Experimental Study on Classification

Transcription

1 Chapter 7. Expermental Study on Classfcaton 7.1 Characterzaton of Explosve Materals Atomc effect number and densty Theoretcally, most explosves fall wthn a relatvely narrow wndow n Z eff and n densty, and can be dstngushed from other organc and norganc materals (see Fgure 7.1-1). For a compound materal, the effectve atomc number Z eff s the characterstc value of a hypothetcal substance havng an equvalent x-ray attenuaton effect as the compound. We assume that a materal s a unform compound consstng of M elements, havng an atomc number Z and contrbutng mass m. Z eff can be estmated wth followng formula [JOH83] [EIL96], 1/ 3.5 M M 3.5 Z eff = a Z a (7.1) = 1 = 1 where a = m Z / A, and A s the atomc weght for element. From (7.1), t s known that to estmate Z eff of a compound, we need to estmate how many elements are n the compound, what they are, and to measure or estmate the contrbutng mass of each element. It s almost mpossble to get ths nformaton by usng dual-energy transmsson and scatter x-ray

2 magng technques so far. Nor can the densty of a compound be measured drectly wth sngle vew dual-energy system. Z eff Inorganc materals Other organc materals Explosves Densty Fgure Characterzaton of common materals found n luggage Classfcaton feature space n the prototype scannng system As stated n Chapter 1, the overall goal of ths research s to develop an x-ray scannng system that uses dual-energy transmsson and scatterng to detect explosves. To realze ths goal, sx types of mages are avalable n the prototype scannng system. Rght now, four of them are processed to classfy materal types. They are, Transmsson of hgh energy: T H Transmsson of low energy: T L Chapter 7: Expermental Study on Classfcaton Page 163

3 Back scatter of low energy: B L Forward scatter of low energy: F L By combnng these sensors together, a feature vector n 2-dmensonal space ( R, L ) s formed wth Equatons 7.2 and 7.3. Any object scanned n the luggage bags wll be mapped onto ths 2-dmensonal plane. ψ R = (7.2) ψ j 2 2 ( a F + a F + b B + b B ) log 0 L 1 L 0 L 1 L L = (7.3) log( T ) L In these equatons, ψ and ψ j are the area attenuaton coeffcents, estmated by Algorthm 5.1, at low and hgh x-ray energes respectvely; a 0, a 1, b 0, and b 1 are coeffcents found n Equaton 6.12 or Equaton Actually, R s close to Z eff, and s farly good at dstngushng organc materals from norganc materals. L s related to densty, and s very effectve for separatng thn materals from thck materals. Fgure gves an example scanned from real luggage bags. In the fgure, sx explosve smulants provded by FAA are represented as +. They are smulants for hgh-densty ammona ntrate, low densty ammona ntrate, smokeless powder, black powder, semtex, and dynamte. The explosve smulants wll be descrbed further n Secton 7.3. Three step wedges, represented as o, are shown n three dfferent boxes. Other materals, such as clothes, shoes, books, plastcs, woods, toletry formulatons, chocolates, and so on, are also represented as o. We see that (R, L) s a pretty good feature space. Based on (R, L), statstcal decson rules have been developed to dstngush explosves from other materals. Chapter 7: Expermental Study on Classfcaton Page 164

4 Fgure Measurements on real luggage materals, step wedges and explosve smulants: + represents explosve smulants, o represents the other materals. Chapter 7: Expermental Study on Classfcaton Page 165

