NOVEL METHOD FOR SAR IMAGE SEGMENTATION WITH APPLICATION TO BRIDGE DETECTION Yilun Chen, Jiong Chen, Jian Yang Department of Electronic Engineering, Tsinghua University [email protected] ABSTRACT A new method for SAR image segmentation is proposed in this paper. Region segmentation can be achieved by contour tracking, and we use the general Bayes tracking framework to solve this problem. Due to the non-linearity of the tracking problem and the non-Gaussian noise of SAR image, Monte Carlo based particle filtering algorithm is adopted to obtain the Bayes optimal solution. Based on the tracking framework, a particle filter based contour tracking method is proposed for region segmentation in SAR images. In this method, each particle is assigned to a linear segment with specific location and direction. The response of the local edge detector is used to calculate the particle weight while the global contextual knowledge, such as the smoothness of the region boundary, is guaranteed by the propagation of particles. The proposed method is employed for river boundary extraction on the SAR image. Furthermore, bridges over a river are detected. 1. INTRODUCTION With the emergency of well-developed Synthetic Aperture Radar (SAR) technologies, SAR image processing techniques have gained more and more attention in recent years, e.g., target detection, terrain classification and etc. As a typical kind of military targets, automatic bridge detection is an important research topic which has been studied by [5]-[7] and etc in recent years. To detect bridges in SAR images, it is more appropriate to identify the river regions first. Effective river segmentation methods could reduce the false-alarm from other bridge-like objects. However, previous methods tend to use simple image processing methods to solve the river-segmentation problem, such as morphology operators, edge detectors and etc.However, due to the speckle noised SAR images and the complicated scenarios, such simple segmentation techniques may fail in error results. This work was supported by the National Important Fundamental Research Plan of China(2001CB309401) and by the Fundamental Research Foundation of Tsinghua University.

In [8], a particle filter based method for road tracking in SAR image was presented, which could extract curves in SAR image with efficient and robust performance. In this paper, similar idea is adopted for region segmentation, where the particle filter based algorithm in [8] is modified and refined for region contour tracking. The paper is organized as follows: in section 2, a tracking framework is set up for contour extraction. Then a brief review of Bayesian filter and particle filter is provided in section 3. The proposed particle based segmentation method is presented in section 4 and validated by experimental results in section 5. The whole paper is concluded in section 6. 2. THE TRACKING FRAMEWORK OF CONTOUR EXTRACTION The problem of image segmentation can be equally treated as tracking its contour. Suppose a contour of a given shape can be described by the following parametric equation: ½ x = α (t) (1) y = β (t) where t is a parameter. If the denotation of t is considered as time, the curve of a contour can be regarded as the trace of a “moving object” (Please notice that the mentioned object, which actually does not exist, is just used to demonstrate the idea). Therefore, the extraction of a contour can be utilized by tracking the trace of the ”moving object” via estimating the object position at each time (see Fig. 1). For a tracking problem we usually take t into discrete values, denoted as t = {t0 , t1 , t2 ...}. If the position and the direction of the ”moving object” at time tk is denoted as (xk , yk ) and θk , respectively, a sequence of directed points, {xk , yk , θk }k=0,1,... , can be adopted to model the contour of the segmented region. Denote the state vector sk as sk = (xk , yk , θk ),

(2)

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However, for most cases in image processing problems the linear Gaussian hypothesis does not hold. So the Monte Carlo implementation is a recommended solution. t4

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Fig. 1. The tracking framework for contour extraction. the problem of region segmentation from an image is equivalent to sequentially estimate the mentioned state vector sk in such an image, using pixels around the supposed boundary of the region, denoted as zk . From the Bayesian perspective, the tracking problem is to recursively calculate the belief of sk given the data z1:k = {z1 , ..., zk }, i.e., to construct the p(sk |z1:k ). Based on the above description, the general Bayesian tracking framework, which will be explained briefly in the following section, can be adopted to solve the problem of region segmentation as well as contour extraction. 3. THE BAYESIAN FILTER WITH ITS MONTE CARLO IMPLEMENTATION

