Ship detection algorithm in SAR images based on Alpha-stable model Changcheng Wang*a, Mingsheng Liaoa, Xiaofeng Lib,d, Liming Jianga,c and Xinjun Chend a State Key Laboratory of Information Engineering in Survey, Mapping and Remote Sensing (LIESMARS), Wuhan University, Wuhan, Hubei 430079, China; bNOAA Science Center, WWBG, Room 102, 5200 Auth Road Camp Springs, MD 20746, U.S.A.; cInstitute of Space and Earth Information Science, Chinese University of Hong Kong Shatin, N.T., Hong Kong; dShanghai Fisheries University, 334 Jungong Road, 200090, Shanghai,China ABSTRACT This paper proposes a new ship detection algorithm based on Alpha-stable model for detection ships in the spaceborne synthetic aperture radar (SAR) images. The current operational ship detection algorithm is based on Constant False Alarm Rate (CFAR) method. The major shortcoming of this method is that it requires an appropriate model to describe statistical characteristic of background clutter. For multilook SAR images, the Gaussian model can be used. However, the Gaussian model is only valid when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian model often fails to describe background sea clutter. In this study, we replace Gaussian model with Alpha-stable model, which is widely used in the application of impulsive or spiky signal processing, to describe the background sea clutter in SAR images. Similar to the typical Two-parameter CFAR algorithm based on Gaussian distribution, we move a set of local windows through the image and finds bright pixels that are statistically different than the surrounding sea clutter. Several RADARSAT-1 images are used to validate this Alpha-stable model based algorithm. The experimental results show improvements of using Alpha-stable model over the Gaussian model. Keywords: Alpha-stable model, ship detection, Synthetic Aperture Radar, Constant False Alarm Rate (CFAR).
1
INTRODUCTION
Synthetic Aperture Radar (SAR) is an active radar that can provide high resolution images in microwave band under all weather conditions. SAR images have been widely used for fishing vessels monitoring, traffic and immigration controls, and military reconnaissance. Numerous works have been done to detect ships in SAR images automatically [1]. In general, the Radar Cross Section (RCS) of ships is higher than the surrounding sea clutter. This is due to the effect of multiple bounces from the ships superstructure. So, ships can be separated from the sea cluster with an appropriate choice of RCS threshold. The Constant False Alarm Rate (CFAR) algorithm is a widely used algorithm for computing the adaptive threshold. To use the CFAR algorithm, one must first determine an appropriate probability density function (PDF) that can describe statistical characteristic of background clutter well. For multilook SAR images, a commonly used statistical model is the Gaussian model. However, it is only appropriate when a large number of looks have been averaged so that the central limit theorem can be applied to the average [2]. Other models such as the Weibull or K distribution have also been suggested [3,4]. In general, as sea clutter in SAR images always shows spiky or heavy-tailed characteristics, these models often fail to describe heavy-tailed sea clutter in many real applications. When using these models for modeling the sea clutter in a CFAR algorithm, it will either produce a lot of false alarms or omit some ship targets. In this paper, the Alpha-stable model is employed to model the sea clutter in the SAR images. A CFAR algorithm based on the Alpha-stable model is proposed for ship detection in SAR images. Alpha-stable model based CFAR shows improvements over Gaussian model in identifying ships in the SAR images. *
[email protected]; phone: +86-27-68778092 ext.8320; address: P.O BOX c310, Luoyu Road 129#, Wuhan 430079, P. R. China MIPPR 2007: Automatic Target Recognition and Image Analysis; and Multispectral Image Acquisition, edited by Tianxu Zhang, Carl Nardell, Duane Smith, Hangqing Lu, Proc. of SPIE Vol. 6786, 678611, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.747389 Proc. of SPIE Vol. 6786 678611-1
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2
CFAR ALGORITHM
The CFAR algorithm is used for setting a threshold so that we can find targets that are statistically significant above the background signal. A distribution function that fits distribution of region of interest (ROI) of sea clutter is first computed for determining the threshold. Then the pixel whose value is higher than the threshold is a target. Let f ( x) be the probability density functions (PDF) of the background sea clutter. The probability of false alarm Pfa and threshold T is given by the equation: ∞
T
Pfa = 1 − ∫ f ( x)dx = ∫ f ( x)dx 0
(1)
T
For a specified probability of false alarm Pfa and a probability density function f ( x) , we can get the threshold T by solving equation (1).
