜ Γ(α ) ⋅η ⎜⎜ 1 + ν 4 ⋅α ⎝ ⎞ 2 ⎟ ⎟ ⎟ ⎟⎟ ⎠ (α −1) (α −1) ⋅h 2 1⎫ ⎧ ⎤ 2 ⎪⎪ ⎛ν ⎞ ν 2 ⎞⎟ ⎪⎪ 2 ⎡⎛⎜ ⋅ I 0 ⎜⎜ ⋅ h ⎟⎟ ⋅ Kα −1 ⎨ ⋅ ⎢ 1 + ⋅ α ⋅ h⎥ ⎬ ⎟ ⎜ ⎥⎦ ⎪ ⎝η ⎠ ⎪η ⎢⎣⎝ 4 ⋅ α ⎠ ⎭⎪ ⎩⎪ (3) where Γ(·) is the Eulerian gamma function and Kα-1(·) is the modified Bessel function of the second kind of order α-1 and η is due to the dominant scatterer It is also important to note that proper estimation of the K-generalized three parameters is required in order to fully characterize the model. This is actually a delicate matter which must be carefully considered. In fact, the assumption of the underlying statistical model is not fully satisfied when real SAR data are considered. In this study, a simple estimation procedure of the three parameters developed in [8] and based on the χ2 test has been considered. 3 EXPERIMENTAL RESULTS In this section we investigate the sensitivity of the three K-generalized parameters as descriptors of dark features over marine single-look complex (SLC) SAR images. SAR images were acquired by the AMI sensor mounted on board of the ERS-2 satellite operated by the ESA. Specifically, three SAR images have been considered. A brief description of such three SAR images is due: the first SAR image is relevant to the acquisition of 21 January 2002, 10:01 (ERS-2, SLCI, orbit 35318, frame 2763, center lat. 41.763N, center lon 10.678E, descending pass) off the coast of Orbetello, Tuscany, Italy. The image is completely over the sea. A meteorological front is present together with an elongate multiple oil spill aligned to the wake of a ship (see Fig. 1). This image shows the typical features associated to an illegal oil spill. The second SAR image is relevant to the acquisition of 02 June 2003, 21:02 (ERS-2, SLCI, orbit 42439, frame 1089, center lat. 54.409N, center lon 14.161E, ascending pass) over the Baltic Sea at south of Sweden near the border between Germany and Poland. On left side we have land with lagoon, in the center is present an oil spill the rest of the image shows large free sea area (see Fig. 2). The third and last SAR image is relevant to the acquisition of 1 February 2003, 11:25 (ERS-2, SLCI, orbit 40701, frame 2745, center lat. 42.718N, center lon 9.912W, descending pass) off the Galicia coasts after the Prestige oil tanker sinking (see Fig. 3). It is a more complex scene with respect the previous ones. A meteorological front (high wind on the right side), a small portion of land (top-right), several oil patches and ships are recognizable in the image. Fig. 1 - Zoom of the area of interest relevant to quicklook of the SAR acquisition of 21 January 2002, 10:01. The stained areas are relevant to the selected sub-scenes for the sensitivity study. Fig. 2 - Zoom of the area of interest relevant to quicklook of the SAR acquisition of 02 June 2003, 21:02. The stained areas are relevant to the selected sub-scenes. Fig. 3 - Zoom of the area of interest relevant to quicklook of the SAR acquisition of 1 February 2003, 11:25. The stained areas are relevant to the selected sub-scenes for the sensitivity study. The sensitivity study is conducted estimating the K-generalized three parameter relevant to specific areas, highlighted by colours, manually selected in the SAR images. In each image is always first selected a free sea surface area for reference (blue area) and an oil covered surface (red area). Land and ships are indicated with green and fuchsia, respectively. In the third image two sea area in correspondence of a meteorological front are considered too (light blue and yellow areas). The amplitude data set relevant each specific area is analyzed and the corresponding K-generalized three parameter are evaluated. To perform the physical interpretation, the wind information is taken into account. However, the different time/spatial co-location between SAR and wind data provides only rough information on meteo-marine conditions. On a quantitative basis it is interesting to proceed systematically among the three cases which represent an increasing level of difficulty for the physical interpretation process. The list of the three parameters estimated making use of the Kgeneralized model is reported in Tables 1 to 3. Table 1 deals with the K-generalized parameters relevant to the selected areas belonging to the first image. Table 1 shows that the free sea areas are comparable, especially for the α and η values. In fact, the difference between the α values is approximately 7.4% (Δα) and it is approximately 2.7%(Δη) for the η values. As far as we move to consider the areas relevant the oil we learn that α and η decrease with respect to the free sea areas while ν value is unchanged. Let us compare now each oil areas with the corresponding sea areas. α varies of about 50% for the areas nearby the ship and of about 28% for the areas selected far from the ship. Generally, the difference of the α variations are expected to be affected by the type of the spilled oil, its age and the meteo-marine conditions. In this case, since the oil is spilled by the same ship in different phases, it is mostly likely that the α variations are due to weathering processes which has been affecting for a longer time the areas far from the ship. TABLE 1 - Estimated values of the K-generalized three parameters