Bayesian Oil Spill Segmentation of SAR Images via Graph Cuts 1

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1 Bayesian Oil Sill Segmentation of SAR Images via Grah Cuts 1 Sónia Pelizzari and José M. Bioucas-Dias Instituto de Telecomunicações, I.S.T., TULisbon,Lisboa, Portugal sonia@lx.it.t, bioucas@lx.it.t Abstract. This aer extends and generalizes the Bayesian semisuervised segmentation algorithm [1] for oil sill detection using SAR images. In the base algorithm on which we build on, the data term is modeled by a finite mixture of Gamma distributions. The rior is an M- level logistic Markov Random Field enforcing local continuity in a statistical sense. The methodology roosed in [1] assumes two classes and known smoothness arameter. The resent work removes these restrictions. The smoothness arameter controlling the degree of homogeneity imosed on the scene is automatically estimated and the number of used classes is otional. Semi-automatic estimation of the class arameters is also imlemented. The maximum a osteriori (MAP) segmentation is efficiently comuted via the α-exansion algorithm [2], a recent grah-cut technique, The effectiveness of the roosed aroach is illustrated with simulated (Gaussian or Gamma data term and M-level logistic classes) and real ERS data. 1 Introduction Segmentation of dark atches in SAR images is an imortant ste in any oil sill detection system and many different aroaches to the roblem have been roosed so far. These aroaches are buit on off-the-shelf segmentation algorithms such as Adative Image Thresholding, Hysteresis Thresholding, Edge Detection (see [3] and references therein), and entroy based methods like the Maximum Descritive Length technique [4]. Work [1] introduces a Bayesian segmentation algorithm where the observed data (oil and water) data is modeled by a finite Gamma mixture, with a given redefined number of comonents. To estimate the arameters of the class conditional densities, an exectation maximization (EM) algorithm was develoed. The used rior is a second order Markov Random Field (MRF), more secifically an isotroic Ising Model. To estimate the labels, the osterior distribution is maximized (MAP) via grah-cut techniques [5]. Notwithstanding the romising results rovided by the above described segmentation method, it has restrictions that the resent work overcomes. The first restriction 1 The work was suorted in art by the Portuguese Fundação ara a Ciência e Tecnologia (FCT) under the grant PDCTE/CPS/49967/2003 and by the Euroean Sace Agency (ESA) under the grant ESA/C1:2422.

2 concerns the number of classes that is limited to two. The second restriction concerns the smoothness arameter that has to be manually tuned. Furthermore, the class arameters estimation rocess is comletely suervised, requiring an interaction with the user in order to manually select a region containing oil ixels and a region containing water ixels. In the resent work we generalize [1] by: (1) extending the number of segmented classes to a redefined otional number c, (2) automatically estimating the homogeneity arameter β in the MRF, and (3) automatically estimating the class arameters. To extend [1] to an otional number of classes, the so-called α-exansion algorithm [2] is imlemented. In order to estimate the smoothness arameter, two different techniques are tested, namely the Least Squares (LS) Fit and the Coding Method (CD) [6]. A first attemt is carried out to imlement unsuervised segmentation using a semi-suervised initialization. To evaluate the accuracy of the algorithm, different simulations are carried out. The simulations address both the Gamma and the Gaussian data model. For the real images, the Gamma mixture data model roosed in [1] is adoted to model the observed SAR intensity values. The article is organized as follows: Section 2 gives a short overview of the original algorithm that builds the base to this work; Section 3 describes, in seudo-code, the main stes of the roosed segmentation methods; Section 4 resents simulation and real results, and finally Section 5 contains concluding and future work remarks. 2 Overview of Base Algorithm The algorithm roosed in [1] addresses the roblem of finding an estimation fˆ of a labeling for a set of N ixels P := {1, 2,, N}. When c ossible classes are available, a labeling f := {f 1,f 2, f N } is a maing from P to L, where L := {l 1,l 2,,l c } is the set of discrete values that the ixels may take. The vector y:={y 1,y 2, y N } stands for the observed data, corresonding to the image intensity measurements at the ixels. In order to infer fˆ, we adot the MAP criterion. This amounts to maximize the osterior density of the labeling given the observed data. As described in [1] in detail, this is equivalent to minimizing the obective function where, P are ixel locations, E( f,..., f E N, ) = E ( f ) + E ( f, f ), (1) 1 N = 1 < E is the negative likelihood given by ( f ) = log( ( y f )), (2) where (y f ) is the conditional density of y given f, called data model or sensor function, and E, is the rior clique otential associated with the the clique {,}

