Chapter 5 THE MODULE FOR DETERMINING AN OBJECT S TRUE GRAY LEVELS

Transcription

1 Qian u Chapter 5. Determinin an Object s True Gray evels 3 Chapter 5 THE MODUE OR DETERMNNG AN OJECT S TRUE GRAY EVES This chapter discusses the module for determinin an object s true ray levels. To compute the true ray levels of an object of interest requires the removal of the overlappin backround effects. This problem is quite complex and takes several steps to be resolved. irst in Section 5., it will be shown that an n-object-overlappin problem can always be simplified to a two-object-overlappin problem. So the research focus turns to computin true ray levels for two-object-overlappin problem. Since there is no existin method for accomplishin this task in either the transmission or the scatter imae modalities, it was necessary to develop models that can be used to remove the backround object overlappin effects. Section 5. discusses the development of the mathematical models for removin the overlappin effects for the transmission modalities. Section 5.3 discusses the models for the forward-scatter modality. Section 5.4 discusses the models for the backscatter modality and summarizes the mathematical model development. n luae inspection, it is difficult to identify the correct object that is overlapped with the object of interest. Section 5.5 analyzes the luae inspection problem, and ives an alorithm that determines the true ray level of an object of interest in the luae environment. Section 5.6 concludes this chapter. This chapter documents this research work, which is a unique contribution to the explosive detection community.

2 Qian u Chapter 5. Determinin an Object s True Gray evels 3 5. The asic Method for Removin Overlappin Effects This section beins by illustratin the method for determinin the true ray level of an object of interest when it only overlaps with another object. t will show that an n-objectoverlappin problem can always be simplified to a two-object-overlappin problem. So bein able to determine the true ray level in a two-object-overlappin problem means the ability to determine the true ray level in any overlappin problem. iure 5.- illustrates the method for determinin the true ray level in a two-objectoverlappin problem. n this fiure, several symbols are used. Symbol Obj refers to an object. Obj is the object of interest, and Obj is the backround object that overlaps with Obj. Symbol refers to a reion in an x-ray imae. is a reion uniquely formed by Obj ; is a reion uniquely formed by Obj ; and 3 is the reion formed by Obj overlappin with Obj. Please note that ray level is used in sinular form because the discussion here assumes to be in one sensin modality rather than in all four sensin modalities. Also the sementation alorithm has semented an imae into reions with relatively uniform ray levels. Thus each reion can be characterized usin its averae ray level.

3 Qian u Chapter 5. Determinin an Object s True Gray evels 3 Obj Obj X-ray Source (b) 3 (a) Obj Obj X-ray Source (c) iure 5.- llustration of two-object-overlappin scenarios. a) Three reions are formed in the projected x-ray imae. and are formed by Obj and Obj respectively. 3 is formed by Obj overlappin with Obj. b) Obj may be in front of Obj. c) Obj may be behind of Obj.

4 Qian u Chapter 5. Determinin an Object s True Gray evels 33 The averae ray level of is the true ray level of Obj. A typical two-objectoverlappin scenario is that does not appear in an imae, and only the overlapped reion 3 and the backround object reion appear. Thus the averae ray level of cannot be directly measured. ortunately there is a fixed relationship between the ray level of 3 and the true ray levels of Obj and Obj. rom Section 5. to Section 5.4 mathematical equations are established to model this relationship for the different sensin modalities. Those mathematical equations are called overlap models. Each model allows the computation of the ray level of the overlapped reion 3 in an imain modality usin the true ray levels of Obj and Obj. Most importantly, each model, after careful manipulation, also allows the computation of the true ray level of Obj once the ray level of 3 and the true ray level of Obj are known. Usin these models, the overlappin effects are removed from the object of interest, and the true ray levels can be computed for the object of interest in all four sensin modalities. Due to x-ray physics, the relative positions of Obj to Obj makes no difference in the transmission modality. t does make difference in the either scatter modality. So there should be one model for low-enery transmission modality; one model for hih-enery transmission modality; two models for forward scatter modality; and two models for backscatter modality. To understand that all overlappin problems can be simplified to a two-objectoverlappin problem, first, a three-object-overlappin problem is examined. Assume that three objects are overlapped as seen in iure 5.-. Since is formed by Obj overlaps with Obj 3, Obj and Obj 3 toether can be viewed as one pseudo-object Obj rather than two separate objects. This pseudo-object overlaps with Obj, and it also forms a neihborin reion. The true ray level of Obj can be directly measured at reion without the knowlede of true ray levels from either Obj or Obj 3. Since the imae reion is formed by Obj overlapped Obj, by removin the overlappin effects caused by Obj, the true ray level of Obj is revealed. The three-objectoverlappin problem is thus simplified to a two-object-overlappin problem.

