Statistical detection of circular and linear defects in radiographic

DGZfP-Proceedings BB 84-CD

Poster 3

CT-IP 2003

Statistical detection of circular and linear defects in radiographic images of welds

Daniel Kazantsev, Department of Geophysics, University of Novosibirsk, Novosibirsk, Russia; Gennady Salov, Inst. of Computational Math. and Mathematical Geophysics, Novosibirsk, Russia; Ignace Lemahieu, ELIS Department, Ghent University, Ghent, Belgium; Ivan Kazantsev, Department of Radiology, University of Pennsylvania, Philadelphia, USA

Abstract In this paper we investigate applicability of statistical techniques for defect detection in radiographic images of welds. The defect detection procedure consists in a statistical hypothesis testing using several nonparametric tests. A comparison of rules derived for image thresholding for a given level of false alarm is presented. In this work we consider circular defects such as cavities and voids, and linear flaws similar to cracks. Numerical experiments with real and test data are performed.

1

Introduction

Film radiography is a traditional imaging inspection technique for nondestructive examination of industrial equipment components in order to locate any cavities, inclusions, lack of fusion and so on that may have been formed during the manufacturing or operation process [2]. Sophisticated image analysis of digitized films and digital radiographs is a widely studied research field, with much recent approaches using adaptive thresholding, a wavelet–based multi–resolution image representation [7], a model–based statistical segmentation, mathematical morphology and pattern recognition. We refer to the works [1, 3, 4, 6] where reviews with a comparative study of the methods can be found. The objective of this work is as follows: given a false alarm level, detect blob– and line–like defects in welds in realistic computer time. We try to investigate the possibilities of automatic image processing of weld defects with the help of statistical hypothesis testing using nonparametric statistical tests. We consider several tests which theoretically, for a given level of false alarm , provide us with a threshold resulting in a map of possible defects. The software is tested on images of welds of austenitic pipes acquired by radiography.

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Figure 1: Top: Radiographic image of 30.5 mm wall thickness austenitic pipe obtained using the conventional X–ray system. The visualized part of the pipe has horizontal and vertical sizes of about 92 mm and 15 mm respectively. The image is a result of median filtering. Its size is 1143 × 179 (after zooming the original digital version with factor 2) with pixel resolution 80 µm. Middle: The image is a result of subtraction from each profile its closest parabola. Bottom: The image is a result of subtraction from each profile its smoothed version.

2

Acquisition of radiographs and field flattening

Original X–ray films were of about 6 cm wide and about 335 cm long. They were laid on a 30.5 mm thickness pipe in a circumferential way to embrace the weld area. Image acquistion was carried out by radiography. Exposed and developed X–ray films were digitized by portions of about 10 cm long using the Umax Powerlook 3000 digitizer. Refer to the web site http://www.umax.com for a detailed description of the digitizer. The films were digitized at 600 dpi (about 40µm) resolutions and each pixel has a depth of 16 bits with 14 bits of them as meaningful. This results in large X–ray images that must be processed to find anomalies in welds. A typical image is shown in Figure 1 (top). An overview about the applicability of existing film digitization systems to nondestructive testing can be found in [8]. There are two main areas in the weld image : the base (parent) metal area and the weld area. The weld area is more bright than the parent metal area, due to the normal overthickness of the weld. The weld area consists of a middle area and two side areas , clearly distinguishable. Watching the profiles of the filtered image columns we observe that the profiles roughly resemble a nonsymmetric gaussian. Segmentation techniques [1, 4] that are widely used in extraction of objects from background use, as a rule, an assumption that the image under investigation is a composition of piecewise constant functions. Therefore we need to flatten the profiles of the weld images. Methods of field flattening [2] mostly perform a subtraction of a smooth component from the original image. This procedure is nonstable and results in an image with high gradients that needs

