Interest of Data Fusion for Improvement of Classification in X-ray Inspection

Transcription

1 Internatonal Symposum on Dgtal Industral Radology and Computed Tomography - We.4. Interest of Data Fuson for Improvement of Classfcaton n X-ray Inspecton Ahmad OSMAN *, Ulf HASSLER *, Valere KAFTANDJIAN ** * Fraunhofer Development Center X-ray Technology EZRT, Dr.-Mack-Str. 8, 9076 Fuerth, Germany ** Natonal Insttute of Appled Scences INSA- Lyon, Bat. St. Exupery, 0 Avenue Albert EINSTEIN, 696 Vlleurbanne, France Abstract. Dempster-Shafer (DS) evdence theory s developed as an attempt to overcome the lmtaton of conventonal probablty theory by handlng uncertan, mprecse and ncomplete nformaton. In ths paper we present a classfcaton system based on ths fuson theory. The performance of ths system s evaluated on D and 3D X-ray data. Obtaned results are very promsng and encourage us to use ths system n other applcatons, namely for ultrasound data classfcaton.. Introducton X-ray nspecton s a tradtonal non destructve testng method used to thoroughly test ndustral parts, such as alumnum castngs n the automotve sector. Safety specfcatons and qualty control task are the man focus of the nspecton process. Dgtal mage processng, computatonal ntellgence and hardware progress allowed automatng ths task. Whle the detecton of true defects s the objectve, one man dffculty n X-ray nspecton s the detecton of false alarms (or false defects), especally f very small and low contrasted defects have to be detected. Therefore, reducng the rejecton rato of good parts wthout rskng mssng true defects s a serous challenge. The automatc detecton and recognton of defects requres computerzed mage processng, mage analyss, and decson process. The mage processng step s crtcal to detect potental defects. Durng the mage analyss step, features are extracted to be further used n classfcaton between true defects TD and false defects FD. Our nterventon s n the classfcaton step, where we developed a specfc approach based on data fuson theory to combne dfferent sources of nformaton together n order to mprove the true classfcaton rates of true defects and false alarms. To make fuson between dfferent sources possble, a transton from the source space nto a common space called mass values space takes place. We present a completely automatc mass value attrbuton procedure wth no need for expert supervson. Performances of the classfer are quantfed n terms of correct classfcaton rates respectvely for true defects and false alarms, and also usng Recever Operatng Characterstcs curves (ROC). The developed classfcaton system, called Data Fuson Classfer (DFC), was used to classfy defects from segmented D radographc mages and 3D-CT volumes where t gave n both cases hghly precse and relable decsons. Lcence:

2 In the next secton, the data fuson theory s brefed, and then secton three descrbes the classfcaton algorthm. Afterwards applcatons and results are resumed n secton four. Dscussons and future mprovement are brefed n secton fve.. Data Fuson Data fuson fnds ts useful applcaton n multsource contexts, when data are uncertan and mprecse and where there s possblty of mssng data. In decson makng process, the applcaton of data fuson ams at buldng a more pertnent decson. The general concern s to successfully classfy an element x nto a class C of the frame of dscernment, usng nformaton f j provded by the source j.. Prncpe The most used models n data fuson are the probablty approach, the possblty approach and the Evdence theory (Dempster-Shafer theory). These theores of uncertanty represent the mperfectons of nformaton through a confdence measure. For each class C of, a value M ( x C / f j ( x )) represents the confdence accorded to the fact that an element x belongs to a class C, usng f j nformaton provded by the source j. The data fuson process nvolves three steps llustrated n fgure. Fgure. Data fuson process steps: knowledge modelng, confdence combnaton and decson []. The am of pre-processng s to extract the parameters of x. The selected parameters must be pertnent regardng the objectves. In some applcatons, lke castng defects, expert choce can serve us to select the mportant parameters. The classes, whch are provded by the frame of dscernment, must correspond to the needs of the applcaton and dependng on the type of the problem these classes can be exclusve (one true and others false) or not (ntermedate symbols OR). A measure M(C ) allows us to quantfy the confdence n the hypothess that an element x s n class C of. Confdence measures proposed by each theory ft nto a common mathematcal framework but are dstngushed by ther ablty to model some nuances of language (probablty, plausblty, belef, necessty, credblty). In the next step we combne the confdence measures of varous sources for obtanng a sngle set of confdence measures. Fnally, dependng on the decson crtera, we choose the class whch has the hghest confdence.