3 containing the air of neighboring ixels and [6]. Since we have adoted an MLL, we have, E ( f, f ) = βδ ( f, f ), (3) where δ is the discrete delta function and β controls the degree of homogeneity we wish to imose on the scene. Note that < E, ( f, f ) = β nrneighbours( f ), (4) with N nrneighbours( f ) = n( ), (5) i= 1 f i where n(f i ) is the number of neighbors in neighborhood N i having the same label as ixel i. As demonstrated in [1], E(f 1, f N ) is grah reresentable for c = 2 and in these circumstances, the global minimum of the obective function may be comuted by alying the grah-cut algorithm described in [5]. 3 Proosed Segmentation Methods In the next Sections we roose suervised and unsuervised aroaches to the segmentation. The first aroach assumes known class arameters, whereas the second does not. In both methods, the smoothness arameter is assumed unknown. 3.1 Suervised Segmentation with Beta Unknown In the first segmentation method, we adot iterative labeling-estimation, with the two stes being erformed alternately, insired by the EM algorithm [6]. The initial values for the labeling and the arameter estimator are otional and don t seem to have a relevant influence on the final erformance. Since the class arameters are assumed known, they are omitted from the seudo-code. Algorithm-1: 1. Start with an arbitrary initial labeling f 0 and arbitrary arameter βˆ=β 0 2. While ˆ β δ or nriterations < ItMaxNr do 2.1 Find fˆ = α_exansion( f 0, βˆ) 2.2 Find βˆ=ls_estimation( fˆ)or CodingMethod( fˆ) 3. Return ( fˆ, βˆ)

4 3.2 Unsuervised Segmentation with Semi-Suervised Initialization In this second method, we have also adoted iterative labeling-estimation as in Algorithm-1, but now the class arameters are also iteratively estimated. The initialization of the class arameters is erformed in a semi-automatic way: the user rovides a region of ixels corresonding to one (for examle the most frequent) of the classes (class1). This region is then used to estimate the ML (Maximum Likelihood) arameters of the class1 distribution. In a second ste, ixels are clustered in two sets, class1 and not-class1, by alying a simle threshold to the estimated distribution. Then, the arameters of the remaining classes are initialized by alying an EM mixture estimation rocedure to the ixels clustered in the set notclass1. Algorithm-2: 1. Start with an arbitrary arameter βˆ=β 0 and arbitrary initial labeling f 0 2. Provide initial class arameter estimations θˆ=θ 0 3. Provide initial fˆ = α_exansion( f 0,β 0, θ 0 ) 4. While ˆ β δ or nriterations < ItMaxNr do 4.1 Find θˆ= ML_Estimation( fˆ) 4.2 Find fˆ= α_exansion( f 0, βˆ,θˆ) 4.3 Find βˆ=ls_estimation( fˆ,θˆ)or CodingMethod( fˆ,θˆ) 5. Return ( fˆ, βˆ,θˆ) 4 Results: Simulated and Real Images This section resents results for simulated and for real SAR images. In the first case, different test scenarios are rovided, corresonding to Gaussian and Gamma data terms. Although simulations have been restricted to one Gamma mode er class, the develoed rocedure also works with Gamma mixtures as develoed in [1]. 4.1 Simulated Images Three different test scenarios have been adoted: Scenario 1: the simulated image contains three classes generated by an MLL Markov- Gibs distribution corruted with Gaussian noise. Segmentation is erformed alying Algorithm-1, described in Section 3.1. The arameter estimation is erformed using the LS method and the class arameters are known (same values as used for the simulation). The test is erformed for five different images, corresonding to an increasing difficulty grade of segmentation. Each test is run three times and the mean

5 values of the overall accuracies (OA) corresonding the ercentage of correct label are comuted. For comarison, the estimation of β is erformed in a suervised way, alying the LS method to the ground-truth image and running the α-exansion algorithm once with the estimated β. Scenario 2: here a simulated image of three classes corruted by Gamma noise is used. The ground-truth is hand-made and contains structures resembling those that may be found in oil-sill scenarios. The same algorithm as in Scenario 1 is used, both with the LS and the CD estimation methods. The unsuervised segmentation is comared with the results given by the best achievable segmentation using α- exansion, corresonding to tuning the β arameter manually. Scenario 3: here, for the same simulated image used in scenario 1, the class arameters estimation is also incororated in the algorithm, by alying Algorithm- 2, described in Section 3.2. Initial class arameters estimation is rovided by erforming a one-class suervised estimation based on one-class clustering. Scenario 1: To assess the segmentation erformance, we comare the OA with that obtained without the MRF rior, i.e., β=0. For Gaussian classes with equal standard deviation σ, means equally D-saced, we have c 1 D / 2 OA ( β = 0) = 1 erfc 100 2, (9) c σ where erfc(.) is the comlementary error function and c is the number of classes. Figure 1 shows the OA s obtained by segmenting the image using Algorithm-1 (legend: unsuervised) and using the suervised estimated beta value (legend: suervised) against the values rovided by (9). Fig. 1. On the left: overall accuracies against OA MAP (β=0). On the right: uer image is the MLL ground-truth with 3 classes; lower image are the simulated intensity values. Scenario 2: In Figure 2 and 3 as in Scenario 1 but the OA(β=0) is now estimated by running the algorithm with β=0, since there is no close exression for it.