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additional smoothing. In this paper we use two approaches to the problem. As a first rough approximation, we assume that each weld’s profile w(x), x ∈ [x0 , x1 ], where [x0 , x1 ] is the support of w(x), is nearly a parabola p(x) = ax2 + bx + c with coefficients which can be found from boundary conditions f (x0 ) = p(x0 ), f (x1 ) = p(x1 ) by least squares fitting. Subtracting parabola p(x) from the weld’s profile w(x), we obtain the “softly” flattened version of the original image (Figure 1, middle). We refer to this type of flattening as a parabolic fitting. The second method of flattening we explore is subtraction from each profile w(x) its smoothed versionP s(x), where smoothing is fulfilled within a window of 2m + 1 pixels: s(x) = 1/(2m + 1) i=m i=−m w(x + i). Figure 1 (bottom) shows the resulting image with smoothing parameter m = 20. We can see that subtraction from the profile its smoothed version gives us more severe flattening than that of the parabolic background. After the flattening procedure, the next task is a detection of low–contrast spot (line)–like isolated objects on inhomogeneous and noisy background.

3

Detection of an object in a random background

We consider the detection problem as a problem of hypothesis testing, in the most important practical formulation – the absence of a priori information about brightness distribution in the points of object and background. We assume that an image under investigation is inhomogeneous and anisotropic and all observed variables have continuous probability distribution functions. In case the image does not contain an object, we suggest that the observations are statistically independent. Let us define a shape of an investigated object by the form of the window (square, circular, etc.) which moves along the image. For each possible discrete location, size and orientation of the window we investigate a problem of defect detection by testing the null hypothesis H0 : ”Absence of a defect” against the alternative H1 : ”Presence of a defect”. Rejection or acceptance of H0 is based on values of some test statistics that are functions of the observed data. Hypothesis H0 is rejected when values of the statistics achieve a critical level (threshold). Denote Z as the entire number of all tests of hypothesis H0 . Generally, some of the Z decisions can be false. If the threshold is chosen in a way that the probability of rejection of H0 when it is true is α, then under H0 , for large Z stochastically, αZ decisions can be false approximately. For each current pixel we choose two circular concentric windows W1 and W2 centered at the pixel with radii R1 and R2 respectively, R1 < R2 (Figure 2, left). It is suitable to operate with circular windows and describe their sizes by a single parameter - by radius, although the technique suggested is easily generalized for windows designed in accordance with different shapes of the detected objects. Let W1∗ = W2 − W1 denote the set of all those points W2 which do not belong to W1 . We will associate the domain W1 with a suspect defect area and domain W1∗ will often be called as a surrounding background. The value of the radius R2 is fixed by the user. Changing values of the radius R1 from Rmin up to R2 − 1 and testing hypothesis H0 , we decide whether to reject or accept the hypothesis and to mark or not the pixel position under investigation as a center of the defect zone with radius R1 . If the number of tested central pixels is denoted as Np , then the entire number of all tests is Z = Np × (R2 − Rmin ). Let x1 , x2 , . . . , xN be arbitrary pixel values from W1 and y1 , y2 , . . . , yM be arbitrary pixels from W1∗ . Denote x = {xi }, i = 1, . . . , N ; y = {yj }, j = 1, . . . , M . In this work we choose

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Object’s border

Current pixel y3

y y 1

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Figure 2: Circular and longitudinal schemes of scanning samples located on circles with radii R1 and R2 (Figure 2, left) or sampples located on lines of distances R1 and R2 (Figure 2, right). For detecting the object we test the null hypothesis H0 : ”values xi and yj are stochastically equal” against the two–sided alternative hypothesis H1 : ” xi are stochastically larger (or less) than yj ”. For testing, we need appropriate statistics. We are going to test the hypothesis H0 with the use of statistics which do not depend on the form of the image brightness distribution functions unknown to the observer. Such statistics and the corresponding tests are often called nonparametric. One of the simplest nonparametric tests is a sign test. Put M = N and assume that the pixels from the object are stochastically more brighter (larger) than those from the background (one-sided alternative). The Sign Criterion for testing the null hypothesis H0 is based on the following statistic: ν=

N X

I{xi − yi > 0},

(1)

i=1

that is the number of positive signs among x1 − y1 , . . . , xn − yn . We define I{A} = 1 if event A occurs and I{A} = 0 if it does not. The sign test rejects the null hypothesis H0 when ν ≥ λ, where the threshold λ = λ(α) is determined by the acceptable level α and equals the smallest integer such that N µ ¶ X i i=λ

N

2−N ≤ α.

