Общие вопросы неразрушающего контроля
УДК 620.179
EXTRACTION OF WELD DEFECTS DIMENSION FROM RADIOGRAPHIC IMAGES USING THE LEVEL SET DEGMENTATION WITHOUT RE-INITIALIZATION
Mohammed Halimi1, Nam Ramou2 Image and Signal Processing Laboratory Route Dely Brahim BP, 64, Cheraga, Algiers, Algeria E-mail: Halimi_md@yahoo.fr; 2naimramou@gmail.com
Abstract. Radiographic images segmentation is the major interest for the weld defect diagnosis and monitoring in the field of industry. In this work we present a method that takes ownership of local segmentation geodesic active contours. The goal of the method presented in this paper is to automate the process of extracting dimension of weld defects from radiographic images using level set segmentation. The information would be used in the area of nondestructive testing (NDT). This method is found to be effective and robust.
Key words: radiographic method, weld inspection, defect dimensions, signal processing.
ПОВЫШЕНИЕ ВЫЯВЛЯЕМОСТИ ТРЕЩИН ПРИ ДЕФЕКТОСКОПИИ МЕТОДОМ ТРЕХМЕРНОЙ ТОМОГРАФИИ
М. Халими, Н. Рамоу Лаборатория обработки сигналов и изображений Роут Дели Брахим БП, 64, Черага, г. Алжир, Алжир
Сегментация радиографических изображений представляет собой главный интерес для диагностики дефектов сварки и мониторинга в промышленности. В работе показан метод, относящийся к локальной сегментации геодезически активных контуров, цель которого — автоматизировать процесс выделения размера дефектов сварки по радиографическому изображению с использованием сегментации множества уровней. Информация может быть использована в области неразрушающего контроля. Этот метод является эффективным и надежным.
Ключевые слова: радиографические методы, контроль сварных швов, размеры дефектов, обработка сигналов.
I INTRODUCTION
Methods of nondestructive testing (NDT) have been the subject of much research and developments during the last thirty years. The methods of investigation radiology radiation (mainly X-ray), have significantly improved their performance. A chain of X-ray inspection includes:
A source of X-rays.
A mechanical support for the object which can be rotated or translation if necessary.
A detector, which is associated with an imaging system (display screen) to get a two dimensional image of the object.
Radiographic inspection is widely used for weld inspection to provide image information about weld defect. Unfortunately these information are extremely difficult to be used in a quantitatively and objectively way. Consequently research has to offer new methods of image segmentation in order to increase the quality of information and to speed up the diagnosis. Several mathematical models have been developed to achieve image segmentation [1]. The last promising models to solve the image segmentation problem are based on level set and related to partial differential equations (PDE) based methods [2]. We have used the level set method without re-initialization in order to speed up the evolutionary process.
noBtimeHHe BLiflBJiaeMOCTH Tpern^H.
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II. EXTRACTING THE WELD DEFECTS DIMENSION
The analysis of image radiographic should allow extracting information relating to defects [3]. In our study, the regions darker than their neighborhood can poten tially be a default, ie voids or gas cavities. Image segmentation allows us to identify these regions. A step of extracting relevant features allows us to classify them according to the NDT criteria. Here we are talking about the surface and perimeter which are calculated from radiographic image segmentation as follows:
Surface: number of pixels in weld defect sur face (N) multiplied by dimension factor of a pixel a (mm2). So that area A = N x a.
Perimeter: number of pixels in weld defect contour (M) multiplied by dimension factor of pixel r (mm). So that length L = M x r.
In the next section we present the extraction of the number N and M using level set segmentation.
III. WELD DEFECT SEGMENTATION USING LEVEL SET WITHOUT RE-INITIALIZATION
Using image segmentation, we want to calculate the area and perimeter of weld defect. To do this, we have applied the level set method [4] to the radiographic image segmentation and used the level set function to obtain the characteristics of the perimeter and surface. From the practical point of view, the implementation of the traditional level set equation [5] can be quite complicated, expensive, because of the operation of a reinitialization and also because of the numerical schemes used to ensure stability of the solution.
Consequently, the research community in the field of image processing moves towards the reduction of time and cost of calculation by offering new models which are stable and fast in execution time as the one proposed by Li and al. [6] which is a level set method without re-initialization. The evolution PDE of the level set function can be derived directly from the problem of minimizing a certain energy functional defined on the level set function. This type of variational method is known as variational level set methods [7]. The variational level set methods are more convenient for incorporating additional information. As stated before, re-initialization is a necessary step in numerical implementation for traditional level set methods. Using variational level set method, the re-initialization phase can be embedded in the equation and the re-initialization step can be removed.