relevant to the colored areas shown in Fig. 1 SEA LAND OIL η α ν 1.100E-2 1.121E-2 9.764E-3 22.00 13.00 16.00 7.67 6.09 6.38 TABLE 3 - Estimated values of the K-generalized three parameters relevant to the colored areas shown in Fig. 3. SEA MET. FRONT 1 MET. FROMT 2 LAND OIL 1 OIL 2 OIL 3 SHIP 1 SHIP 2 η α ν 1.138E-3 7.531E-3 1.200E-2 7.351E-2 6.701E-3 4.489E-3 5.329E-3 9.574E-3 9.421E-3 26.00 19.00 10.00 18.00 16.00 20.00 22.00 23.00 20.00 6.93 6.23 5.31 6.35 6.47 6.97 7.12 6.97 6.32 TABLE 2 - Estimated values of the K-generalized three parameters relevant to the colored areas shown in Fig. 2 SEA 1 SEA 2 OIL 1 OIL 2 η α ν 8.232E-3 8.464E-3 4.578E-3 6.561E-3 27.00 25.00 13.00 18.00 6.93 7.45 6.41 7.03 TABLE 4 - Summarizing scheme of the η and α parameters values for different marine scattering scenarios. SEA LAND OIL LOOK-ALIKE SHIP η α HIGH HIGH LOW LOW LOW HIGH LOW LOW LOW HIGH The parameter estimation results relevant to the second SAR image confirm what experienced in the first case (see Table 2). With reference to the sea and oil areas, we have a difference of approximately 13% for η and 27% for α. With reference to the land η is comparable with the sea value (Δη=2%) while α decreases of about 41%. The parameter estimation results relevant to the third SAR image show that, as we expected, the presence of the oil decreases the value of α. The differences between the free sea areas and the oil covered ones are Δα=38% a Δα=23% a Δα=15% for the oil patches 1,2 and 3 respectively. In this case, since the deploying mechanism is linked to a ship sinking, the values variation is mainly due to the meteo-marine conditions rather than the emulsification processes. In the areas corresponding to the meteorological front, since the wind low producing a look-alike we have a decreasing of α and η values. The values corresponding to the land are similar as regard η (Δη=10%) and low with respect α (Δα=31%). The values corresponding to the ships are low as regard η and high with respect α. In all cases ν values are comparable. In conclusion it is possible to state: • the α, η and ν parameters of the K-generalized pdf show a different sensitivity with regard to the hydrocarbon presence on the sea surface; • the most sensible parameters are α and η; • the values of these parameters are influenced by: kind of the oil, age (weathering processes) of hydrocarbon and meteo-marine conditions. To further emphasize these results a summary Table is reported, see Table 4. 4 CONCLUSIONS The K-generalized distribution is a three parameters probability density function (pdf) and is here considered to provide a statistical speckle model which is able to characterize the different scattering scenarios over marine SAR images. Hence, by means of a differential analysis, first a free sea area has been selected in order to deduce the reference parameters, and then the variations relevant to hydrocarbon, rather than to a look-alike, have been estimated. Since it has not been possible to achieve wind fields perfectly space/time co-located with respect to the SAR images, only rough information on meteo-marine conditions have been considered to carry out the physical interpretation. The preliminary analysis has shown that: • the presence of oil-spill causes a decreasing of the α and η parameters; • the look-alike due to low wind speed areas, wind front areas and areas sheltered by land introduce a decreasing of the α and η parameters comparable to those caused by the presence of an oil-spill. Therefore, the discrimination between oil spill and look-alike is possible if the wind field is perfectly known; • the land surfaces are characterized by high values of η (like for the sea) and by relatively low values of α; • the presence of a ships causes low values of η and high values of α. ACKNOWLEDGEMENT The authors acknowledge the ESA for providing the SAR data (C1P-2769) and the NASA for providing the scatterometer data. REFERENCES 1. E. Jakeman and P. N. Pusey, A Model for Non-Rayleigh Sea Echo, IEEE Trans. Antennas Propag., vol. 24, pp. 806– 814, June 1976. 2. A. L. Maffett and C. C. Wackerman, The Modified Beta Density Function as a Model for Synthetic Aperture Radar Clutter Statistics, IEEE Trans. Geosci. Rem. Sensing, vol. 29, no. 2, pp. 277-283, 1991. 3. F. T. Ulaby and M C. Dobson, Handbook of Radar Scattering Statistics for Terrain. Norwood, MA: Artech House, 1989. 4. C. J. Oliver, A model for non-Rayleigh scattering statistics, Optica Acta, vol. 31, pp. 701-722, 1984. 5. C. J. Oliver, The interpretation and simulation of clutter textures in coherent images, Inverse Problems, vol. 2, pp. 481-518, 1986. 6. E. Jakeman and J.A. Tough, Generalized K Distribution: a Statistical Model for Weak Scattering, J. Opt. Soc. Am. A, vol. 4, no. 9, pp. 1764–1772, September 1987. 7. R. Barakat, Weak-Scatterer Generalization of the K-density Function with Application to Laser Scattering in AtmosphericTturbulence, J. Opt. Soc. Am. A, vol. 3, no. 4, pp. 401–409, April 1986. 8. P. Corona, G. Ferrara and M. Migliaccio, Generalized Stochastic Field Model for Reverberating Chambers, IEEE Trans. Elettromagn. Compat., vol. 46, no. 4, pp. 655–659, November 2004. 9. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces. Norwood, MA: Artech House, 1987.