5 7.2 Test Objects Descrpton of test objects To verfy the capablty and to study the lmtatons of materal characterzaton method, experments were performed usng partcular test objects and actual passenger luggage bags, wth and wthout explosve smulants. Twenty unclamed luggage bags were purchased from a major arlne. Also, we obtaned some explosve smulants n two orders from FAA; they are plastc smulants, and explosve smulants. By nsertng dfferent objects nto these luggage bags, hundreds of expermental scenaros were created. The objects that were nserted nto bags nclude: explosve smulants, whte and clear plastc step wedges, an alumnum step wedge, a walkman player, shampoo bottles, bottles of honey, sugar, har dryers, pllows, clothes, towels, books, a steel step wedge, etc. A typcal bag s shown on Fgure 7.2-1, where (a) gves the outward appearance, and (b) shows some contents nsde. Our research efforts focused on detectng explosves n luggage. But usng real explosves as the testng objects poses serous safety concerns at a unversty. The SDA lab does not have the necessary means to obtan, transport, and store these hazardous materals. However, to perform meanngful experments some types of llct materals have to be used. Explosve smulants are beleved to be resonable substtutes for the real explosves. Explosve smulants are nert materals that exhbt accurately controlled physcal propertes. They specfcally and relably duplcate selected characterstcs, such as densty and Z eff, of real explosve materals, and those characterstcs are recognzed by usng explosve detecton technologes such as x-ray detecton technologes [EIL96] [SPA96]. Chapter 7: Expermental Study on Classfcaton Page 166

6 Rgd plastcs were also used n ths work. They have lmted usefulness n accurately smulatng explosve devces, tranng operators, and testng automated detecton systems that use x-rays. The plastc smulants n our study are shown n Fgure They have a smlar Z eff to the actual explosves, but not the same densty. Fgure shows a pcture of sx explosve smulants. They are all members of a new class of explosve smulants. These smulants are mxtures of two or more components. The nert propertes of each component have been verfed by analyses, and none of these components s regulated by the government. They closely match both the Z eff and densty of real explosves. Also snce they are all powders, ths makes them lke real explosves as well. All these smulants have demonstrated stablty of more than sx months, as long as they are approprately wrapped and stored. Descrpton of both explosve and plastc smulants s lsted n Table Table Lst of standard smulants used n the expermental study Smulant name RXN-08-AJ RXN-11-GE-AB RXN-07-AE RXN-04-AF RXN-06-AF RXN-10-AF Plastc #1 Plastc #2 Plastc #3 Plastc #4 Descrpton Smulant for smokeless powder Smulant for hgh-densty ammona ntrate Smulant for black powder Smulant for semtex Smulant for dynamte Smulant for low-densty ammona ntrate Sold square plastc object Sold square plastc object Sold square plastc object Bundle of three sold cylnder plastc objects Chapter 7: Expermental Study on Classfcaton Page 167

7 (a) (b) Fgure A typcal luggage bag used n these experments. (a) Outward appearance. (b) Contents of the bag. Chapter 7: Expermental Study on Classfcaton Page 168

8 Plastc #3 Plastc #4 Plastc #1 Plastc #2 Fgure Plastc smulants used n ths research. RXN-06-AF RXN-11-GE-AB RXN-08-AJ RXN-04-AF RXN-07-AE RXN-10-GE-AF Fgure Explosve smulants used n ths research. Chapter 7: Expermental Study on Classfcaton Page 169

9 7.2.2 Image examples collected usng the prototype scanner For each scenaro, mages were collected usng the prototype x-ray scannng system. As stated n Secton 7.1.2, these mages nclude a hgh-energy transmsson mage, a low-energy transmsson mage, a low-energy backward scatterng mage and a low-energy forward scatterng mage. Fgure shows the mages scanned for sx explosve smulants. From left to rght, they represent smokeless powder, hgh-densty ammona ntrate, black powder, semtex, dynamte, and low-densty ammona ntrate. From the fgure, we can observe that explosve smulants exhbt only a small dfference between low and hgh transmssons, and have a hgh scatterng. Ths characterzaton s what we have seen n the prevous secton, where they fall n a block havng hgher value of L n (R, L) space. Fgure gves the mages scanned for four plastc smulants. They are packaged n a typcal test bag from FAA. They have smlar characterstcs as the explosve smulants. The scatterng mages for three step wedges are gven n Fgures to Ther transmsson mages have been shown n Secton through Fgures to Step wedges are very useful to our expermental study n ths dssertaton based on the followng consderatons: 1) alumnum step wedges stand for a typcal object of norganc materal, whle whte and clear plastc step wedges are typcal objects of organc materal; 2) by consderng step wedges, we can verfy the thckness effects on both transmsson and scatter magng; 3) by usng step wedges, t s very convenent to evaluate new methods for mprovng object classfcaton (such as wth or wthout copper flter, the numercal method, and so on). Several typcal magng examples of luggage bags are gven n Fgures to Chapter 7: Expermental Study on Classfcaton Page 170

