·Home ·Table of Contents ·Methods and Instrumentation  3D System for Non Destructive Testing Analysis
F. Bettayeb,
Scientific Research Center on Welding And Non Destructive Testing,
C.S.C, Route de Dely Brahim, BP: 64, Chéraga, Algiers.
Tel/fax: (2132) 361850. Email: bettayeb@excite.com; Email: f_bettayeb@email.com
A. Bouzid, A. Bechkett
University of Science and Technology USTHB, El Alia BP:32, Algiers.
Contact

Abstract
In the field of weld inspection, it is known that all the different types of defects cannot be detected by only one Ndt method. Ultrasonics and radiography are in most case complementary and are often used together on the same specimen.
In this paper and within the philosophy of complementarity between ultrasonic and radiographic techniques, we try to build an image of the ultrasonic controlled component, by an image processing method. And, In order to carry out this modelling a set of IIS reference radiograms were digitised, and stored in Data banks.
There are some theoretical developments of methods allowing solving 3Dreconstruction problem. The algebraic reconstruction method, exact solutions, image processing methods are the frequently used techniques. Our solution is based on image processing models, and the software has to combine data analysis feature of established 2D packages with advanced facilities of data rotation, projection, slicing and 3D sizing tools.
During the reconstruction process, the defect shape is correctly positioned within the welding geometry, and its map is generated in 2D and 3D image making, according to the extracted
profile of a similar defect from radiograms.
Key words:
CAD, image transformation, shape detection, 3D vision, xray image, radiograms, object oriented model.
1. Introduction
Nowadays, computer vision is a powerful tool in simulation problems and in real time processing. Edge detection, boundary representation and shape classification are basic problems in computer visualisation. As well, in industrial environments, the computer imaging tools will be very helpful for the testing procedures, by appending more extended imaging features to the traditional ones or producing new ones. Until the advent of ultrasonic inspection, radiography was the only available method for finding defects into welds, the diagnosis is based on radiogram image interpretation without providing any measurements of the flaw. However, the ultrasonic Ndt of materials produces a more detailed characterisation about sizing and position of the defect, but the testing results is only signal interpretation basis, without any visual setting.
In the aim to improve the ultrasonic testing by imaging capabilities, we attempt in this work to produce a visual environment for the defect shape inside the joint geometry of the tested material. The approach is based on 2D defect geometry extracted from radiograms, since the general form of the flaws is well known and is regular i.e. porosities are easily distinguished from stag inclusions or lack of fusion or from a crack for example.
Thus the obtained flaw matrix is submitted to geometric transformations from zooming and orientation, and then projected in the plan of the joint geometry. Here the 2D image will be submitted to other conversions in 3D viewing, by simulating the image projection and rotation transforms in an (x,y,z) plan.
2. Image processing overview
Designing interfaces for scientific visualisation and 3D illustration, presents many challenges. However the geometric relation between 3D object and their views is a key component for various applications in computer vision and animation[1]. And representation is always an important issue in computer vision. Once a digital image is given to the computer , the commonly used methods for its study are a filtering, a segmentation with edge and region detection, and specific processing. Many techniques dealing with digital image processing and edge detection have been explored, and each one have its advantages and disadvantages according to its context of application, among them the algebraic reconstruction method, exact solutions and image processing methods are the frequently used techniques[1]. In this paper we have worked with image processing techniques combined with computer aided design 'CAD' models in an object oriented approach.
3. Edge detection
The objective is to obtain the commonly known drawing section of a welding flaw. This can be procured on radiograms, which provide a 2D defect indiscriminate sizing area. The purpose is then to classify and record the defects shape recovered from radiograms image processing. So, after a radiograms scanning operation, a digital xray images are acquired and stored into a database. At this time, on each image some transformations are performed in order to obtain a pixel matrix representing the defect contour, which will be stored for further processing. How this will be obtained ?
Well, by definition a contour represents the grey levels discontinuities from the image. The contour is determined when an abrupt variation of the grey levels of consecutive pixels is detected [2]. Its principle is summarised in 2 basic operations: a filtering of the image from disturbing noise and an edge detection by the use of a differential operator.
