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FEXP models for oil slick and low-wind areas analysis and discrimination in sea SAR images

Massimo Bertacca(1) , Fabrizio Berizzi(1) , and Enzo Dalle Mese(1)

(1) University of Pisa, Via Caruso 16, 56122 Pisa , Italy

Abstract

FEXP models for oil slick and low-wind areas analysis and discrimination in sea SAR images

Authors: Massimo Bertacca, Fabrizio Berizzi, Enzo Dalle Mese

Dept. of Information Engineering- University of Pisa, Via Caruso, 16 56122 Pisa (Italy), Ph. +390502217673, Fax +390502217626, e-mail: massimo.bertacca@iet.unipi.it

The dark areas, which sometimes appear in sea SAR PRI images, are mainly caused by a little surface wind speed. Other possible causes, such as the presence of oily substances that defile the water, targets, presence of phytoplankton, algae or natural films can cause similar effects. In the literature, the areas on the sea surface that give rise to these shady regions on sea SAR images are generally referred to as “sea surface anomalies”. The aim of this paper is the discrimination of dark areas corresponding to low wind areas from those caused by oil slicks and spills. It is a matter of fact, however, that analogous procedures might be used to identify all the other sea surface anomalies. Our analysis deals with the theory of discrete stochastic long-memory processes and, in particular, we have made use of FEXP (fractionally exponential) models. In recent years, the analysis of natural clutter in high-resolution synthetic aperture radar (SAR) images has been improved by using self-similar random process models. Many natural surfaces, like terrain, grass, trees and also sea surfaces, correspond to SAR precision images (PRI) that exhibit long-range dependence behaviour and scale-limited fractal properties. Among the possible self-similar models, two classes have been used in the literature to describe the spatial correlation properties of the scattering from natural surfaces: fractional Brownian motion (fBm) models and Fractionally Integrated Autoregressive Moving Average (FARIMA) models. In particular, fractional Brownian models provide a mathematical framework for the description of scale-invariant random textures and amorphous clutter of natural settings. Datcu (1992) used an fBm model for synthesizing SAR imagery [1]. Stewart, Moghaddam, Hintz and Novak (1993) proposed an analysis technique for natural background clutter in high-resolution SAR imagery [2]. They employed fractional Brownian motion models to discriminate between three clutter types: grass, trees and radar shadows. If the fBm model provides a good fit with the periodogram of the data, it means that the power spectral density (PSD), as a function of the frequency, is approximately a straight line with negative slope in a log-log plot. For particular data sets, the estimated PSD cannot be correctly represented by an fBm model. There are different slopes that characterize the plot of the logarithm of the periodogram versus the logarithm of the frequency. They reveal a greater complexity of the analyzed phenomenon. Therefore, we can utilize FARIMA models that preserve the negative slope of the long-memory data PSD near the origin and, through the so-called short-range dependence functions, allow the shape and the slope of the PSD to be modified with increasing frequency. The short-range dependence part of a FARIMA model is an ARMA process. Ilow and Leung (2001) used the FARIMA model as a texture model for sea SAR images to capture the long-range and short-range spatial dependence structure of some sea SAR images collected by the RADARSAT sensor [3]. Their work was limited to the analysis of isotropic and homogeneous random fields, and only to AR or MA models, (ARMA models were not considered). Unfortunately, sea SAR images cannot be considered simply in terms of homogeneous, isotropic or amorphous clutter. The action of the wind contributes to the anisotropy of the sea surfaces and the particular self-similar behaviour of sea surfaces and spectra, correctly described by means of the Weierstrass-like fractal model [4], strongly complicates the self-similar representation of sea SAR imagery. Bertacca, Berizzi and Dalle Mese (2004-2005), extended the work of Ilow and Leung to the analysis of non-isotropic sea surfaces [5-6]. The authors made use of ARMA processes to model the short-range dependence part of the mean radial PSD of sea ERS1 and ERS2 SAR Precision Images (PRI). They utilized a FARIMA analysis technique of the directional spectra of sea SAR images to discriminate low wind from oil slick areas on the sea surfaces. A limitation to the applicability of FARIMA models for sea SAR imagery is the high number of parameters required for the ARMA part of the PSD. Using an excessive number of parameters is undesirable because it increases the uncertainty of the statistical inference and the parameters become difficult to interpret. From a mathematical point of view, fractionally exponential (FEXP) models, allowing the representation of the logarithm of the SRD part of the long-memory PSD, strongly reduce the number of the parameters to estimate and provide the same goodness of fitting of FARIMA models at very low computational costs. We have experimentally obtained that only three parameters are sufficient to characterize the SRD part of sea SAR images PSD corresponding to lacks of wind, low surface wind speeds or to oil slicks (or spills) on the sea surface. In our method we first consider some homogeneous sub-images of a sea SAR image. They can correspond to a windy and clean sea area, to a low wind area or to an oil slick or spill on the sea surface. Then we calculate the directional spectra of the considered sub-images by using the 2-D periodogram. To decrease the variance of the spectral estimation we average spectral estimates obtained from nonoverlapping squared blocks of data. The characterization of isotropic or anisotropic 2-D random fields is obtained first using a rectangular to polar coordinates transformation of the 2-D PSD, and then considering, as radial PSD, the average of the radial spectral densities for θ ranging from zero to 2π radians. This estimated mean radial PSD (MRPSD) is finally modelled using a FARIMA and a FEXP model independently of the anisotropy of sea SAR images. The innovative contributions of this work are: 1. We have defined a reliable procedure to estimate the fractional differencing parameter d and the parameters characterizing the short-range dependence part of the MRPSD of sea SAR images, for FARIMA and FEXP models. 2. We have analysed some ERS1 and ERS2 PRI containing dark areas which correspond to oil slick (or spills) or to low wind areas on the sea surface. We have estimated the MRPSD for the different sea surface anomalies SAR images and represented it using a FARIMA model and a FEXP model. Then, we have compared the orders of the numerator and denominator polynomials of the ARMA part of the FARIMA models to the order of the polynomial representing the SRD component of the FEXP model. Our experimental results demonstrate that using the FEXP model we improve the goodness of fitting with a lower number of parameters. 3. We use FEXP model parameters to discriminate the dark areas produced by oil slicks (or spills) from those produced by low wind areas on the sea surface. The presented method demonstrated reliable results when applied to ERS1 and ERS2 SAR PRI of the Mediterranean Sea and North Sea and of the Atlantic and Pacific oceans. References