10 Fgure Images scanned for sx explosve smulants: (a) low-energy transmsson, (b) hgh-energy transmsson. Chapter 7: Expermental Study on Classfcaton Page 171

11 Fgure 7.2-4, contnued. (c) Low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 172

12 Plastc #2 Plastc #1 Plastc #3 Plastc #4 Fgure Images scanned for plastc smulants: (a) low-energy transmsson, (b) hghenergy transmsson. Chapter 7: Expermental Study on Classfcaton Page 173

13 Fgure 7.2-5, contnued. (c) Low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 174

14 Fgure Images scanned for whte plastc step wedge: (a) low-energy backward scatterng, and (b) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 175

15 Fgure Images scanned for clear plastc step wedge: (a) low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 176

16 Fgure Images scanned for alumnum step wedge: (a) low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 177

17 RXN-04-AF Steel Book Fgure Images scanned for a common luggage bag wth one explosve smulant: (a) low-energy transmsson, and (b) hgh-energy transmsson. Chapter 7: Expermental Study on Classfcaton Page 178

18 Fgure 7.2-9, contnued. (c) Low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 179

19 Alumnum step wedge Clear plastc wedge Fgure Images scanned for a common luggage bag nserted wth two step wedges: (a) low-energy transmsson, and (b) hgh-energy transmsson. Chapter 7: Expermental Study on Classfcaton Page 180

20 Fgure , contnued. (c) Low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 181

21 Wood board RXN-06-AF Fgure Images scanned for a common luggage bag wth one explosve smulant: (a) low-energy transmsson, and (b) hgh-energy transmsson. Chapter 7: Expermental Study on Classfcaton Page 182

22 Fgure , contnued. (c) low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 183

23 Chocolate bar Alumnum wedge RXN-10-AF RXN-08-AJ Fgure Images scanned for a common luggage bag wth three explosve smulants: (a) low-energy transmsson, and (b) hgh-energy transmsson. Chapter 7: Expermental Study on Classfcaton Page 184

24 Fgure , contnued. (c) Low-energy backward scatterng, and (d) low-energy forward scatterng. Chapter 7: Expermental Study on Classfcaton Page 185

25 7.3 Expermental Study on Classfcaton Bayes decson theory Bayes decson theory serves as a fundamental statstcal approach to the problem of pattern recognton. Ths approach s based on the assumpton that the decson problem s posed n probablstc terms, and that all of the relevant probabltes are known [DUD73] [SCH96] [SCH92]. We assume ths s the case n our analyss on materal characterzaton. The feature vector x, whch wll be used n analyss, combnes dual-energy and scatterng measurements, (R, L). Let ( x ) p be the probablty densty functon for x gven that the state of nature s C j, C j where C Ω = { C, C, 2, } j 1 C s, and s s the number of states of nature. In ths dssertaton, C j represents the materal type j characterzed by R and L. Then the dfference between p ( x ) and ( x ) C k materal n p descrbes how lkely that materal k may be dstngushed from C R L feature space. Suppose that we know both the a pror probablty P(C j ) and the condtonal densty ( x C j ) posteror probablty, ( C x) condtonal densty by Bayes rule [DUD73]: p. Suppose further that we measure x = ( R, L), the a P j, then can be computed from a pror probablty and ( x) P C j ( x C ) P( C ) p j j = (7.4) p ( x) where Chapter 7: Expermental Study on Classfcaton Page 186