5 Qian u Chapter 5. Determinin an Object s True Gray evels 34 3 (a) Obj 3 Obj Obj (b) iure 5.- llustration of a three-object-overlappin problem. a) The imae reions that are formed by three overlapped objects. b) The three objects that are overlapped.

6 Qian u Chapter 5. Determinin an Object s True Gray evels 35 The simplification procedure is enerally true for any n-object-overlappin problem. When an object of interest is overlapped with (n-) objects, those (n-) objects can always be considered as one pseudo-object. The true ray level of this pseudo-object can always be measured from one of the neihborin reions. y removin the overlappin effect caused by this pseudo-object, the true ray level of the object of interest is revealed. The n-object-overlappin problem is thus simplified to a two-objectoverlappin problem. 5. Transmission Overlap Models n eneral, the method for developin an overlap mathematical model for a certain sensin modality is as follows. irst, a mathematical model is established to formulate the overlappin relationship. Each mathematical model contains undefined constants. A number of overlappin experiments was desined to obtain the data that can later be used to define values for those constants. Note that the physical interactions that are occurrin can be quite complex. However, the purpose for the model development is to compute true ray levels of object of interest in real-time. Consequently each model must be mathematically simple. efore ettin into the discussion of the development of the low-enery transmission overlap model, it is important to know the relationship between the x-ray sinal intensity and imae ray level. All the x-ray physics analysis that is used to establish the overlap models is in terms of x-ray beam intensity. However, the AS&E system can only collect x-ray imaes that are in terms of pixel ray levels. n order to find the values for the constants in those mathematical models, ray levels must be converted to x-ray intensities. n order to use the overlap models to compute the true ray levels of an object of interest, the models must be converted into equations that are in terms of ray levels. n Section 3.3 it was found that imae ray level is a linear function of x-ray sinal intensity:

7 Qian u Chapter 5. Determinin an Object s True Gray evels 36 = c (3.3-6) where is the ray level of a pixel, is the x-ray beam intensity, and c is a conversion constant. The value of c is different for different sensin modalities. So for different sensin modalities: H H H = c (5.-) = c (5.-) = c (5.-3) = c (5.-4) where c H, c, c, and c are the conversion constants for hih-enery transmission, lowenery transmission, forward scatter, and backscatter modalities respectively. Those constants need not to be solved, because they are eventually canceled out in the derivation. Also, in transmission modalities, the ray level of an incident x-ray beam is 55, thus: H c H = 55 (5.-5) c = 55 (5.-6) where H and are the intensity of the hih- and low-enery incident x-ray beams respectively. n low-enery transmission modality, when the incident x-ray beam an object, its intensity is reduced to: traverses throuh σnx = e (5.-7)

8 Qian u Chapter 5. Determinin an Object s True Gray evels 37 The attenuation coefficient e σnx of this object is computed as: σnx e = (5.-8) et us examine the two-object-overlappin problem as seen in iure 5.-. or convenience, denote the overlapped reion as, and its x-ray intensity as. The attenuation coefficients of Obj and Obj are n e σ x nx and e σ intensity at the overlapped reion can be computed as: respectively. The x-ray σn x σ nx = e e (5.-9) The attenuation coefficient n e σ x can be computed as e σ n x, and can be computed as, where is the x-ray intensity after interacts with Obj, and is the x-ray intensity after reion can also be written as interacts with Obj. So the x-ray intensity at the overlapped ( )( ) = (5.-) Since x-ray intensities cannot be directly measured but ray levels can, the above equation must be converted to a form for ray levels. So the ray level of reion becomes = = = = = = c c σ nx e c ( )( ) c ( c c )( c c ) ( c )( c ) c 55 e σ nx (5.-)

9 Qian u Chapter 5. Determinin an Object s True Gray evels 38 where and are the true ray levels of Obj and Obj respectively. This equation establishes the relationship between the ray level of the overlapped reion and the true ray levels of objects that form this reion. Knowin the true ray levels of the objects, the ray level of the overlapped reion can be computed. Knowin the ray level of the overlapped reion and the true ray level of one of the object, the true ray level of another object can be computed. Equation 5.- is derived under the assumption that the x-ray source is a monochromatic source. However the x-ray source of AS&E system is polychromatic. To account for the polychromatic x-ray source spectrum, a constant a is added to Equation 5.-. The modified equation becomes: = a (5.-) 55 Constant a is then computed usin experimental data. Experimental data are collected from three step wedes a clear plastic step wede, an alumni step wede, and a white plastic step wede. A step wede is shown at the top part of iure 5.-. Each step is treated as an individual object. The averae ray level is computed for each step in order to remove the noise in the imae. Table 5.- lists the thickness of each step for each step wede. Table 5.- lists the averae ray levels of each step. Assume the step wede shown in iure 5.- is a clear plastic step wede. The thickness of step is.6 cm; the thickness of step 3 is.8 cm; and the thickness of step 4 is.4 cm. f step is considered as Obj, step 3 is considered as Obj, then step 4 can be considered as the overlapped object formed by Obj and Obj. This is because the thickness of step 4 is equal to the thickness of step plus the thickness of step 3, and step 4 is made of the same material as step and 3. So by measurin the ray levels of step, 3, and 4, measured.,, and can be

10 Qian u Chapter 5. Determinin an Object s True Gray evels 39 A step wede + = Step Av: 5 Step 3 Av: 74 Step 4 Av: 57 iure 5.- llustration of data collection from a step wede.

