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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Segmentation of high noise imagery like Synthetic Aperture Radar (SAR) images is still one of the most challenging tasks in image processing. While level set, a novel approach based on the analysis of the motion of an interface, can be used to address this challenge, the cell-based iterations may make the process of image segmentation remarkably slow, especially for large-size images. For this reason fast level set algorithms such as narrow band and fast marching have been attempted. Built upon these, this paper presents an improved fast level set method for SAR ocean image segmentation. This competent method is dependent on both the intensity driven speed and curvature flow that result in a stable and smooth boundary. Notably, it is optimized to track moving interfaces for keeping up with the point-wise boundary propagation using a single list and a method of fast up-wind scheme iteration. The list facilitates efficient insertion and deletion of pixels on the propagation front. Meanwhile, the local up-wind scheme is used to update the motion of the curvature front instead of solving partial differential equations. Experiments have been carried out on extraction of surface slick features from ERS-2 SAR images to substantiate the efficacy of the proposed fast level set method.

From the time of its inception, Synthetic Aperture Radar (SAR) imaging systems have provided a remote sensing resource complementary to optical and thermal-infrared sensors. SAR Imagery has been applied in a gamut of areas including ecological observation, surface monitoring, target detection, and mapping. Primary among the advantages of SAR imaging are day-night and all-weather operation, wide area coverage and sensor height-independent image resolution. These functionalities have also led to an escalating interest in the last decade towards the usage of SAR imagery for ocean environment monitoring.

Nevertheless, the multiplicative speckle noise caused by microwave illumination degrades the quality of the SAR imagery. Speckle impedes visual interpretation of SAR images and may lead to interclass confusion. This is particularly so in the quick detection of oil slicks on the sea surface. The low backscatter cross section of the surface of oil spillages causes Bragg wave dampening effects on the sea. As a result of this an oil spill comes out on the image as a dark slick or dark spot, whereas the surrounding water appears bright. Consequently, oil slicks in SAR images are characterized by a high noise and low contrast, disturbing their extraction and analysis.

A variety of methods have been developed to reduce speckles. For example, geometric filters such as those of Frost [

Level set was proposed by Osher and Sethian [

In the traditional level set technique, instead of tracking the points on the interface itself, the interface is embedded as the zero level set propagates by iterations. For this reason the standard level set algorithm could possibly be rather slow for real-time or near real-time image processing. Algorithms such as the narrow-band algorithm [

Based upon our previous work using a level set for image segmentation [

Level set is an efficient numerical technique for interface propagation. A brief introduction of this method is given here. The detailed explanation can be found in Sethian (1999)[

In the level set method, a scalar Lipschitz function, ^{n+1} space surface, where x ∈ R^{n+1}, and t = time t (

The essential idea of the level set is to represent the moving front ∂

Moreover, the level set is supposed to be topology free, since different topologies of the zero level set do not imply the different topologies of a level set

In accordance with the propagation of the front, the first order partial differential equation (PDE) of the level set is represented as:

The speed term in which the front propagates is defined by the function _{prop}_{curv}_{adv}_{adv}_{prop}_{curv}_{prop}_{curv}

As the level set method is formulated from numerical equations for interface propagation, the iteration periods of the standard algorithm for boundary expansion are invariably longer. Taking into consideration a single pixel and its neighboring pixels, one solution is obtained by updating the value of each pixel till the final boundary is reached. For such a solution, O(^{2}^{3}

Level set computations are usually carried out using the narrow-band algorithm as described by Malladi

A one-dimensional array is employed to keep track of the points in the narrow band. Assuming the number of points in the front to be ^{3}

In a situation wherein the speed function depends only on the interface position, the speed function _{curv}_{curv}

A min-heap is a complete binary tree in which the value at any given node is less than or equal to the value of its child nodes. In general, finding the smallest element in the min-heap requires O(^{2}logN

On the whole, the fast marching method is more efficient than the narrow-band algorithm; however, it does not take into account the effect of image intensity, which attracts the interface inward or outward. Moreover, on above methods, the PDE is solved with a tube in the neighborhood of the zero level set, and at every iteration the level set function should be reinitialized and pixels in the tube be updated dynamically by solving a PDE for a fixed number of steps. This might well result in a tendency to ‘leakage’. Thus, in spite of the advances made by the aforementioned level set methods, there still exists room for more improvement.

In image processing, the accuracy is usually limited by pixel size, especially for the segmentation in a noisy image, the achieved boundary is expected to be smooth and quick. The algorithm proposed herein, in addition to incorporating the advantages of the aforementioned methods, also functions more efficiently. Firstly, considering high noise in the SAR ocean image, a level set formulation is ingrained with the intensity and curvature models to construct extension velocity, in order to handle topological changes automatically. Subsequently, refer to narrow-band and fast marching methods, the tube is simplified to four neighborhood pixels just near the zero level set, and a list is used to replace min-heap in order to accelerate. Finally, the upwind partial differential equation approximation is used to optimize reinitialization and propagate the boundary with available information to a stable boundary.