3 In the next secton, the Demspter-Shafer theory (also called evdence theory) s descrbed.. Evdence theory Dempster-Shafer (DS) theory, [] and [3], s a general framework whch offers more flexblty than probablty theory. It s sutable to reason wth uncertanty and allows to dstngush between uncertanty and mprecson. Ths s acheved n partcular by makng t possble to handle composte hypotheses. DS theory s also sutable for combnng nformaton from dfferent sources. For a gven frame of dscernment (a set of classes or hypotheses), the partcularty of DS theory s that any source of nformaton can gve a pece of evdence on any subset of whch can be a smple hypothess H or a unon of smple hypotheses. Furthermore, theses hypotheses are not necessarly exclusve, e.g. {frend, enemy, neutral}; Hence, represents the workng space for the applcaton beng consdered snce t conssts of all propostons for whch the nformaton sources can provde evdence. Informaton sources can dstrbute mass values on the subsets of the frame of dscernment m : [0,] A m(a ) s called mass dstrbuton f and only f: m( ) 0 m(a) A The dervaton of the mass dstrbuton s the most crucal step, snce t represents the knowledge on the actual applcaton, as well as uncertanty ncorporated n the selected nformaton source [4]: 0 m(a) As already mentoned, an nformaton source assgns mass values to any hypothess of. That s, f an nformaton source cannot dstngush between two propostons A and A j, t assgns a mass value to the set ncludng both propostons (A A j )..3 Fuson process The combnaton rule of Dempster provdes a mathematcal relaton to combne measures of confdence (called mass values) from dfferent sources of nformaton. Mass dstrbutons m, m from two dfferent sources are combned wth Dempster's orthogonal rule (conjunctve combnaton). The result s a new dstrbuton, m = m m, whch carres the jont nformaton provded by the two sources: m(x C) (m m )(x C) K A A j C m (x A ) m (x A ) K m (x A ) m (x A j) A A j where K s the measure of conflct between sources and t s ntroduced n ths equaton as a normalzaton factor. The larger K, the more the sources are conflctng and the less sense ther combnaton. As a consequence some authors, Smets n partcular [5], requre the use of the Dempster combnaton rule wthout normalsaton. Indeed, when K ncreases, the j 3

4 fused mass ncreases although t s not related to an ncrease of confdence. For ths reason, when the normalzed rule s used, the conflct K must be ncluded n the decson crtera. In case of M dfferent nformaton sources B, B...B M, the DS rule s: m(x C) B BBN C m (x B ) m (x B ) m (x B K where K m (x B ) m (x B ) m (x B ) N M B BBN It s possble to show, through successve combnaton of mass values teratons, that the operator of Dempster strength the certanty [6]. In other words, when the actons of two separate sensors lead to prefer one hypothess, the trust granted n ths hypothess wll be larger after mergng, whch s not necessarly the case wth Bayes probablty. 3. Classfcaton algorthm: Data Fuson Classfcaton (DFC) The ssue s to classfy each detected object n one of the two classes: defect (TD) or false defect (FD). In the frame of Dempster-Shafer theory, ths corresponds to three hypotheses: H : ths object s a defect H : ths object s a false alarm H 3 = H H : gnorance Detected objects are descrbed va a lst of geometrc and grey level based features. Each measured feature s consdered as a source of nformaton, and the combnaton of two or more features s expected to mprove the classfcaton performance. In order to be combned, features values must be translated nto mass values for each hypothess of the frame of dscernment. We have developed an orgnal method for automatc attrbuton of mass values to features measured on a detected object. The mplemented method uses each feature hstogram as a source of nformaton. The hstogram s used to dvde the feature s space nto regons and specfy for each one of these regons a correspondng mass value to the H hypothess. The complement to one s affected to the H 3 hypothess, and no mass s assgned to H n order to avod any conflct durng combnaton. A smooth transton between regons s obtaned through the use of fuzzy sets, such as ntroduced n [4]. The method can be summarzed as follows: 3. Learnng on a set of known objects Features extracton and hstogram computaton From features to regons: computaton of true defect proporton p() n each hstogram nterval. A regon s defned by a stable true defect proporton (va a crteron on the dervatve of p()) Masses attrbuton : m(h ) = p(regon), m(h 3 ) = - m(h ) ; m(h ) = 0 Dfferent masses combnaton rules: normalsed Demspter orthogonal rule (par wse, three or all features together) and statstcal rules (mean and medan masses). Selecton of best sources (successful sources) relatvely to an orgnal external nspecton system or satsfyng an nput demand on overall detecton rate. N M ) 4