11 Qian u Chapter 5. Determinin an Object s True Gray evels 4 Table 5.- Thickness of each step of each step wede Step Number Clear Plastics (cm) White Plastics (cm) Aluminium (cm) Table 5.- True ray levels of steps in low-enery transmission modality Step Number Clear Plastics White Plastics Aluminium

12 Qian u Chapter 5. Determinin an Object s True Gray evels 4 Applyin the same techniques to the steps of all three step wedes, one can et 8 sets of experimental data, and each set contains used, a can be computed as,, and. f only one set of data is a 55 = (5.-3) To minimize the error, all 8 sets of data are used to compute a. The formula used is a = n 55 n (5.-4) where n is the number of sets of data that are used for computin a. n this case, n is equal to 8. After computation, a is found to be.898. n order to determine the precision of Equation 5.-, the experimental data are collected from real-world objects as well as from the previously described step wedes. The real world objects included books, explosive simulants, Walkman cassette players, shampoo bottles, etc. The averae ray level is computed for each object. An object, such as a book, is then overlapped with another object, such as a cassette player to form an object overlapped imae reion. The averae ray level of this overlapped reion is then measured. Usin Equation 5.- and the true ray levels of objects, a ray level is computed for this overlapped reion. The error is computed usin the followin equation: a err = 55 % (5.-5)

13 Qian u Chapter 5. Determinin an Object s True Gray evels 4 Table 5.-3 ives some of the results obtained from this experiment. Column is the ray level of Obj ; column is the ray level of Obj ; column 3 is the measured ray level of the overlapped reion ; column 4 is the computed ray level of reion ; and column 5 is the errors computed usin Equation The mathematical model of Equation 5.- is quite precise in computin the ray levels for the overlapped reion. or the 4 sets of data collected from the step wedes and the real-world objects, the errors are less than 4% for all the data sets. or some data sets, the errors are less than %. Equation 5.- can only be used to predict the ray level of an overlapped imae reion. Now, this equation is manipulated so that once the ray level of the overlapped reion and the true ray level of the overlappin backround object Obj are known, the true ray level of the object of interest Obj can be correctly computed. The equation for computin the true ray level of Obj is as follows: = 55 (5.-6) a One way to verify the precision of Equation 5.-6 is to use a step wede, for example, the clear step wede as seen in iure 5.-. Step 3 can be seen as step overlaps with step. So knowin the ray level of step and 3, the true ray level of step can be computed usin Equation n iure 5.-, the measured ray level of step is 5; the computed true ray levels usin step is 9, step 3 is, step 4 is, step 5 is 3, step 6 is, step 7 is, and step 8 is 4. The verification in this case shows that the precision of Equation 5.-6 is quite hih. This is enerally true for the other data sets that were collected.

14 Qian u Chapter 5. Determinin an Object s True Gray evels 43 Table 5.-3 Computed ray levels of an overlapped reion vs. the measured ray levels for some real-world objects in low-enery transmission modality Errors a % % % % % % % % % % % % % % % % % % % % % % % % % % % %

15 Qian u Chapter 5. Determinin an Object s True Gray evels 44 The derivation process of the overlap model for the hih-enery transmission modality is exactly the same done for the low-enery transmission modality. The resultin equation is H H H H = a (5.-7) 55 where H is the true ray level of Obj, the object of interest; of Obj, the backround overlappin object. H is the true ray level H is the ray level of the overlapped reion that is formed by Obj overlappin with Obj. a H was found to be.46 usin experimental data that were collected and processed the same way as in low-enery transmission case. Table 5.-4 ives some of the results obtained from the experiment in hih-enery transmission modality. or the 4 sets of data collected from the step wedes and the real-world objects, the error of this formula is less than %. The error rate in hih-enery transmission modality is smaller than in low-enery transmission modality because hih-enery transmission imaes are less noisy than low-enery transmission imaes. To compute the true ray level of Obj, the followin equation can be used H H 55 =. (5.-8) H a H The precision of Equation 5.-8 is also verified usin a similar technique that was used in the low-enery transmission. Equation 5.-8 is quite accurate in determinin an object s true ray levels.

