Statistical Detection of Defects in Radiographic Images

Signal Processing 82 (2002) 791–801www.elsevier.com/locate/sigpro

Statistical detection of defects in radiographic images innondestructive testing

I.G. Kazantseva ;∗, I. Lemahieub, G.I. Salova, R. Denysc

aInstitute of Computational Mathematics and Mathematical Geophysics (Computing Center), 630090, Novosibirsk, RussiabSint-Pietersnieuwstraat 41, Electronics and Information Systems Department, Ghent University, B-9000, Ghent, Belgium

cSint-Pietersnieuwstraat 41, Department of Mechanical Construction and Production, Ghent University, B-9000, Ghent, Belgium

Received 11 August 2000; received in revised form 21 December 2001

Abstract

In this paper, we investigate applicability of statistical techniques for defect detection in radiographic images of welds. Thedefect detection procedure consists in a statistical hypothesis testing using several nonparametric tests. A comparison of rulesderived for image thresholding for a given level of false alarm is presented. In this work we consider circular defects such ascavities and voids. Numerical experiments with real data are performed. ? 2002 Elsevier Science B.V. All rights reserved.

Keywords: Defect detection; Radiographic 5lm; Nondestructive testing; Nonparametric tests; Thresholding

1. Introduction

Film radiography is a traditional imaging inspectiontechnique for nondestructive examination of industrialequipment components in order to locate any cavities,inclusions, lack of fusion and so on that may have beenformed during the manufacturing or operation process[2]. Radiographic testing with 5lm is an expensive andtime-consuming technique (exposure time and devel-opment of the 5lm). Some attempts have been madeto speed up and automate di:erent stages of the ra-diographic inspection cycle. Digital radioscopy, us-ing X-ray detectors coupled to an image acquisitionand processing system, permits real-time inspection.

∗ Corresponding author. Current address: Medical Image Pro-cessing Group, Department of Radiology, University of Pennsyl-vania, Blockley Hall, Fourth Floor, 423 Guardian Drive, Philadel-phia, PA 19104-6021, USA.

E-mail address: [email protected] (I.G. Kazantsev).

However, as the resolution of 5lm is higher than thatof digital radiographs, 5lms are still considered as areference for all the imaging systems, especially incases of detecting very small defects. To process the5lm by computer, one needs to digitize the 5lm by ascanner. After that, digital image processing methodsare used for both techniques to help a human operatorin the interpretation of visual data. This makes the in-spection system more reliable, but in return requiresthe development of high-level image processing meth-ods to replace the expert’s knowledge.Sophisticated image analysis of digitized 5lms

and digital radiographs is a widely studied research5eld, with much recent approaches using adaptivethresholding [8,9], a wavelet-based multi-resolutionimage representation [24], variational methods [14],a model-based statistical segmentation [19], mathe-matical morphology [10,11,22], pattern recognitionand neural techniques [13,23] and data fusion [4,6].We refer to the works [1,3,8,19] where reviews with

0165-1684/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved.PII: S 0165 -1684(02)00158 -5

792 I.G. Kazantsev et al. / Signal Processing 82 (2002) 791–801

a comparative study of the methods can be found.The general failings of the majority of publishedtechniques can be attributed to four areas: (1) unac-ceptable false alarm rates due to component structureand noise, (2) inability to detect defects of all orien-tations and types, (3) inability to detect defects acrossdi:erent applications, (4) nonrealistic computationtimes. For these reasons, e:orts to solve at least partof the problems, are continuing.Matching the aforementioned classi5cation, we

restrict ourselves to the objective of this work asfollows: (1) given a false alarm level, (2) de-tect blob-like defects (as cavities or voids) in (3)austenitic welds in (4) realistic computer time. Wetry to investigate the possibilities of automatic im-age processing of weld defects with the help ofstatistical hypothesis testing using nonparametricstatistical tests. We consider several tests whichtheoretically, for a given level of false alarm, pro-vide us with a threshold resulting in a map ofpossible defects. Practical problems of traditionalimage enhancement—5eld Kattening and noise re-duction are discussed as well as the task of au-tomatic thresholding. The software is tested onimages of welds of austenitic pipes acquired byradiography.