26 p s ( x) = p( x C j ) P( C j ) j= 1 (7.5) Suppose that we observe a partcular measurement x and that we contemplate takng an acton α, where α = { α, α 2,, } A α a 1, and a s the number of possble actons. If the true state of nature s C j, we wll ncur the loss λ ( α ). Snce ( C x) C j p j s the probablty that the true state of nature s C j, the expected loss assocated wth takng acton α s s ( x) = λ( α C j ) P( C j x) Θ α (7.6) j= 1 In decson theoretc termnology, an expected loss s called a rsk, and ( α x) Θ s known as the condtonal rsk. Whenever we encounter a partcular observaton x, we can mnmze our expected loss by selectng the acton that mnmzes the condtonal rsk. Ths justfes the followng statement of the Bayes decson rule: To mnmze the overall rsk, compute the condtonal rsk ( α x) ( α x) Θ wth (7.6) for = 1, 2,, a and select the acton α for whch Θ s mnmum. Two possble actons, dentfcaton as explosves or other materals, could be taken n the context of luggage scannng Mnmum-error-rate classfcaton In classfcaton problems, each state of nature s usually assocated wth a certan class. If acton α s taken and the true state of nature s C j, then the decson s correct f n error f = j, and j. If errors are to be avoded, t s natural to seek a decson rule that mnmzes the average probablty of error,.e., the error rate. Chapter 7: Expermental Study on Classfcaton Page 187

27 A loss functon of partcular nterest for ths case s the so-called symmetrcal or zero-one loss functon [DUD73], 0 for = j λ ( α C j ) = (7.7) 1 for j Ths loss functon assgns no loss to a correct decson, and a unt loss for any error. From (7.4), the condtonal rsk s thus equal to, s ( x) = λ( α C j ) P( C j x) = 1 P( C x) Θ α (7.8) j= 1 Snce ( C x) P s the condtonal probablty that acton α s correct, the overall rsk s precsely the average probablty of error. Remember that Bayes rule mnmzes rsks by selectng the acton that mnmzes the condtonal rsk. Thus to mnmze the average probablty of error, we should select C that maxmzes the a posteror probablty ( C x) > for all j. In other words, for mnmum error rate, decde C f P( C x) P( C x) j P Classfers, dscrmnant functons and decson boundares There are many dfferent ways to represent pattern classfers. One way s n terms of a set of dscrmnant functons g (x), vector x to class C f = 1,, s, [DUD73]. The classfer s sad to assgn a feature g ( x) > g j ( x), for all j (7.9) Chapter 7: Expermental Study on Classfcaton Page 188

28 The classfer, therefore, s vewed as a machne that computes s dscrmnant functons and selects the category correspondng to the largest dscrmnant. Ths representaton of a classfer s llustrated n Fgure g 1 (x) x 1 g 1 g 2 (x) x 2 g 2 MAX α(x) x d g d (x) g s x Dscrmnant calculators Maxmum selector Decson Fgure A pattern classfer [DUD73]. A Bayes classfer can be easly represented n ths way. Generally, we can let g ( x) = Θ( α x), snce the maxmum dscrmnant functon wll then correspond to the mnmum condtonal rsk. For the mnmum error rate case, we can smplfy the expresson further by takng g x) P( C x) ( =, so that the maxmum dscrmnant functon corresponds to the maxmum a posteror probablty. It should be ponted out that the choce of the dscrmnant functons s not unque. We can always multply the dscrmnant functons by a postve constant or bas them by an addtve constant wthout nfluencng the decson. For a more general case, f we replace every g (x) by f(g (x)), the resultng classfcaton s unchanged as long as f() s a monotoncally Chapter 7: Expermental Study on Classfcaton Page 189