3.2. Particle Filter Particle filter is a technique for implementing a recursive Bayesian filter by Monte Carlo simulations. The key idea is to approximate the distribution via discrete random measures defined by random samples with associate weights, named The particle set is often denoted as χ = ª © (i) particles. s , w(i) i=1:N , where s(i) is the ith random sample and w(i) is its weight. For instance, if the distribution of interest is p (s)ªand its approximating random measures are χ = © (i) s , w(i) i=1:N , χ approximates the distribution p (s) by p (s) ≈

XN i=1

³ ´ w(i) δ s − s(i)

where s(i) and w(i) are the samples and their weights, respectively, N is the number of particles used in approximation, and δ (·) is the Dirac delta function. Based on the discrete approximation of the pdf p (sk |z1:k ), the complete procedure of particle filtering is described in the following paragraph. (i)

(i)

1. Initialize: s0 ∼ p (s0 ) and w0 = 1/N , where i = 1, · · · , N

3.1. Bayesian Filter For a tracking problem, the hidden state of a given system sk needs to be estimated using the observations stochastically related to that state, denoted as z1:k = {z1 , z2 , · · · , zk }. Consider a dynamic system with a model defined by the state equation and the observation equation sk = fk (sk−1 , uk )

(3)

zk = hk (sk , vk )

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where uk and vk are supposed to be noises. Moreover, it should be pointed out that linearity hypothesis on function fk and hk are unnecessary. The Bayesian filter calculates p(sk |z1:k ) sequentially by the following two stages: Z p(sk |z1:k−1 ) = p(sk |sk−1 )p(sk−1 |z1:k−1 )dsk−1 (5) p(sk |z1:k ) = αp(zk |sk )p(sk |z1:k−1 ),

(7)

(6)

where α is a normalizing constant. The recurrence relations, eq.(5) and eq.(6), however, are only a conceptual solution, for the integration in whole space is intractable in practice. In the case of a linear model and the Gaussian noise, the recursive construction of the posterior distribution can be handled analytically yielding the Kalman filter.

2. For k = 1, 2, · · · (a) Propagate: for i = 1, · · · , N (i) (i) sample sk from q(sk |sk−1 , zk ) (b) Calculate weight: i. Calculate un-normalized weights: for i = 1, · · · , N (i) (i) calculate wk for each particle sk ii. Normalize weight: for i = 1, · · · , N (i)

wk =

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w PN k j=1

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(c) Estimate: E {g(sk )} =

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wk g(sk )

(d) Resample: ˆeff i. Calculate N ˆeff ≤ Nth , for i = 1, · · · , N , ii. If N PN (i) (j) (j) sk ∼ j=1 wk δ(sk − sk ), and (i)

wk = 1/N One may refer to [1], [2] for detailed deduction and analysis.

4. PARTICLE FILTER BASED CONTOUR EXTRACTION As mentioned above, the contour extraction problem can be achieved via tracking solutions. In addition, particle filtering algorithm, which is derived from Bayesian theory and implemented by Monte Carlo simulation, has shown its efficiency and robustness to deal with the nonlinear and nonGaussian problems. Consequently, a new road extraction method based on particle filter is proposed in this paper. 4.1. State Model and Propagation According to the contour model introduced in section 2, the state vector of the particle tracker is defined as by 2. Based on the state model defined above,i.e., sk = (xk , yk , θk ), the particles are propagated by  (1) (2)   xk = xk−1 + d cos θk−1 uk + d sin θk−1 uk (1) (2) (8) yk = yk−1 − d sin θk−1 uk + d cos θk−1 uk   (3) θk = θk−1 + uk (i)

where uk ,i = 1 . . . 3 are random perturbation which determine the central point and orientation of next line, respectively.

Fig. 3. The regions of the modified ROA detector, region1 and region 3 denote the bilateral sides of the contour,respectively. Region 2 is the edge region. The central line denotes the line segment. The corresponding detector is defined as r(s(i) ) = max(

µ1 µ3 , ), µ3 µ1

(9)

where µj is the radiometric empirical mean value of a given region j = 1, 3. One can figure out that the larger value r(s(i) ) is, the more likely this line segment behaves like a edge. The response of the modified ratio line detector is then mapped to the particle weight utilizing w(i) = √

r 2 (s(i) ) 1 e− 2σ2 , 2πσ

(10)

where σ is a constant parameter. 4.3. Starting Point Selection and Stopping Rule

Fig. 2. Propagation of a given particle.