We have chosen the variational level set method modelwhere proposed by Li and al. [6] to be applied in image segmentation. They have defined the following functional
8(<fr) = + 8», (1)
where:
E(§) = J QP ( ) dQ is the penalty term;
8» = AL^) + vAg(^):
Lg(^) = J QW 1^1 dQ is the length term;
Ag(^) = J QgH dQ is the area term;
1
g =-x— (p = 1 or 2) is the edge
1+ II V I ||p
indicator function.
The equation 1 consists in:
AN INTERNAL ENERGY TERM
This term avoids the re-initialization of the level set function and its deleterious numerical errors. Minimizing the functional E will follow the following procedures:
^(MNH. (2)
The function P can take two values:
Single-well Potential for Distance Regularization
1 2
P(s) = 2 (s -1)2 (3)
Double-well Potential for Distance Regularization
The energy functional was proposed as a penalty term in the preliminary work [6] in an at tempt to maintain the signed distance property in the entire domain. However, the derived level set evolution for energy minimization has an undesirable side effect on the level set function in some circumstances. To avoid this side effect, Li and al. [8] propose in recent paper a new Potential function for the distance regularization term:
P(s) =
—(l — cos (2%s)), if s < 1 (2*) (4)
2(s-l)2, if s * 1
which is aimed to maintain the signed distance property = 1 only in a vicinity of the zero level set, while keeping the level set as a constant, with | V^| = 0, at locations far away from the zero level set.
AN EXTERNAL ENERGY TERM ej^)
This term drives the motion of the zero level set towards the object boundaries e» = + vAg(^),
where
Lg(® = Jqg5(<fr)|V<fr| dQ
and
Agfo) = JQgH (-<fr)dQ .
THE FINAL MODEL
In the end, the energy functional e(^) is then approximated by
e(<fr) = |JqP (|V<fr|)dX + ^Jq g8(<fr)|V<fr| dX + vJQ gH (-<fr) dX. (5)
The steepest descent process for minimizing this functional is the following gradient flow
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a< = - as. (6)
et e<
1 2
For the potential P(s) = — (s -1) we obtain
Ht
=i
A< - div
X5 (<) div
r|V<|
-vg 8(<).
(7)
In the case of the Double-well Potential defined in 4, we have
^ = -|div ( dv<|)v<) and the PDE can be expressed as
-|div (dp (V<|) V<) + X5 (<) div
et
r|v<|
vg5 (<),
(8)
P'(s )
where d is a function defined by d (s) =A ——; 5 is a Dirac function; H is the
p p s
Heaviside function; | = 0.04 is a parameter controlling the effect of penalizing the
deviation of < from a signed distance function; X = 5 and v = 1.5 are two constants that weight each term.This PDE can be solved by applying central difference scheme for spatial partial derivatives and forward difference scheme for temporal partial derivatives. The initialization is not necessarily a signed distance function, but can be arbitrary functions.
Initial level set function
Fig. 1. Image segmentation using level set method withoutout re-initialisation.
100 150 200 250
50 100 150 200 250 300 350
50 100 150 200
Single-well Potential, 335 iterations
50 100 150 200 250
Double-well Potential, 335 iterations
50 100 150 200 250 300 350
50 100 150 200 250 300 350
50
Fig. 1 shows the results of applying the level set without re-initialization with Single and Double-well Potential for Distance Regularization. As comments we can say: First, that we have the possibility to use a wider time step of about 4 to 6 without affecting the stability of the algorithm. Second, we have obtained less computing time because of the elimination of re-initialization step, and finally
the use of double well potential can avoid the side effect that occurs in the case of single well potential.
Initial levet set function
Single-well Potential, 335 iterations
Double-well Potential, 335 iterations
Fig. 2. 3D-representation image segmentation using level set method without re-initialisation.
From fig. 2 it is clear that one can calculate the surface of the object using a simple threshold, and we obtain an estimate of surface which is the number of pixels above this threshold (M).
To calculate the perimeter of our object, we use the gradient norm of the level set function with a simple threshold to calculate the number (N) of edge pixels. From fig. 3 we note that we have a better estimation of the level set function in the case of double well than the single well case because of side effect.
Single-well Potential Double-well Potential
Fig. 3. Gradient norm of image segmentation using level set method without re-initialisation.
IV. EXPERIMENTS
In this section we a
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