2. Acquisition of radiographic images

Original X-ray 5lms were of about 6 cm wide andabout 335 cm long. They were laid on a 30:5 mmthickness pipe in a circumferential way to embrace theweld area. Image acquisition was carried out by ra-diography. Exposed and developed X-ray 5lms weredigitized by portions of about 10 cm long using theUmax Powerlook 3000 digitizer. Refer to the website http://www.umax.com for a detailed descriptionof the digitizer. The 5lms were digitized at 600 dpi(about 40 �m) resolutions and each pixel has a depthof 16 bits with 14 bits of them as meaningful. This re-sults in large X-ray images that must be processed to5nd anomalies in welds. The images contain referencemarks to identify positions in the welds, identi5cationletters, etc. Since only the items within a weld are ofinterest for the purposes of image processing, we ex-tracted the weld areas free of letters and reference ob-jects interactively. A typical image is shown in Fig. 1

(top). An overview about the applicability of existing5lm digitization systems to nondestructive testing canbe found in [26].

3. Image analysis and �eld �attening

A radiograph is a photographic record produced bythe passage of X-rays through a steel pipe onto a 5lm.After developing the 5lm, the darker regions representthe more penetrable parts of the object, and the lighterregions, those more opaque [2]. The gray-levels ofthe digitized 5lms are inverted in a way that darkerareas on the digitized version of the 5lm correspondto the darker regions in the original X-ray 5lm. In thiscase, brighter gray-level pixels store information aboutmore dense (than the base metal) areas (for instance,dense metal inclusions). Porosities are seen as darkerblobs with a round shape. Pixels from darker areasof digital images have less values than pixels frombrighter areas. Another agreement we use is that theweld seam is located horizontally in our illustrations sothat columns are vertical sections of the weld picture(Fig. 1). We call them as pro5les as well.There are two main areas in the weld image: the

base (parent) metal area and the weld area. The weldarea is more bright than the parent metal area, dueto the normal overthickness of the weld. The weldarea consists of a middle area and two side areas,clearly distinguishable. X-ray imaging is inherentlynoisy because of the quantum nature of radiation; theremay be only a few photons per pixel per exposuretime. In addition there is a noise contribution from thedigitizing procedure. The image su:ers severely fromboth types of noise and a median 5lter is applied forits suppression.Watching the pro5les of the 5ltered image columns

we observe that the pro5les roughly resemble a non-symmetric Gaussian (Fig. 2, top left). Segmentationtechniques [1,11,14] that are widely used in extractionof objects from background use, as a rule, an assump-tion that the image under investigation is a compo-sition of piecewise constant functions. Therefore, weneed to Katten the pro5les of the weld images. Meth-ods of 5eld Kattening [2,10] mostly perform a subtrac-tion of a smooth component from the original image.This procedure is nonstable and results in an imagewith high gradients that needs additional smoothing.

http://www.umax.com

I.G. Kazantsev et al. / Signal Processing 82 (2002) 791–801 793

Fig. 1. Top: Radiographic image of 30:5 mm wall thickness austenitic pipe obtained using the conventional X-ray system. The visualizedpart of the pipe has horizontal and vertical sizes of about 92 and 15 mm, respectively. The image is a result of median 5ltering. Its sizeis 1143 × 179 (after zooming the original digital version with factor 2) with pixel resolution 80 �m. Middle: The image is a result ofsubtraction from each pro5le its closest parabola. Bottom: The image is a result of subtraction from each pro5le its smoothed version.

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Fig. 2. Upper left: Plot of w(x)—the 570th pro5le of the weld. Upper right: Plot of p(x)—the parabolic background (dashed) ands(x)—window-smoothed version of the pro5le (solid). Lower left: Plot of the weld’s pro5le after parabolic Kattening. Lower right: Plotof the weld’s pro5le after smoothing-based Kattening.


