Proc. of World Cong. on Multimedia and Computer Science
Weld Radiographic Images Segmentation and Restoration Via Local Binary Fitting Energy and Binary Level Yamina Boutiche Welding and NDT Research Center CSC,Image and Signal Processing Laboratory BP 64 Chéraga, Algiers, ALGERIA.
[email protected]
Abstract: The present paper is devoted to discuss a region-based active contour model formulated via level set method. Region-based models have more advantages over edgebased models, especially by introducing local statistical image intensities instead of the global statistical image intensities. This propriety makes those models well adapted to segment weld radiographic images in the aim to get image with less complexity and to extract weld defects in order to use them in NDT (Non Destructive Testing). Keywords: Segmentation, Restoration, Weld radiographic images, region-based active contours, LBF model, Level Set.
I. INTRODUCTION Nowadaysthe visual information has being introduced in very large applications, thank to that image processing possesses more and more a crucial importance. The first and the primordial task in image analysis is the segmentation which is defined as follows: segmentation is a partition of the image into subsets , called regions, so no region is empty, the intersection between two regions is empty, and all regions cover the whole image. A region is a set of connected pixels having common properties that distinguish them from pixels of neighboring regions; those ones are separated by contours. The most difficulty in segmenting image is the non uniform of intensity distribution, so there isn't a model that can segment any kind of image. This last decade, much functional have been proposed to achieve good segmentation results and expanded the image modalities (x-ray, ultrasonic). We distinguish, essentially, two classes of active contour (deformable models): Edge-based models [1][2][3] [4] [5] [6] and Region-based models [7] [8][9] [10] [11] [12] [13]. We focus on methods which are based on region due to their advantages over the once based on contour. They do not use image gradient, they are less sensitive to noise, they can successfully segment objects with weak edges or without edge, interior contours can be automatically detected, and they are less sensitive to initial contour position. In this context, the older and famous functional is Mumford-Shah model [14], this one had limit application due to its high complexity. Later some functionals had been proposed. They are known as weak formulation of Mumford-Shah, because they approximate the result image u by simple functions. We cite the one called piecewise constant approximation, proposed by Chan and Vese [7], where u is approximate by a set of constants. This model has known great success in segmenting homogenous images especially when it was improved by introducing multiphase level set [11]. Even though, this model fails within inhomogeneous DOI: 02.WCMCS.2013.1.14 © Association of Computer Electronics and Electrical Engineers, 2013
intensity distribution which is the case for large real images. To overcome this limitations, the same authors proposed piecewise smooth approximation, here the result image u is approximated by set of function of class. More recently, functionals based on computing local statistic image intensity are proposed [15][16] [17] [18] [19] [20]. The rest of the paper is structured as follows: section 2 is devoted to Region-Based segmentation background in which we display the most famous models based on statistical image intensity. Section 3 titled the LBF model formulated via Level set function detailed the model on which we are interested. discussions on some influencing parameters are presented on section 4. The paper is closed by conclusion and future vision on weld radiographic image segmentation. II. REGION-BASED SEGMENTATION BACKGROUND A. Mumford-Shah model The most old and popular model in image segmentation is the one proposed by Mumford and Shah [14]. they have proposed the following energy: (1) E (u, C) = (u − u ) dx + µ |∇u| dx + ν|C| Where µ > 0, ν > 0 are constants to penalize the terms, u is the optimal approximation of the original image u , Ω is the image domain. In practice, it is so difficult to solve equation (1) due to two serious problems: the different dimensions of u and C, and the non convexity of E (u, C) which can provide multiple local minima. B. Piecewise Constant approximation PC This model was proposed by Chan and Vese [7] to overcome the difficulties in solving equation (1). The first PC model is based on simplifying Mumford-Shah functional by approximating the image u to set of constants (tow constants). The functional to be minimized is given by equation (2): (2) E (c , c , C) = λ ∫ (u − c ) dx + λ ∫ ( ) (u − c ) dx + v|C| ( ) Where λ ,λ > 0; c and c are the average image intensity inside and outside curve, respectively. The model has great success due to its multiple advantages such as its less sensitivity to initial condition, its capacity to extract blurred boundaries and its ability to segment noise images. Nevertheless those successful results are getting within image with homogenous intensity distribution, but the model fails when the image intensities are inhomogeneous, this is explained by the fact that PC model compute the global average intensity inside and outside curve that can be far different from the original image. The authors have improved their model by introducing multiphase level set [11] on which u is approximate by more than two constants. Even though efforts the problem with inhomogeneous images persists. C. Piecewise Smooth approximation PS In the aim to treat largest modalities of images, Chan and Vese proposed functional that approximate u by two piecewise smooth functions u and u [11]. F(u , u , Φ) =
|u − u | H (Φ)dx
+
|u − u | 1 − H (Φ) dx + µ
+µ
|∇u | 1 − H (Φ) dxdy + v
|∇u | H (Φ)dx
(3)
|∇H (Φ)|dx
Where u and u are two functions of C class that approximate smoothly the inside and outside of C. Φ is the level set function, H (Φ) is the regularized version of Heaviside function. The PS model has limited applications in practice, due to its high algorithm complexity [21] : we have to solve in each iteration two partial differential equations to get u and u which is very expensive in time cost. Also, u and u must be extended to the whole image domain, which is difficult to implement and increases the computational cost. Another PDE is necessary to update the level set function. Further an initialization step is suggested in some cases. 88
D. Local Binary Fitting model LBF More recently, Based region segmentation has been efficiently improved by introducing LBF model. C. Li and al. [17] [18] proposed a model based on approximating locally the image intensities inside and outside curve. The energy functional is defined as follows: E (C, f , f ) = λ ∫ ( ) K (x − y)|u (y) − f (x)| dy (4) +λ ∫ ( ) K (x − y)|u (y) − f (x)| dx Where σ, λ ,λ are positive constants, K is Gaussian kernel which is a weighting function with a localization property. f ( ) and f ( ) are the two numbers that fit image intensities near the center point x. As it is known the Gaussian kernel K (x − y) takes large values at the points y near the center point x, and radically decreases to 0 as y goes away from x(K (x − y) → 0 when |x − y| → ∞). However the value of f (x) and f (x) for each point x are dominated by the image intensities near the center point x. E. Local Image Fitting model (LIF) The model was proposed by Zhang and al. [21], it is also based on local image information. The energy functional is the difference between the fitted image u and the original image, so the formulation is given by: ( )= ∫ | =(
With Where
,
( )+
( )−
(5)
|
(1 − ( )))
the two fitting functions defined as =
∈
∈
( )