5 3. Valdaton on a set of unknown objects Features extracton usng selected sources only Attrbuton of masses Masses combnaton Performance test A more detaled descrpton of the method s gven n [7]. 3.3 Performance measures In order to measure the performance of a source, a threshold S s appled on the mass value m(h ) for each feature, and after each combnaton. The objects whose mass m(h ) s above the threshold are consdered as true defects, and the others as false. The classfcaton results s then compared to the true decson gven by the expert, and the followng rates are computed : - Correct decsons rate (PCD): number of truedefectscorrectly classfed falsedefectscorrectly classfed PCD total number of true defectsand falsedefects - True Defects classfcaton rate (PTD): number of true defects correctly classfed PTD total number of true defects - False Defects classfcaton rate (PFD): PFD number of false defects correctly classfed total number of false defects - Overall classfcaton rate (R): a R PCD b PTD c PFD a b c The rate R was ntroduced n such a way to gve the user the possblty to attrbute more mportance to the correct classfcaton of ether TD or FD. Usually more mportance s gven to TD detecton. Thus, the overall rate R s computed wth a=c=, and b=5. 4. Applcatons and results We tested the proposed classfcaton algorthm DFC on D radography dataset and on 3D computed tomography (CT) dataset. In the frst case, the DFC system s compared wth the Intellgent System for Automated Radoscopy (ISAR), developed by EZRT Fraunhofer and used for radoscopc qualty control n the producton of castngs. Informaton about the ISAR system can be found n the reference [8]. In ths paper, we resume the obtaned results. For detaled explanatons about each applcaton, please refer to papers [9] and [0]. 5

6 4. Castngs radography dataset Ths dataset s extracted from ndustral radoscopc mages of castngs. After segmentaton, detect objects are characterzed by an array of eleven features (such as area, contrast, volume, etc...). Each object s classfed manually nto TD and FD by a radologcal expert, hs decsons are consdered as the true decsons. The dataset s formed of 36 objects. It contans 3 true defects TD ncludng oxdes, gas vods and porostes and 30 false defects FD (see fgure ). The dataset s dvded nto two parts, a learnng database (formed of 65 FD and 5 TD), and a testng dataset (formed of 65 FD and 6 TD). Fgure. The true or false defects appear as a brghter zone n the red rectangle. On the left sde appears a true defect and on the rght sde appears an artefact caused by the structure of the nspected part. Frst the learnng process takes place on the learnng dataset. Then a selecton of the best sources whch gve the hghest overall classfcaton rate R. Afterwards the testng dataset s classfed usng the selected best sources. Ther performance on the learnng and testng datasets are compared to the ISAR s performance. Results are resumed n the followng table ordered by decreasng overall classfcaton rate R obtaned on the testng dataset. Learnng process Testng process Source R PFD PTD R PFD PTD Mean Mass DFC(MaxElongaton & InOutContrast) DFC(DepthThckness & InOutContrast) ISAR Table. Acheved overall rates R performances on D castngs radography by classfcaton usng ISAR and data fuson classfers. 4. Castngs 3D CT dataset The 3D CT dataset s for alumnum castngs. It contans 44 object (or potental defects) classfed by an expert between true and false defects (see fgure 3). Only 44 objects are true defects and the remanng 398 objects are false defects, therefore ths dataset s very unbalanced. Exstng defects are from dfferent types: porostes, cracks and vods. False defects are due to nose, CT artefacts and the segmentaton of structural elements as potental defects. For automatc classfcaton purpose, a total number of 30 features are measured on each object. These features represent the nput sources of nformaton for DFC system to automatcally classfy the entry object as true or false defect. 6