A window for smoothing should be of the same (orlarger) size as the expected Kaw, in order to avoid re-dundant borders inside the Kaw area. In [2], the authorswrite: “: : : the 5eld Kattening is an absolutely crucialphase of computer-based analysis”. In this paper weuse two approaches to the problem.As a 5rst rough approximation, we assume that each

weld’s pro5le w(x); x∈ [x0; x1], where [x0; x1] is thesupport ofw(x), is nearly a parabolap(x)=ax2+bx+cwith coeQcients which can be found from bound-ary conditions f(x0) = p(x0); f(x1) = p(x1) byleast-squares 5tting. Subtracting parabola p(x) fromthe weld’s pro5le w(x), we obtain the “softly” Kat-tened version of the original image (Fig. 1, middle).We refer to this type of Kattening as a parabolic 5tting.The second method of Kattening we explore is sub-traction from each pro5le w(x) its smoothed versions(x), where smoothing is ful5lled within a windowof 2m+ 1 pixels: s(x) = 1=(2m+ 1)

∑i=mi=−m w(x+ i).

Fig. 1 (bottom) shows the resulting image withsmoothing parameter m = 20. We can see that sub-traction from the pro5le its smoothed version givesus more severe Kattening than that of the parabolicbackground. Fig. 2 shows us results of Kattening ofa single pro5le. Local smoothing (averaging by 3–5pixels window) is additionally applied to the resultsof Kattening.The radiograph is a kind of shadow picture, its

shadow being more determined by geometrical opticsprinciples than by wave scattering in comparison withultrasonics. The size and form of the shadow, for ex-ample cast by voids, cracks or inclusions present inthe test object, depend on the distance and angle be-tween the radiation source and the defect and the dis-tance and angle between the defect and the 5lm. Inthis work, we do not use physical parameters of theradiographic data acquisition such as size and energylevel of the source, the 5lm grain size and character-istic curve, the exposure factor and others. However,we exploit a kind of geometrical model in the form ofthe parabolic weld pro5le. Due to asymmetry in theweld’s pro5les, this approximation looks more realis-tic than the methodology based on the assumption thatthe intensity plot of a weld is Gaussian [15]. Gener-ally, the problem of 5eld Kattening is still open. Afterthe Kattening procedure, the next task is a detectionof low-contrast spot-like isolated objects on inhomo-geneous and noisy background.

4. Detection of an object in a random background

We consider the detection problem as a problem ofhypothesis testing [16], in the most important practi-cal formulation—the absence of a priori informationabout brightness distribution in the points of objectand background. We assume that an image under in-vestigation is inhomogeneous and anisotropic and allobserved variables have continuous probability distri-bution functions. In case the image does not containan object, we suggest that the observations are statis-tically independent.

4.1. General scheme of detection

Let us de5ne a shape of an investigated object bythe form of the window (square, circular, etc.) whichmoves along the image. For each possible discretelocation, size and orientation of the window weinvestigate a problem of defect detection by testingthe null hypothesis

H0: absence of a defect

against the alternative

H1: presence of a defect:

Rejection or acceptance of H0 is based on values ofsome test statistics that are functions of the observeddata. Hypothesis H0 is rejected when values of thestatistics achieve a critical level (threshold). DenoteZ as the entire number of all tests of hypothesis H0.Generally, some of the Z decisions can be false. Ifthe threshold is chosen in a way that the probabilityof rejection of H0 when it is true is �, then under H0,for large Z stochastically, �Z decisions can be falseapproximately.For each current pixel we choose two circular con-

centric windows W1 andW2 centered at the pixel withradii R1 and R2, respectively, R1 ¡R2 (Fig. 3). It issuitable to operate with circular windows and describetheir sizes by a single parameter—by radius, althoughthe technique suggested is easily generalized for win-dows designed in accordance with di:erent shapes ofthe detected objects. Let W ∗

1 = W2 − W1 denote theset of all those points W2 which do not belong to W1.We will associate the domain W1 with a suspect de-fect area and domain W ∗