29 ncreasng functon. Ths observaton can lead to sgnfcant analytcal and computatonal smplfcatons. Even though the dscrmnant functons can be wrtten n a varety of forms as stated above, the decson rules are equvalent. The effect of any decson rule s to dvde the feature space nto s regons, whch can be represented as, R 1, R 2,, R s. If g ( x) > g j ( x) for all j, then we say that x s n R, and decson rule calls us to assgn x to C. The regons are separated by decson boundares, surfaces n the feature space where tes occur among the largest dscrmnant functons. If R and R j are contguous, the equaton for the decson boundary s g ( x) = g j ( x) (7.10) For ponts on the decson boundary the classfcaton s not unquely defned. Because the condtonal rsk assocated wth ether decson s the same for the Bayes classfer, t does not matter how tes are broken Classfcaton rules n the prototype x-ray magng system The two-category classfcaton problem s merely a partcular case of above dscusson, where Ω = { } and A = { } C 1,C 2 α 1,α 2. Let C 2 be explosves and C 1 stand for other materals, suppose we want to detect C 2 from C 1 ; then under the assumptons stated earler Θ( α x ) s the probablty of mssed detecton, and ( x ) rate. 1 C 2 Θ α 2 C 1 s the false alarm In ths dssertaton, a statstcally determned decson boundary s used to dstngush explosves from other materals. From theoretcal analyss and expermental measurements, t Chapter 7: Expermental Study on Classfcaton Page 190

30 s known that: 1) explosves fall n a regon of the ( R, L) space, not a pont; 2) we have only a lmted set of testng materals, both explosve smulants and nnocent materals; 3) decson surfaces of separatng explosves from other materals are not convex. So the proposed classfcaton procedure s as follows: Threshold on transmsson magng. A threshold s selected for removng the objects exhbtng hgh attenuaton. Ths may be caused ether by hgh Z materals or by very thck low Z materals. In ths case, x-rays are not strong enough to penetrate the materal, resultng n a bgger error. Dscrmnant functons. There are only two dscrmnant functons for our case. They are g ( x) = p( x C ) P( C ) and ( x) p( x C ) P( ) g = respectvely. The a 2 2 C2 pror probablty P(C j ) can be selected as follows: 1) for the system test at laboratores, we can set P ( C ) = P( C ) =, whch means that explosves and other materals are equally lkely to appear n luggage bags; 2) for the luggage scannng at arports, we may select ( C ) P( ) P >, dependng on the rsks of 1 C 2 mssed detecton and false alarm. The dscrmnant functon g (x), therefore, s only determned by the probablty densty functon p x C ). ( Decson boundary. Two methods have been used to desgn decson boundares n ths research. 1) Under the assumpton of normal dstrbutons, t s possble to estmate the parameters of p x C ) by usng the measurement data. The ( j procedure s as follows: (a) compute the mean values µ j and covarance matrx Ω j for both classes: explosves and other materals; (b) obtan the normal densty functons p(x C j ); (c) draw the decson boundary, whch satsfes p(x C 1 ) = p(x C 2 ). In Secton 7.3-5, a decson boundary based on the approach above wll be shown as an example. 2) A pecewse lnear boundary can also be used to dstngush explosves from other materals. The reason to use pecewse lnes s that t provdes us a way to treat concave decson regons. The pecewse lnes Chapter 7: Expermental Study on Classfcaton Page 191

31 used n ths research were selected manually based on the actual measurement data. Ths method s not further dscussed n the dssertaton Classfcaton results As stated above, by nsertng the explosve smulants nto common bags, we can nvestgate object classfcaton under varous scenaros. More than one hundred scenaros were created and scanned to verfy the performance of the prototype x-ray scannng system. Some typcal mage examples scanned by usng the prototype scannng system have been shown n Secton The dual-energy and scatter-energy values for some materals are gven n the followng tables. Table shows observed transmsson and scatter values as well as the computed (R, L) values for sx explosve smulants (mages gven n Fgure 7.2-4). The transmssons and scatters as well as the computed (R, L) values for three step wedges are shown n Tables to (see Fgures to for scatter mages, and Fgures to for transmsson mages). Wth (R, L) values gven n Tables to 7.3-4, we wll show an example to derve the decson rules based on our dscusson n Secton Let s consder the 2-class case as follows, explosve materals (C 2 : data gven n Table 7.3-1) and other organc materals (C 1 : data gven n Tables and 7.3-4). Inorganc materals, such as alumnum, are not ncluded n our dscusson because t can be easly elmnated by pre-usng a pece-wse lne boundary due to ther bg dstance to explosve materals. Chapter 7: Expermental Study on Classfcaton Page 192