In a SAR image, the intensity difference is regarded as the primary factor influencing the front propagation of an oil slick edge. Therefore, _{prop}_{lower}_{high}_{lower}_{high}

Besides intensity, curvature is another important factor in determining the propagation. The mean curvature of the front at any point can be obtained from the divergence of the unit normal vector to the front, i.e.:

An up-wind partial differential scheme is employed to obtain the stability of a boundary. This scheme is based on a one-sided derivative that looks in the up-wind direction of the moving wave front, thereby avoiding the over-shooting associated with finite forward differences.

To compute the derivatives for the level set, three difference operators, i.e. the forward difference D^{+}, backward difference D^{-}, and central difference, are used with the eight neighboring pixels. For instance, the differences in the x direction on the SAR image with spacing h at time t, i.e. u(x, y, t), are defined by first and second order terms as:
_{x}

In a similar manner, the forward, backward or centered Taylor series expansions in the x direction can be derived:

The curvature is computed using the above derivatives and the difference of the normals method introduced by Whitaker and Xue (2001)[^{+} and n^{-}, are then computed by:

The components of divergence are then computed as:

Finally, the curvature model is formulated as:

Using this equation, the direction and velocity of the speed dependent on the curvature can be easily derived. The propagating front of an initial level set to the object boundary starts from inside the selected region, and grows outward. This outward growth is influenced by the image intensity and curvature. The front propagates till the speed function

The initial estimation of

The implementation of the proposed level set method has been done through the extraction of the surface slick boundaries. For improving computation efficiency, a list is used to record the inside or upwind side neighboring pixels, and a 2-dimenation array for storing the level set function

As shown in

A single seed (or multiple seeds) of surface slick signatures on the image is (or are) selected and used as the starting interface (i.e. the zero level sets). The grayscale upper and lower limits (i.e. _{lower}_{high}

The pixels in the image are divided into two sets: the upwind set wherein the pixels are in the interface with

Subsequently, the front pixel in the list is popped and tagged as the upwind known set. Four neighboring pixels are selected and their speed functions F are calculated. Then, update

Fast update level set function. If a pixel is located upwind neighboring to curvature and

Lastly, all pixels in the list will be subjected to computation until none of it remains in the list.

The above algorithm is further illustrated by an example in

The stable segmentation boundary, which distinguishes the surface slick from different background such as sea surface and land, serves as the line between the upwind set and downwind set. While selecting a known surface slick pixel as an inner seed in the oil slick, only the interface front expanding outwards is considered. Hence if an outer seed (i.e. non surface slick pixel) is selected, the interface front will expand inwards.

The list is a simple but efficient data structure. In the worst scenario, the operation for push back, pop front, inserting, or deleting element take O(

To confirm the efficiency gain of the proposed level set method as shown in _{lower}_{high}

In the first experiment (_{lower}_{high}_{prop}_{curv}

In the second experiment with a low contrast SAR image (_{lower}_{high}_{prop}_{curv}

The result for the fast marching method, which only depends on the curvature flow, is displayed in

To test the efficiency of the proposed method, it was compared with the ordinary level set and fast marching methods in terms of mean processing time for oil slick patches (

As recorded in the calculation, with the first SAR image, the extracted oil slick amounts to 79,796 pixels, whereas in the second image, the extracted oil slick amounts to 87,116 pixels. Apparently, the ordinary level set method lags behind the fast marching and the proposed methods because it has to iterate calculations on the entire image. Although the fast marching and the proposed fast level set methods deal with the pixels close to the slick propagation boundary in a similar way, the proposed method is more efficient than the fast marching method in both the images (

For accuracy assessment, we compared the segmented results using the proposed, seed filling, and fast marching methods with the boundary interpreted manually, and the results for the images in

In this paper a more efficient level set method for the feature extraction of oil slicks in SAR images has been proposed. It is based on the theory of level set flow propagation, which uses the intensity gradient as the front advancing impetus. The segmentation of oil slicks in oceanic SAR images has been carried out to verify the effectiveness of the proposed method and the results showed that it can arrive at more smooth and ideal boundaries than other level set segmentation methods that only depend on the curvature flow.

The algorithm developed in this paper not only relies on the image intensity and curvature speed functions, but also employs a list to accelerate the interface front processing. The experimental results show that the proposed method is more efficient than other level set methods, especially for large-size image segmentation. This enables the proposed method to be used in near real-time image processing. Furthermore, the high noise can be removed simultaneously and the accuracy of the boundary can be maintained. It is expected that the proposed method epitomizes a prototype for comprehensive processing of high noise and low contrast remote sensing images.

This research was funded by the Ministry of Science and Technology of PRC under Contract No. 2006AA12Z116 and the State Key Laboratory of Remote Sensing Science, IRSA, CAS. Their Support is gratefully acknowledged.

Illustration of level sets.

Narrow-band of level set.

SAR image segmentation using the proposed fast level set method

Example of processing stages by the proposed fast level set method.

The proposed fast level set method with single seed for initialization of level sets.

The proposed fast level set method with multiple seeds for initialization of level sets.

Comparison of the proposed method with the ordinary level set and fast marching methods

Accuracy assessment between the proposed, seeding filling, and fast marching methods

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Experiment |
Area matching error | 4.1% | 4.9% | 9.1% |

Perimeter matching error | 22.5% | 43.0% | 24.7% | |

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Experiment |
Area matching error | 1.9% | 3.1% | 6.1% |

Perimeter matching error | 19.3% | 34.3% | 23.9% |