1 will often be called as asurrounding background. The value of the radius R2


RR11xy1

Nx

x3

x2

yM

yM-1

xN-1

2y

3y

1W

W2

Object’s border

Current pixel

2

Fig. 3. Scheme of scanning.

is 5xed by the user. Changing values of the radius R1

from Rmin up to R2 − 1 and testing hypothesis H0, wedecide whether to reject or accept the hypothesis andto mark or not the pixel position under investigation asa center of the defect zone with radius R1. If the num-ber of tested central pixels is denoted as Np, then theentire number of all tests can be expressed as follows:

Z = Np × (R2 − Rmin):

Let x1; x2; : : : ; xN be arbitrary pixel values fromW1 andy1; y2; : : : ; yM be arbitrary pixels from W ∗

1 . Denotex= {xi}; i=1; : : : ; N ; y= {yj}; j=1; : : : ; M . In thiswork we choose samples located on circles with radiiR1 and R2 (Fig. 3). For detecting the object we testthe 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 go-ing to test the hypothesis H0 with the use of statisticswhich do not depend on the form of the image bright-ness distribution functions unknown to the observer.Such statistics and the corresponding tests are oftencalled nonparametric. A statistical approach using aparameterized hypothesis testing method for anomaly

detection and localization from limited tomographicdata can be found in [5]. The tomographic theory canbe applied to defect detection in a single radiographonly in rare cases when a geometry of the specimenand a forward model of image formation are fully de-termined [12].

4.2. Sign test

One of the simplest nonparametric tests is a sign test[18]. Put M = N and assume that the pixels from theobject are stochastically more brighter (larger) thanthose from the background (one-sided alternative).The Sign Criterion for testing the null hypothesis H0

is based on the following statistic:

�=N∑i=1

I{xi − yi ¿ 0}; (1)

that is the number of positive signs amongx1−y1; : : : ; xn−yn. Here and in what follows, we de-5ne I{A}=1 if event A occurs and I{A}=0 if it doesnot. The sign test rejects the null hypothesis H0 when�¿ �, where the threshold �= �(�) is determined bythe acceptable level � and equals the smallest integersuch that

N∑i=�

(iN

)2−N 6 �: (2)

4.3. Rosenbaum test

As a second example, consider the Rosenbaumstatistic [20]. Denote

A1 = the number of x larger than ymax = max{yj}:(3)

Given the integer r, it can be shown (see [21]) thatthe probability of event {A1¿ r} under the null hy-pothesis H0 has the form

Pr(A1¿ r|H0) =(N +M − r)!N !(M + N )!(N − r)!

: (4)

The one-sided Rosenbaum test is as follows. Reject H0

only if A1¿ �, where the threshold � is the smallest


integer such that

(N +M − �)!N !(M + N )!(N − �)!

6 �: (5)

Let

A2 = the number of y larger than xmax = max{xi}:(6)

The two-sided Rosenbaum test for H0 against thetwo-sided alternative H1 is as follows. Reject H0 onlyif T1 ≡ A1 − A2¿C1 or T16− C2.Critical levels C1 and C2 depend upon the entire

number Z of tests. In case of a single test, the probabil-ity of false alarm Pr(A1¿C1 |H0)+Pr(A2¿C2 |H0)is expressed as a ratio

=(N +M − C1)!N !(M + N )!(N − C1)!

+(N +M − C2)!M !(M + N )!(M − C2)!

;

(7)

where C1 and C2 should be chosen so that the fractionsin (7) are approximately the same and they are thesmallest integers for which the relationship

6 � (8)

is hold.If M = N , then C1 = C2 and calculations are es-

sentially simpler. In this case, given the probability offalse alarm �, we reject the hypothesis H0 when

|T1|¿C1;

where the threshold C1 is chosen as the smallest inte-ger such that

2(2N − C1)!N !(2N )!(N − C1)!