6 Fig. 2. Uer image: OA s obtained by unsuervised segmentation using LS and best achievable results with manually tuned β. Lower image: LS estimated β and best β. Fig. 3. Overall accuracies obtained by unsuervised segmentation using CD and best achievable results with manually tuned α-exansion. Figure 2 shows the results obtained with the LS method and Figure 3 the results obtained with the CD method. Figure 4 dislays an examle of simulated image and corresonding segmentation results. Scenario 3: By alying Algorithm-2 to an MLL image like the one adoted in Scenario 1, for a OA(β=0) of 85.9% given by exression (9), the achieved OA value is 94.5% using LS estimation. The Best achievable OA is 99.1%.

7 . (a) (b) (c) (d) Fig. 4. (a) Density functions used to generate the simulated image with suerimosed histogram of generated data set. (b) Ground-truth (c) Simulated image (d) Segmentation result using Algorithm-1 : unsuervised LS estimated β = , OA = 95.3%. The best achievable OA for this image was determined to be 95.4%. The OA for β = 0 is 83.2%. 4.2 Real Images The Algorithm-1 has been alied to a real ERS-1 SAR image fragment. The scene (frame 2367, orbit 17211) containing the fragment has been acquired on 30 October 1994, and covers several oil latforms in the Norwegian and British sector of the North Sea. The image has been radiometric calibrated and corrected for the incidence angle effect. We have assigned a class to oil, a class to water and a class to latform and learned the class arameters using the suervised method described in [1]. Figure 6 dislays the obtained results after alying Algorithm-1. (a) (b) (c) Fig. 6. (a) ERS image: intensity values (b) Segmentation with LS (c) Segmentation with CD.

8 6 Conclusions The first results of alying the roosed methodology to simulated images with Gaussian and Gamma data models and to real ERS SAR data are romising. With Algorithm-1 higher OA accuracies have been achieved. The analysis of the resulting OA lots for Gamma data exhibits a maximum around circa OA no rior = 85%. This value corresonds to a value for the estimated β equal to the best β. At this oint the add-on value rovided by introducing a rior into the segmentation starts to decrease. Regarding Algorithm-2, the adoted methodology seems to be adequate but needs further assessment. In the examle given in Scenario 3, the inclusion of the arameter estimation into the segmentation rocedure only reduces the OA from 97,3% to 94,5%. By alying Algorithm-1 to a real ERS image, we have been able to successful segment a latform of reduced size, the water and the oil. Hereby, the CD estimation method seems to rovide a better segmentation than the LS method, contrarily to what haened for simulated images, where the LS method rovided slightly better results. These are reliminary results and more tests, with more trials er test, are required to fully determine the accuracy of the roosed methods.. Acknowledgments. The authors acknowledge Vladimir Kolmogorov for the maxfow/min-cut C++ code. References 1. S. Pelizzari, José M. B. Dias: Bayesian Adative Oil Sill Segmentation of SAR Images via Grah Cuts. Proceedings of the SeaSAR 2006 (2006), Frascati, Italy. 2. Y. Boykov, O. Veksler and R. Zabih: Fast Aroximate Energy Minimization via Grah Cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, No.11 (2001). 3. A. Montali, G. Giacinto et al: Suervised Pattern Classification Techniques for Oil Sill Classification in SAR Images: Preliminary Results, Proceedings of the SeaSAR 2006 (2006). 4. F. Galland: Synthetic Aerture Radar oil sill segmentation by stochastic comlexity minimization. IEEE Geoscience and Remote Sensing Letters, Vol. 1, issue 4 (2004). 5. V. Kolmogorov and R. Zabih: What Energy Functions Can Be Minimized via Grah Cuts? IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No.2, (2004). 6. S.Z.Li: Markov Random Field Modeling. Comuter Vision, Comuter Science Workbench, Sringer (1995).