32 Table R and L values for sx explosve smulants. Smulants T L T H B L F L R L Smokeless powder Ammona ntrate (hgh densty) Black powder Semtex Dynamte Ammona ntrate (low densty) Table R and L values for alumnum step wedge. Thckness (cm) T L T H B L F L R L Chapter 7: Expermental Study on Classfcaton Page 193

33 Table R and L values for clear plastc step wedge. Thckness (cm) T L T H B L F L R L Chapter 7: Expermental Study on Classfcaton Page 194

34 Table R and L values for whte plastc step wedge. Thckness (cm) T L T H B L F L R L Chapter 7: Expermental Study on Classfcaton Page 195

35 (1) Normal densty functons For a two-dmensonal varable x [ x x ] T 1 2 normal densty functon p ( x) can be wrtten as follows: =, ts mean value µ, covarance matrx Ω, and µ = [ µ ] T 1 µ 2 (7.11) where N 1 µ =, and N s the number of samples; x j N j= 1 ω Ω = ω ω12 ω 22 (7.12) N 1 where ω ( x µ )( x µ ) kl = N 1 j= 1 kj k lj l ; p ( x) = 1 1 T 1 exp ( x µ ) Ω ( x µ ) (7.13) 1 / 2 2π Ω 2 (2) Dscrmnant functon The dscrmnant functon for class can be obtaned by takng logarthm on (7.13) and by removng the constant away from the equaton, yeldng, Chapter 7: Expermental Study on Classfcaton Page 196

36 T T g ( x) x W x + w x + w0 = (7.14) 1 where W = Ω, w 1 T 1 = 2 Ω µ, and w = µ Ω µ log( Ω ). 0 (3) Decson boundary For class C 1 : other organc materals, ts mean value µ 1 and covarance matrx Ω 1 can be obtaned drectly by usng (7.11) and (7.12): µ 1R µ 1 = = (7.15) µ 1L Ω1 = (7.16) For class C 2 : explosve materals, we have, µ 2R µ 2 = = (7.17) µ 2L Ω 2 = (7.18) By submttng Equatons (7.15) and (7.16) nto (7.14), we obtan the dscrmnant functon g ( R, ) for class 1, 1 L Chapter 7: Expermental Study on Classfcaton Page 197

37 g ( R, L) R L RL R L = (7.19) Smlarly we have g ( R, ) for class 2, 2 L 2 2 ( R, L) = R L RL R L g (7.20) 2 The decson boundary s therefore obtaned wth g R, L) g ( R, L) 0, yeldng, 2 ( 1 = 2 2 D ( R, L) = R L RL R L = 0 (7.21) (4) Decson rules Equatons (7.19) and (7.20) represent two ellpses n 2-dmensonal space. The te between them results n a hyperbola (7.21). The decson rules therefore can be stated as follows: for any object havng a (R, L) value, f ts D ( R, L) s greater than zero, we decde t as explosve materals (shown as dark area n Fgure 7.3-4); otherwse t s decded to be other organc materals. We started our test wth smple luggage bags, then wth overlappng materals havng regular shapes, fnally wth overlappng materals havng rregular shapes. The probablty of correct classfcaton was mproved to 82% based on lab verfcatons from system group. By correct classfcaton t means that no explosves mssed detecton, and no other types of materals were dentfed as threat. It should be noted that to acheve a good performance, every part n the prototype system should work properly. Durng our expermental study on object classfcaton for real luggage, t was found that the major problem les wth overlappng objects, where the true Chapter 7: Expermental Study on Classfcaton Page 198

38 sgnal ntensty of transmsson and scatter mages should be unquely provded for each object. More analyss on ths ssue s avalable n [LU99]. Also, we found that there s some overlap between nnocent artcles and the compostons of explosve smulants, for example, between whte plastc and smokeless powder. Therefore, we are not surprsed that plastc s used as an explosve smulant adopted by FAA. Fgure An example on decson boundary for dscrmnatng two-class materals. Chapter 7: Expermental Study on Classfcaton Page 199