6 �: (9)

4.4. Haga test

The Rosenbaum test can be modi5ed. Let

B1 = the number of y smaller than xmin ;

B2 = the number of x smaller than ymin :

Then the one-sided Haga test for H0 against theone-sided alternative H1 is as follows. Reject H0 onlyif A1 + B1¿C(�). The two-sided Haga test for H0

is to reject H0 if

T2 = |A1 + B1 − A2 − B2|¿C(�=2): (10)

Critical levels C(�) and C(�=2) can be taken fromtables [7].

4.5. Wilcoxon–Mann–Whitney test

The following nonparametric test for H0 was origi-nally proposed by Wilcoxon [25], Mann and Whitney[17]. The Mann–Whitney test is based on the statistics

U+ =N∑i=1

M∑j=1

I{xi − yj ¿ 0};

U− =N∑i=1

M∑j=1

I{xi − yj ¡ 0};(11)

(U+= number of pairs {xi; yj} with xi ¿yj). ValuesU+ and U− are integers from 0 up to NM and dis-tributed symmetrically near the point NM=2 when H0

is true.The Wilcoxon test is based on the statistics

W = U+ + 12N (N + 1): (12)

Let the integer u¿ 0 be 5xed, then the probabilityP(U+ = u|H0) (P(U−= u|H0)) can be represented inthe form

P(U+ = u|H0) =M !N !

(M + N )!

∑p(M)

1; (13)

where the summation is performed over all partitionsp(M)={m0; m1; : : : ; mN} of the numberM into N+1integer nonnegative addendas

M = m0 + m1 + · · ·+ mN

satisfying the equalityN∑i=1

imi = u:

The two-sided Mann–Whitney test for H0 againstthe two-sided alternative H1 is as follows. RejectH0 only if U+¿CU (�=2) or U−¿CU (�=2). Theone-sided Mann–Whitney test is to reject H0 ifU+¿CU (�). The one-sided Wilcoxon test is to re-ject H0 if W ¿CW (�). Critical values can be takenfrom tables in [17,18,25]. In this work we use the


two-sided Mann–Whitney test

U =max{U+; U−}: (14)

5. Experimental results obtained on radiographs

Defect zones are revealed with actual measure-ments on fracture face using destructive testing.There are three defect clusters in the weld (Fig. 4):defect A—lack of fusion, defect B—Cu-inclusionsand wetting, defect C—porosity and slag inclusions.Radiographic visual inspection overestimates longitu-dinal size of zone A in 6 mm (zone A′′, Fig. 5), doesnot reveal area B at all and underestimates longitu-dinal size of the defect zone C in 15 mm (zone C′′,Fig. 5). Zone B has very low contrast and is dif-5cult to detect without the image enhancementprocedure.A methodology of the numerical experiment is as

follows. We explore three images: original nonKattendversion of the weld (Fig. 1, top), the parabolic 5tting—based Kattened image (Fig. 1, middle) and the localmeans—based Kattened weld (Fig. 1, bottom). We usetwo ways of thresholding:(1) Blind, or maximal thresholding, when only maxi-

mally possible values for test statistics are used. Itmeans that we visualize only the objects that the-oretically correspond to a minimal level of falsealarm, i.e., extreme suspects on defectness.

(2) For a given level of false alarm we computethresholds for di:erent tests with 5xed values ofsuch processing parameters as M , N , Rmin, R2

and Z .The sign test, Rosenbaum test, Haga test andMann–

Whitney test—�, T1; T2 and U are used. In case ofrejection of H0 in favour of H1, we visualize a cir-cle (of maximal screen brightness) with radius R1,(Rmin6R1 ¡R2) corresponding to the biggest value

Fig. 4. Zones A; B and C are defect areas (projections of the defect areas onto the 5lm) revealed by actual measurements on fracture face(destructive testing).

of the test statistics computed R2 − Rmin times at thecurrent pixel. Peak performance occurs when the innerwindowW1 maximally matches the object, leaving thebordering window W2 in a background region. Teststatistics are computed within the sliding window W2

of radius R2. At each pixel we store the maximal valueof test statistics computed for concentric windows W1

with radius R1 changing from Rmin to R2 − 1.