(2)

Description of other tests used (the Rosenbaum test, the Haga test and the WilcoxonMann-Whitney test) can be found in [5].

4

Experimental results obtained on radiographs

Defect zones are revealed with actual measurements on fracture face using destructive testing. There are three defect clusters in the weld (Figure 3): defect A – lack of fusion,

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Figure 3: Zones A,B and C are defect areas (projections of the defect areas onto the film) revealed by actual measurements on fracture face (destructive testing).

Figure 4: Zones A“ and C “ are defect areas revealed by radiographic inspection (nondestructive testing). defect B – Cu–inclusions and wetting, defect C – porosity and slag inclusions. Radiographic visual inspection overestimates longitudinal size of zone A in 6 mm (zone A“ , Figure 4), does not reveal area B at all and underestimates longitudinal size of the defect zone C in 15 mm (zone C “ , Figure 4). Zone B has very low contrast and is difficult to detect without the image enhancement procedure. A methodology of the numerical experiment is as follows. We explore three images: original nonflattend version of the weld (Figure 1, top), the parabolic fitting – based flattened image (Figure 1, middle) and the local means – based flattened weld (Figure 1, bottom). We use two ways of thresholding : 1) Blind, or maximal thresholding, when only maximally possible values for test statistics are used. It means that we visualize only the objects that theoretically correspond to a minimal level of false alarm, i.e. extreme suspects on defectness. 2) For a given level of false alarm we compute thresholds for different tests with fixed values of such processing parameters as M , N , Rmin , R2 and Z. The sign test, Rosenbaum test, Haga test and Mann–Whitney test - ν, T1 , T2 and U are used. In case of rejection of H0 in favour of H1 , we visualize a circle (of maximal screen brightness) with radius R1 , (Rmin ≤ R1 < R2 ) corresponding to the biggest value of the test statistics computed R2 − Rmin times at the current pixel. Peak performance occurs when the inner window W1 maximally matches the object, leaving the bordering window W2 in a background region. Test statistics are computed within the sliding window W2 of radius R2 . At each pixel we store the maximal value of test statistics computed for concentric windows W1 with radius R1 changing from Rmin to R2 − 1.

4.1

Results of detection with maximal threshold (minimal α)

We visualize circles centered in the points at which the test statistics take their maximaly possible values, i.e. , with the lowest possibility of false alarm of the used criterion: 0 ≤ ν ≤ N, 0 ≤ |T1 | ≤ N, 0 ≤ T2 ≤ 2N, 0 ≤ U ≤ N 2 . Results with sign test are shown

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Figure 5: Results of experiments on detection of dark spots with sign test ν, maximal threshold C = 20 is chosen (α = 10−6 ), M = 20, N = 20, Rmin = 2, R2 = 15 . in Figure 5. The experiments show that unlike the visual radiographic inspection (Figure 4), the test statistics successfully detect several defect objects from the area B. After a number of numerical experiments we conclude that the user’s experience and expectations are very important in choosing the parameters R2 and Rmin for each detection procedure. The entire set of possible defects should be divided into several virtual groups, for instance of small, middle and large objects. Given a priori knowledge that sizes of the defects from a certain group are limited by s and S, the user chooses the parameter Rmin slightly less than s and the radius R2 slightly larger than S. Detecting small defects encounters the difficulty of differentiation between true defect pixels and noisy impulses. If parameter Rmin is about a few pixels, we expect more false small defects. Therefore, investigation of small defects shoud be performed separately from the large ones.