Fig 1: " Contour image processing" 
Fig 2: "Digital xray images and defects contour" 
After a selection from radiogram of the defect area, we obtain a new image of the defect region on which the contour assessment is performed. Our approach is based on median filtering since it has given a clear image, and the accentuated gradient operator which has performed a suitable outlined flaw edge. This processing has been Abode PhotoShop software basis and the resulting image is stored in a database of contours.
Let us describe the gradient operator.
The gradient in a point of a function f(x,y), is a vector defined by the following operator[3]:
u & v are unit vectors of x & y
 (1) 
The modulus is then:
 (2) 
and the orientation is:
 (3) 
Given an image L(i,j), its vector gradient is:
 (4) 
With the ameliorate gradient, the gradient image is obtained with the computation of 4 gradients for each 4*4 window, the ameliorate gradient value is obtained by the expression representing the geometric average of A,B,C,D [4]:
 (5) 
with
 is a matrix of 4*4 windowing. 
4. 3D transforms.
The geometric relation between 3D objects and their views is a key component for various applications in computer vision and animation. Lets consider object space to be 3D projective space P^{3} , an image space to be 2D projective space P^{2}, and a view V of the space P^{2} (VÌ
P^{2}). An object is modelled by a set of points. If (x,y) are the image coordinates, then p =[x,y,1] denotes the homogenous coordinates of the image plan, and p^{t} is a point in the projective coordinate representation.
Basically, we need a unique representation scheme that contains no singularity and induces a simple relation ship between the 3D model and its 2D projection. The simplest and most popular way to represent a 3D line is by specifying a 3D point on the line and the direction of that line, therefore a line will be represented by 6 parameters.
Roberts approach
This approach says [5] that a 3D line is represented by the operations needed to bring the line in place with the z axis. To do this 2 rotations about the x and y axis are performed to bring the line parallel to the z axis. Then another rotation about z axis is applied to intersect the line with the x axis. Finally, the line is translated to the origin along the x axis. Hence, a line can be specified by 4 parameters: 3 angles (yaw , pitch, roll) and one signed distance. This method can represent all lines, and each line has one and only one representation if the values of the angles are bounded appropriately.
The resolution scheme
Our resolution is a computer aided design model basis (CAD), which provides a mathematical description of the object shape and formulations of the geometric transforms about zooming, rotating, slicing, projection etc., and an implicit encoding of the object's inter surface relation ships. This is obtained with the an implementation on object oriented computer environment like the Borland Builder C++. For the 3D transforms our solution is a generalised Roberts algorithm, since the composed 'image' is represented by a set of pixels, like the image 'line' in the Roberts method summarised below.
Once the 2D matrix contour is obtained from the extracted profile of the defect (the contour matrix is performed by a computation selection of the pixels highest grey level), a zooming of the image in appropriate coordinates and its projection in the designed view are accomplished. Before that, from a database of welding joints, a selection of the adopted geometry has been done, and the figure is projected in the above view with scaling calculations according to the tested piece measurement and the flaw dimensions within. Then the z axis is related to the depth of the piece with right sizing.
At this time the generalised Roberts algorithm is performed on the new 3D object image composed by the superposition of the object welding joint image and the defect contour image. Since the application is a mouse based system, the animation is then performed on several views about x axis, y axis, and z axis.
6. conclusion
Ultrasonic Ndt is playing an increasingly important role for the reliability and safety of various components. Thanks to the CAD model which allows the representation of manufactured objects, their transformations, and their viewing. This paper aimed to improving the ultrasonic testing by imaging capabilities, so as the method will obtain more efficiency by the visual expertise of the defect. At this time, the software package is still under development, and the 3D representation experiments are not available for printing now. However, the entire displaying will be valid at the poster session.
References
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 T. Law & al., "Image filtering, edge detection and edge tracing ", IEEE transactions on pattern analysis and machine intelligence, Vol. 18, N° 5 May 96.
 W. Bo & al., " 3Dflaw detection for welded seams of pressure vessels", International Journal of pressure vessels and piping", Vol48, N°3, 1991
 T.P. Fang, L.A. Piegl, "Delaunay triangulation in 3D", in IEEE computer graphics, Vol.15, N°5, pp.6269, Sep.95
 Y.L, Chang, J.K. Aggarwal, "Representing and estimating 3D lines", in Pattern recognition journal, Vol.28, N° 8, pp. 11811190, Aug. 95,Pergamon ed.