5.1. Results of detection with maximal threshold(with minimal �)

We visualize circles centered in the points at whichthe test statistics take their maximally possible values,i.e., with the lowest possibility of false alarm of theused criterion

06 �6N;

06 |T1|6N;

06T26 2N;

06U6N 2:

Results with sign test are shown in Fig. 6. Hereand what follows, the results of detection are posi-tioned within illustrations from top to bottom as it is:original image, image Kattened with parabolic 5ttingand image Kattened with local smoothing. The exper-iments with Haga test T2 thresholded with maximallevel C = 40 and with Mann–Whitney test U thresh-olded with maximal level C = 400 result in the im-ages that are very similar to that of Fig. 7, where theRosenbaum test T1 is presented. It con5rms the theo-retical fact about the equivalence of the Rosenbaum,Haga and Mann–Whitney tests when maximal valuesof test statistics are chosen as a threshold. In this casethe sum in Formula 13 is equal to 1 and this formulabecomes identical to Formula 4.


Fig. 5. Zones A′′ and C′′ are defect areas revealed by radiographic inspection (non-destructive testing).

Fig. 6. Results of experiments on detection of dark spots with sign test �, maximal threshold C = 20 is chosen (� = 10−6), M = 20,N = 20, Rmin = 2, R2 = 15.

Fig. 7. Results of experiments with Rosenbaum test T1 thresholded with maximal level C =20 and parameters M =20, N =20, Rmin = 2,R2 = 15.

The experiments show that unlike the visual radio-graphic inspection (Fig. 5), the test statistics success-fully detect several defect objects from the area B.After a number of numerical experiments we concludethat the user’s experience and expectations are veryimportant in choosing the parameters R2 and Rmin foreach detection procedure. The entire set of possibledefects 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 acertain group are limited by s and S, the user choosesthe parameter Rmin slightly less than s and the radiusR2 slightly larger than S. Detecting small defects en-counters the diQculty of di:erentiation between truedefect pixels and noisy impulses. If parameter Rmin isabout a few pixels, we expect more false small de-fects. Therefore, investigation of small defects shouldbe performed separately from the large ones.


Fig. 8. Results of experiments with Mann–Whitney test statistic values—thresholded with level C = 750 and parameters M = N = 30,Rmin = 5; R2 = 10.

Fig. 9. Image with Rosenbaum test T1 values of nonKattened weld’s image calculated for M = N = 20, Rmin = 2; R2 = 15.

5.2. Results with chosen signi:cance level

It is revealed that the images received in experi-ments with the same parameters M = 20, N = 20,Rmin = 2, R2 = 15 and with thresholds C(�) theoreti-cally derived from a false alarm level � = 0:001, areseverely overcrowded by redundantly detected circlesfor all the investigated tests. It turns out that predictedthreshold C = 13 is too low for the sign test (as wellas threshold C=10 is too low for the Rosenbaum testand so on) to provide the user with a minimal numberof false defects. Besides of noise, a lack of precision inrecording the data can be a reason of such relationshipbetween threshold and false objects. Although there isa zero probability of obtaining a sample observationexactly equal to a certain quantity (mean, max, min,etc.) when the population is continuous, neverthelessin practice a sample value equal to the quantity willoften occur due to digitization e:ects.The experiments show that empirically chosen

thresholds often are very close to the upper limit ofthe test statistic values. Varying values of radii Rmin

and R2, we can observe di:erent impacts on thresh-olds. Samples from W1 can be statistically dependentin case of small values of Rmin. The larger Rmin, the

closer the empirical threshold is to its theoreticallypredicted level. Small values of Rmin can also lead todetecting the noise points as a center of a spot-likearea. To illustrate this point we show the result of de-tection by the Mann–Whitney test U thresholded byC=750 with parameters Rmin=5; R2=10,M=N=30in Fig. 8. The method suggested can be improved bytaking sample values not only on circles with radiusR1 and R2 but also inside regions W1 and W ∗