4.2

Results with chosen significance level

It is revealed that the images received in experiments with the same parameters M = 20, N = 20, Rmin = 2, R2 = 15 and with thresholds C(α) theoretically derived from a false alarm level α = 0.001, are severely overcrowded by redundantly detected circles for all the investigated tests. It turns out that predicted threshold C = 13 is too low for the sign test ( as well as threshold C = 10 is too low for the Rosenbaum test and so on) to provide the user with a minimal number of false defects. Besides of noise, a lack of precision in recording the data can be a reason of such relationship between threshold and false objects. Although there is a zero probability of obtaining a sample observation exactly equal to a certain quantity (mean, max, min, etc.) when the population is continuous, nevertheless in practice a sample value equal to the quantity will often occur due to digitization effects. The experiments show that empirically chosen thresholds often are very close to the upper limit of the test statistic values. Varying values of radii Rmin and R2 , we can

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Figure 6: Results of experiments with Mann–Whitney test statistic values - thresholded with level C = 750 and parameters M = N = 30, Rmin = 5, R2 = 10. observe different impacts on thresholds. Samples from W1 can be statistically dependent in case of small values of Rmin . The larger Rmin , the closer the empirical threshold is to its theoretically predicted level. Small values of Rmin can also lead to detecting the noise points as a center of a spot–like area. To illustrate this point we show the result of detection by the Mann–Whitney test U thresholded by C = 750 with parameteres Rmin = 5, R2 = 10, M = N = 30 in Figure 6. Choosing a value of the significance level α, the user should take into account that this choice relates to the expectation of about αZ false defects. For instance, if the user intends to escape noisy false defects ( but with a risk to miss a true defect), small values of α have to be chosen. As it is seen from the experiments, the flattening procedure improves image visually but introduce impulse noise, so that some false peaks can be detected as a signal. For unsupervised detection it is better to use “soft” versions of the weld’s flattening techniques. We can derive from the experiments that the smaller the expected size of defect, the less flattening is needed.

Figure 7: Image of 66 × 440 size with two transverese cracks; map of the Mann–Whitney test U statistic values thresholded by C = 6525, when maximal test value is C = 6700, for M = N = 30, Rmin = 1, R2 = 3.

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4.3

Poster 3

CT-IP 2003

Results with linear defects

In Figure 7, we show the results of detection of longitudinal defects - transverse cracks (the image data are downloaded from the website http://www.ndted.org/EducationResources/).

5

Remarks and conclusions

The results presented here demonstrate that the methodology of hypothesis testing based on nonparametric statistics can be applied to problems of defect detection with some hope of success. The benefits in detection of sizes of the defects remain somewhat limited, although we do see images with reliably detected defective zones. Even unsupervised thresholding of the map of the investigated test statistics discloses the defects that are not indicated by visual radiographic inspection.

References [1] H. Boerner, H. Strecker, Automated X–Ray Inspection of Aluminium Castings, IEEE Trans. on Patt. Anal. Mach. Intell. 10 (1) (January 1988) 79-91. [2] L.E. Bryant, P. McIntire, R.C. McMaster (Eds), Nondestructive Testing Handbook, Second Edition, Volume 3, Radiography and Radiation Testing, ASNT, ISBN 0931403-00-6, 1985. [3] R. Halmshaw, N.J. Ridyard, A review of digital radiological methods, British Journal of NDT 32 (1) (1990) 17-26. [4] V. Kaftandjian, Y.M. Zhu, G. Peix, D. Babot, Automatic recognition of defects inside aluminium ingots by X-ray imaging, Insight 38 (9) (September 1996) 618-625. [5] I.G. Kazantsev, I. Lemahieu, G.I. Salov and R. Denys, Statistical detection of defects in radiographic images in nondestructive testing, Signal Processing 82 (2002) 791-801. [6] R.M. Palenichka, U. Zscherpel, Detection of Flaws in Radiographic Images by Hypothesis Generation and Testing Approach, Proc. Int. Workshop Advances in Signal Processing for Nondestructive Evaluation of Materials, X. Maldague (Ed.), ASNT, Topics on NDE(TONE), 1998, pp. 235-243. [7] R.K. Strickland, H.I. Hahn, Wavelet transform methods for objects detection and recovery, IEEE Transactions on Image Processing 6 (5) (1997) 724-735. [8] U. Zscherpel, Film digitization systems for DIR: Standards, Requirements, Archiving and Printing, NDT.net (http://www.ndt.net) vol. 5 No. 05 (May 2000).

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