7 For the learnng and testng processes, the complete dataset s dvded nto: - Learnng dataset: 6 potental defects conssted of: 00 false alarms and 6 true defects. - Testng dataset: 6 potental defects conssted of: 98 false defects and 8 true defects. Fgure 3. Part of a slce vew extracted from a 3D CT volume: on the left sde a true defect (surface defect) appears as a darker area and on the rght sde a false alarm (reconstructon artefact) appears, as a darker area as well. Results for DFC system are presented n table ordered by decreasng R. Source Learnng process Testng process R PFD PTD R PFD PTD Medan Mass DFC(features 5 & 3) Table. Acheved overall rates R performances on castngs 3D CT data by classfcaton usng data fuson classfers. 5. Dscusson and perspectves Frst of all, the nterest of ths classfcaton approach s that t s completely "transparent",.e. t s not a black box such as neural network technques for example. Classfcaton results obtaned are very good n comparson to the actual ndustral system as was proved on D data (no actual system for 3D data). Ths s especally notceable on the false alarms classfcaton rate whch s greatly mproved wth data fuson system. Concernng the combnaton rule, actually mean or medan mass appear better that DFC combnaton, may be because all the features are used, whle wth Dempster Shafer rule, usng all the features decrease the performance. A complete analyss of the Dempster rule and ts behavour wth the number of combned sources s out of scope of ths paper. It s worth notng that the mass attrbuton method (whch can be compared to a confdence measure) s a very useful tool to translate any feature nto a common space allowng ther combnaton (ether usng a statstcal rule, or the orthogonal sum of Dempster). Our present work s to apply a smlar method to other 3D data, namely from ultrasonc testng for composte materals. References [] Dupus. O., Fuson entre les données ultrasonores et les mages de radoscope a haute résoluton: Applcaton au contrôle de cordon de soudure. Rapport de thèse: Insttut Natonale des Scences Applquées de Lyon, 000. [] Dempster A., Upper and lower probabltes nduced by multvalued mappng. Annals of Mathematcal Statstcs. 38, pp , 967. [3] Shafer, G., A Mathematcal Theory of Evdence. Prnceton Unversty Press, Prnceton. p. 97,

8 [4] Kaftandjan V. et al., "Uncertanty modelng usng Dempster-Shafer theory for mprovng detecton of weld defects". Pattern Recognton Letters, Volume 4, pp , 003. [5] Smets P., The combnaton of evdence n the Transferable Belef Model, IEEE trans. Pattern Analyss& Machne Intellgence, vol, n 5,pp , 990. [6] Gacogne L., Eléments de logque floue, Pars : Hermes. ISBN , 997. [7] Osman A. et al., Improvement of X-ray castngs nspecton relablty by usng Dempster Shafer data fuson theory.pattern Recognton Letters 3, pp , 0. [8] Fuchs T., Hassler U., Huetten U., and Wenzel T., "A new system for fully automatc nspecton of dgtal flat-panel detector radographs of alumnum castngs". Proceedngs of 9th European Conference on Non- Destructve Testng (ECNDT), Sept. 5 9, 006, Berln Germany. [9] Osman A. et al., APPLICATION OF DATA FUSION THEORY AND SUPPORT VECTOR MACHINE TO X-RAY CASTINGS INSPECTION. In: 0th European Conference on Non-Destructve Testng, Moscow 00, June 7-. [0] Osman A et al., Automatc classfcaton of 3D segmented CT data usng data fuson and support vector machne. 0th Internatonal Conference on Qualty Control by Artfcal Vson QCAV'0, 8-30 June 0, Sant-Etenne France. 8