[1] M. Datcu, “Model for SAR images,” presented at the SPIE Conf. Int. Symp. Optical Engineering and Photonics in Aerospace Sensing, Orlando, FL, Apr. 1992. [2] C. V. Stewart, B. Moghaddam, K. J. Hintz, and L. M. Novak, “Fractional Brownian motion models for synthetic aperture radar imagery scene segmentation,” Proc. IEEE, vol. 81, no. 10, pp. 1511–1522, Oct. 1993. [3] J. Ilow and H. Leung, “Self-similar texture modeling using FARIMA processes with applications to satellite images,” IEEE Trans. Image Process., vol. 10, no. 5, pp. 792–797, May 2001. [4] F. Berizzi and E. Dalle Mese, “Sea-wave fractal spectrum for SAR remote sensing,” Proc. Inst. Elect. Eng., Radar, Sonar, Navigat., vol. 148, no. 2, pp. 56–66, Apr. 2001. [5] M. Bertacca, F. Berizzi, E. Dalle Mese, A. Capria, “A FARIMA-Based analysis for wind falls and oil slicks discrimination in sea SAR imagery,” Geoscience and Remote Sensing Symposium, 2004. IGARSS '04. Proceedings. 2004 IEEE International, Volume 7, 2004, Page(s):4703 - 4706 vol.7. [6] M. Bertacca, F. Berizzi, E. Dalle Mese, “A FARIMA-Based Technique for Oil Slick and Low-Wind Areas Discrimination in Sea SAR Imagery,” Geoscience and Remote Sensing, IEEE Transactions on, Volume 43, Issue 11, Nov. 2005 Page(s):2484 – 2493.

 

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