

FEXP models for oil slick and lowwind 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 lowwind 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, email: 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 longmemory processes and, in particular, we have made use of FEXP (fractionally exponential) models.
In recent years, the analysis of natural clutter in highresolution synthetic aperture radar (SAR) images has been improved by using selfsimilar random process models. Many natural surfaces, like terrain, grass, trees and also sea surfaces, correspond to SAR precision images (PRI) that exhibit longrange dependence behaviour and scalelimited fractal properties.
Among the possible selfsimilar 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 scaleinvariant 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 highresolution 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 loglog 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 longmemory data PSD near the origin and, through the socalled shortrange dependence functions, allow the shape and the slope of the PSD to be modified with increasing frequency. The shortrange 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 longrange and shortrange 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 selfsimilar behaviour of sea surfaces and spectra, correctly described by means of the Weierstrasslike fractal model [4], strongly complicates the selfsimilar representation of sea SAR imagery.
Bertacca, Berizzi and Dalle Mese (20042005), extended the work of Ilow and Leung to the analysis of nonisotropic sea surfaces [56]. The authors made use of ARMA processes to model the shortrange 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 longmemory 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 subimages 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 subimages by using the 2D 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 2D random fields is obtained first using a rectangular to polar coordinates transformation of the 2D 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 shortrange 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, “Selfsimilar 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, “Seawave 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 FARIMABased 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 FARIMABased Technique for Oil Slick and LowWind Areas Discrimination in Sea SAR Imagery,” Geoscience and Remote Sensing, IEEE Transactions on, Volume 43, Issue 11, Nov. 2005 Page(s):2484 – 2493.
Full paper