1 . Ran-dom choice of samples also can improve performanceof the algorithm.Choosing a value of the signi5cance level �, the

user should take into account that this choice re-lates to the expectation of about �Z false defects.For instance, if the user intends to escape noisy falsedefects (but with a risk to miss a true defect), smallvalues of � have to be chosen. In addition, we show amap of Rosenbaum test T1 values for original nonKat-tened weld’s image in Fig. 9 to illustrate a alternativeto the aforementioned ways of thresholding. We seethat points suspect on defects have essentially largervalues (more bright pixels) and can be segmentedinteractively. The maps for the two Kattened versionsare not shown here because of their similar (but morenoisy) character. As it is seen from the experiments,


the Kattening procedure improves image visually butintroduce impulse noise, so that some false peaks canbe detected as a signal. For unsupervised detection itis better to use “soft” versions of the weld’s Katten-ing techniques. We can derive from the experimentsthat the smaller the expected size of defect, the lessKattening is needed. The problem of regularization ofthe Kattening procedure has a strong task-dependentcharacter and is considered to be closely related withthe size of searched defect. In practice, we would rec-ommend to combine a model-based techniques withaveraging within large windows in order to achievea trade-o: between global and local properties ofestimated background.

6. Remarks and conclusions

The results presented here demonstrate that themethodology of hypothesis testing based on nonpara-metric statistics can be applied to problems of defectdetection with some hope of success. The bene5tsin detection of sizes of the defects remain somewhatlimited, although we do see images with reliablydetected defective zones. Even unsupervised thresh-olding of the map of the investigated test statisticsdiscloses the defects that are not indicated by visualradiographic inspection.The method proposed in this work for detecting

defect indications in radiographic images has a dis-tinction from other well-known procedures. One ofthe most important features is the distribution-freecharacter of the presented statistical approach. Be-ing based on nonparametric test statistics it hassome advantages to other techniques in Kexibil-ity and ability of clear interpretation of the results.For example, it is possible to consider the map oftest statistics as a probability or evidence of defectpresence and therefore it can serve as an input toa data fusion module [6], which often is not possi-ble for existing segmentation methods. The researchpresented here may impact other areas in signal de-tection. For example, a similar technique can beapplied to feature detection in 3D ultrasonic non-destructive data and to the microcalci5cations de-tection problem encountered in mammography. Theauthors consider these topics as subject for futurework.

Acknowledgements

The authors are grateful to Dr. Antoon Lefevre forsupplying us with a description of the defects and toall members of the MEDISIP Group of the ELIS De-partment of Ghent University for their help and sup-port. The authors wish to express their appreciation tothe referees for their helpful suggestions which greatlyimproved the presentation of the paper.

References

[1] H. Boerner, H. Strecker, Automated X-Ray inspection ofaluminium castings, IEEE Trans. Pattern Anal. Mach. Intell.10 (1) (January 1988) 79–91.

[2] L.E. Bryant, P. McIntire, R.C. McMaster (Eds.),Nondestructive Testing Handbook, 2nd Edition, Radiographyand Radiation Testing, Vol. 3, ASNT, 1985, ISBN0-931403-00-6.

[3] C.H. Chen, Pattern recognition in nondestructive evaluationof materials, in: C.H. Chen, L.F. Pau, P.S.P. Wang (Eds.),Handbook of Pattern Recognition and Computer Vision,World Scienti5c Publishing Company, Singapore, 1998, pp.455–471.

[4] A. Dromigny, Y.M. Zhu, Improving the dynamic range ofreal-time X-ray imaging systems via Bayesian fusion, J.Nondestructive Eval. 16 (3) (1997) 147–160.

[5] A.B. Frakt, W.C. Karl, A.S. Willsky, A multiscale hypothesistesting approach to anomaly detection and localization fromnoisy tomographic data, IEEE Trans. Image Process. 7 (1998)825–837.

[6] X.E. Gros, NDT Data Fusion, Arnold, London, 1997.[7] T. Haga, A two-sample rank test on location, Ann. Inst. Math.