4.2. Particle Weight The criteria to calculate particle weight, which is used to measure the confidence of each sample is essential to the tracking performance of particle filter. According to the above state model, the weight of a particle should reflect the probability how the corresponding line segment behaves like a part of a contour of a given region, e.g., the locations, and the edge strength on that line segment. In this paper, a modified ratio of average (ROA) detector is employed and the particle weight is defined based on the response of this edge detector. The ROA detector was firstly introduced in [4]. Given a piece of segment, index 1 denotes the edge region, while indexes 2 and 3 denote its bilateral sides, respectively (Fig.3).

The starting point can be pre-selected or automatically detected by moving window line/edge detector [4, 7]. To avoid false-alarms, the window of the detector should be chosen large enough and the threshold should be chosen strictly. Our method works better with human inspected starting points. For a given particle filter, the tracking process can be terminated for any of the following criteria: 1. The current line segment has been estimated before. 2. The current segment is out of the boundary of an image. The first criteria prevents the contour to be repeatedly tracked and the second one stops the tracking process while reaching the boundary of the image. 5. EXPERIMENTAL RESULTS We use data collected from the X-band PI-SAR in Niigata, Japan. The image resolution is 1.5m × 1.5m, as shown in Fig. 4. The river region is first segmented by our proposed method. The parameters are set as follows: the particle number is 100, σ = 1 and the size of ROA detector is

set to 9 × 9. The segmented river region is shown in Fig. 5. Based on the extracted river region, we detect bridges by projecting all the pixel value across the river side (The projection map is shown in Fig. 6). The peak values in the projection map suggests potential bridges across the river. The final detected bridges are shown in Fig. 7.

Fig. 7. The detected bridges(white points suggests the bridge locations). be also readily employed to images captured by other sensor.

Fig. 4. SAR image from Niigata, Japan.

7. REFERENCES [1] A. Doucet, A. Freitas, and N. Gordon,“Sequential Monte Carlo Methods in Practice,” New York: Springer, 2001

Fig. 5. Segmented river region by the proposed method.

[2] A. Doucet, “On Sequential Simulation-Based Methods for Bayesian Filtering,” Technical report, University of Cambridge, Dept. of Engineering, 1998 [3] J.S. Liu and R. Chen, “Sequential Monte Carlo Methods for Dynamic Systems,” J. Am. Statist. Ass., 1998

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[4] R. Touzi, A. Lopes, and P.Bousquet, “A statistical and geometrical edge detector for SAR images,” IEEE Trans. Geosci. Remote Sensing, vol. 26, pp. 764-773, Nov. 1988.

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Fig. 6. The radius projection map along river side from Fig. 5. We can see that the proposed tracking based method could successfully segment the desired region. Specifically, a well-segmented river region make the bridge detection more effective, as demonstrated in the previous results. 6. CONCLUSION In this paper, a particle filter based segmentation method for SAR image processing is presented. In the proposed method, region segmentation is achieved by tracking its contour. The contour is modelled as multiple line segments with specific central positions and directions. Each line segment is given meaning to a “particle”. The strength of a line segment is reflected in the weight of the corresponding particle, while the propagation of particles guarantees the smoothness of the contour. We demonstrate our algorithm in the application of bridge detection, where the river region is firstly segmented by our method. Based on the wellsegmented river side, the bridges are successfully detected. The algorithm is applied to SAR image segmentation, it can

[5] Y. Wang, Q. Zheng, “Recognition of roads and bridges in SAR images”, Proc. IEEE International Radar Conference, 1995: 399 -404 [6] F.Su, Y.Zhu, H. Ge, “An algorithm of bridge detection in radar sensing images based on fractal”, Proc. 2002 3rd International Conference on Microwave and Millimeter Wave Technology , 2002: 410 - 413 [7] D. Borghys, V. Lacroix and C. Perneel, “Edge and line detection in polarimetric SAR images”, Proc. of International Conference on Pattern Recognition (ICPR), 2002. [8] Y. Chen, Q.Yang, Y. Gu, J. Yang, “Road detection in SAR image using particle filter”, to appear in Proc. of International Conference on Image Processing (ICIP) 2006.