3
ALPHA-STABLE MODEL
Alpha-stable model is widely used in the processing of impulsive or spiky signals [5,6]. The model is derived from the generalized central limit theorem (GCLT). In fact, it is a generalization of the Gaussian distribution, or the Gaussian distribution is a special case of the Alpha-stable distribution [6]. Due to the lack of closed-form formulas for PDF, Alpha-stable model is often described by its characteristic function which is the Fourier transform of the probability density function [6].
⎧⎪exp{ j µ t − γ t α [1 − j β sgn(t ) tan πα2 ]} ϕ (t ) = ⎨ 2 ⎪⎩exp{ j µ t − γ t [1 + j π β sgn(t ) log t ]}
if α ≠ 1 if α = 1
(2)
The characteristic function depends on four parameters: characteristic exponent, αЄ(0,2), measuring the thickness of the tails of the distribution (the smaller the values of α, the thicker the tails of distribution are); symmetry parameter, βЄ[-1,1] setting the skewness of the distribution; scale parameter, γ>0; location parameter, µЄR. In general, no closed-form expression exists for the Alpha-stable model, except for the Gaussian (α=2), Cauchy (α=1, β=0), and Pearson (α=0.5, β=-1) distributions. When β=0 and µ=0, the distribution is called a symmetric Alpha-stable (SαS) distribution. Its characteristic function is then simplified as [6] α
ϕ (t ) = e x p ( −γ t )
(3)
Due to the lack of known closed-form for the probability density functions, most of the conventional methods in statistics cannot be adopted to estimate the four parameters in the Alpha-stable model. However, several numerical methods, such as the maximum likelihood, sample fractiles or negative-order moments, are proposed to solve these parameters [6, 7]. In this study, we apply a Regression-type numerical method developed by Koutrouvelis [7] to estimate these four parameters α, γ, β and µ. In addition, to calculate the PDF f ( x;α , β , γ , µ ) of Alpha-stable distribution, we can firstly compute the PDF f ( z;α , β ) of standard Alpha-stable distribution with two parameters α and β by using the formula z = ( x − µ ) / γ 1 / α . By taking the inverse Fourier transform of the characteristic function, the PDF of the standard Alpha-stable distribution is given by [6]
⎧ 1 ∞ exp( −t α ) cos[ zt + β t α tan( πα )]dt 2 ⎪ π ∫0 f ( z; α , β ) = ⎨ ∞ ⎪⎩ π1 ∫ exp( −t ) cos[ zt + π2 β t log( t )]dt 0
if α ≠ 1 (4)
if α = 1
Nolan proposed a numerical integral method for calculating the PDF of f ( x;α , β , γ , µ ) [8]. We will apply it to calculating the PDF of Alpha-stable distribution.
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4
METHODOLOGY FOR SHIP DETECTION
The proposed adaptive ship detection algorithm is similar to the Two-parameter CFAR algorithm. It moves a set of local windows through the entire SAR image and finds bright pixels that are statistically different from the surrounding sea clutter. In the proposed algorithm, two local windows are specified: a guard window and a background window. They both center on the pixel under test, and the guard window is surrounded by the background window. The background “ring” between the guard window and background window (the gray area in Fig. 1) contains sea clutter samples. The purpose of the guard window is to ensure that no pixel of an extended ship target is included in the background “ring”. So, the background “ring” is purely representative of background sea clutter. With a constant false alarm rate, a threshold for distinguishing ship target from sea clutter is calculated by using equation (1). The PDF f ( x) is estimated from image samples in the background “ring” by using the Alpha-stable model.
— Pixel under test
—
Guard window
_Backgroundwindow Fig. 1. Sliding windows for CFAR algorithm
The procedure of the CFAR algorithm based on the Alpha-stable model is summarized as follows: Step 1: For a given pixel in a SAR image, we first determine a set of windows (Fig. 1) centered at this pixel. Samples in the gray area in Fig. 1 represent background sea clutter. Step 2: Parameters α, β, γ and µ for the background sea clutter are estimated using regression-type method developed by Koutrouvelis. Step 3: We then compute the PDF f ( x;α , β , γ , µ ) by using numerical integral method. Step 4: The threshold T is a positive quantity which satisfies the condition: T
∑
f ( x ; α , β , γ , µ ) ≤ 1 − P fa