Stat. 11 (1959=1960) 211–219.[8] R. Halmshaw, N.J. Ridyard, A review of digital radiological

methods, Br. J. NDT 32 (1) (1990) 17–26.[9] A.K. Jain, M.P. Dubuisson, Segmentaion of X-ray and

C-scan images of 5ber reinforced composite materials, PatternRecognition 25 (3) (1992) 257–270.

[10] V. Kaftandjian, A. Joly, T. Odievre, M. Courbiere,C. Hantrais, Automatic detection and characterization ofaluminium weld defects: comparison between radiography,radioscopy and human interpretation, Proceedings of theSeventh European Conference on Nondestructive Testing,Copenhagen, Denmark, May 1998, pp. 1179–1186.

[11] V. Kaftandjian, Y.M. Zhu, G. Peix, D. Babot, Automaticrecognition of defects inside aluminium ingots by X-rayimaging, Insight 38 (9) (September 1996) 618–625.

[12] I.G. Kazantsev, I. Lemahieu, Reconstruction of elongatedstructures using ridge functions and natural pixels, InverseProblems 16 (2) (April 2000) 505–517.

[13] A. Kehoe, G.A. Parker, An intelligent knowledge basedapproach for the automated radiographic inspection ofcastings, NDT & E Int. 25 (1) (1992) 23–36.


[14] G. KoepKer, G. Lopez, J.M. Morel, A multiscale algorithm forimage segmentation by variational method, SIAM J. Numer.Anal. 31 (1) (February 1994) 282–299.

[15] T.W. Liao, J. Ni, An automated radiographic NDT systemfor weld inspection: Part I—Weld extraction, NDT & Int. 29(3) (1996) 157–162.

[16] E.L. Lehmann, Testing Statistical Hypotheses, Wiley, NewYork, 1986.

[17] H.B Mann, D.R. Whitney, On a test of whether one or tworandom variables is stochastically larger than the other, Ann.Math. Stat. 18 (1947) 50–60.

[18] H.R. Neave, P.L. Worthington, Distribution-free Tests,Unwin, London, 1988.

[19] R.M. Palenichka, U. Zscherpel, Detection of Kaws inradiographic images by hypothesis generation and testingapproach, in: X. Maldague (Ed.), Proceedings of theInternational Workshop Advances in Signal Processing forNondestructive Evaluation of Materials, ASNT, Topics onNDE(TONE), 1998, pp. 235–243.

[20] S. Rosenbaum, Tables for a nonparametric test of location,Ann. Math. Stat. 25 (1954) 146–150.

[21] G.I. Salov, Nonparametric criteria for detection ofcontours, lines, strips and crests of given form againstrandom backround, Optoelectron. Instrumentation DataProcess. (Allerton Press, Inc., the journal’s web pagehttp://www.iae.nsk.su/oidp/) 4 (1) (1994) 46–52.

[22] J. Serra, Image Analysis and Mathematical Morphology,Academic Press, New York, 1984.

[23] F.G. Smith, K.R. Jepsen, P.F. Lichtenwalner, Comparisonof neural networks and Markov random 5eld imagesegmentation techniques, in: D.O. Thompson, D.E. Chimenti(Eds.), Review of Progress in Quantitative NondesstructiveEvaluation, Vol. 11A, Plenum Press, New York, 1992, pp.717–724.

[24] R.K. Strickland, H.I. Hahn, Wavelet transform methods forobjects detection and recovery, IEEE Trans. Image Process.6 (5) (1997) 724–735.

[25] F. Wilcoxon, Individual comparisons by ranking methods,Biometrics Bull. 1 (1945) 80–83.

[26] U. Zscherpel, Film digitization systems for DIR:Standards, Requirements Archiving Printing, NDT.net(http://www.ndt.net) 5 (05) (May 2000).

http://www.iae.nsk.su/oidp/

http://www.ndt.net

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Statistical Detection of Defects in Radiographic Images