16 Qian u Chapter 5. Determinin an Object s True Gray evels Step Computed ray levels Measured ray level: 5 iure 5.- Results of the computed ray levels for step of a clear plastics step wede in low-enery transmission modality.

17 Qian u Chapter 5. Determinin an Object s True Gray evels 46 Table 5.-4 Computed ray levels of an overlapped reion vs. the measured ray levels for some real-world objects in hih-enery transmission modality H H H H H H Errors a % % % % % % % % % % % % % % % % % % % % % % % % % % % %

18 Qian u Chapter 5. Determinin an Object s True Gray evels orward-scatter Overlap Models The mathematical models for forward-scatter and backscatter overlap models are much more complicated than transmission overlap models. However, these formulas can still be derived in a similar manner as was employed to create transmission models. The undefined constants in the scatter overlap models can then be defined usin experimental data. The accuracy of each formula is verified usin more experimental data. n forward-scatter modality, there are two different cases when two objects are overlapped. n case, Obj is in front of Obj as seen in iure 5.- (b). n case, Obj is behind Obj as seen in iure 5.- (c). et us bein with the derivation of the mathematical formula for case from the analysis model as seen in iure The followin is a list of symbols used in the analysis model: Obj The object of interest. Obj The overlappin backround object. The intensity of the incident x-ray beam. The transmission intensity after The forward scatter intensity after The transmission intensity after The forward scatter intensity after a The transmission intensity after a The forward scatter intensity after b The sinal of scatter sinal. c The sinal of traverses throuh Obj. traverses throuh Obj. traverses throuh Obj. traverses throuh Obj. traverses throuh Obj. traverses throuh Obj. bein transmitted throuh Obj. t is still a forward bein scattered by Obj. t is a forward scatter sinal. The forward scatter intensity of the overlapped reion.

19 Qian u Chapter 5. Determinin an Object s True Gray evels 48 Obj a a b Obj c iure 5.3- Analysis model for forward-scatter modality when two objects are overlapped. This fiure shows the end view of the two objects Obj and Obj, where Obj is closer to the x-ray source than Obj.

20 Qian u Chapter 5. Determinin an Object s True Gray evels 49 This analysis model tries to resolve one issue: with knowlede of and from Obj, and and from Obj, how can the forward-scatter x-ray intensity for the overlapped reion be computed when Obj is overlapped with Obj, and Obj is closer to the x-ray source. The assumption is that reardless of the intensity and types of incident x-ray beams, the portions of the x-ray intensity that are bein transmitted and forward scattered by Obj remain constant. The portion bein transmitted can be computed as. The portion bein forward scattered can be computed as. When a beam of x-ray first traverses throuh Obj, then traverses throuh Obj, the followin process happens. The incident x-ray beam interacts with Obj, yields a transmission sinal, and a forward scatter sinal in the forward direction. The transmission sinal interacts with Obj and yields a transmission sinal a and a forward scatter sinal a. The forward scatter sinal interacts with Obj, the sinal bein transmitted when traversin throuh Obj is b, which is still a forward-scatter sinal; and the sinal bein forward scattered by Obj is c., where can be computed as a is the fraction of incident x-ray that is forward scattered. is the incident x-ray beam to Obj, and b can be computed as, where is the incident x-ray forward scatter enery to Obj, and is the fraction of the scattered sinal that is transmitted by Obj. c can be computed as scattered by Obj., where is the fraction of the scattered sinal that is

21 Qian u Chapter 5. Determinin an Object s True Gray evels 5 Thus, the combination of the sinal ( ) c b + can be computed as ( ) +, where and are two constants used to calibrate the results. The calibration is needed because the x-ray source is not an ideal parallel source, and the eometry of the forward-scatter detectors needs to be considered as well. ( ) + is used to account for the non-linear part of the sinal ( ) c b + that is inored by ( ) +. n summary,, the forward scatter intensity of the overlapped reion is the summation of a, b, and c. t can be computed as: ( ) ( ) c b a β β β β β = = + + = (5.3-) The last line of this equation is the expansion of the next to last line. Since the terms of and do not contribute much to the overall computation of, they are inored. After simplification of Equation 5.3-, the equation becomes: = (5.3-) When converted in the form of ray levels, Equation 5.3- becomes:

22 Qian u Chapter 5. Determinin an Object s True Gray evels = (5.3-3) where is the true transmission ray level of Obj ; is the true forward-scatter ray level of Obj. is the true transmission ray level of Obj. is the true forward scatter ray level of Obj. is the computed ray level of the overlapped reion. Note: the conversion factors c and c have been absorbed into,, and 3. The values of,, and 3 are computed usin the experimental data collected from the three step wedes. The method for data collection from those three step wedes is almost exactly the same as the method used in the transmission modality. The difference is that for each step of a step wede, the averae ray level in low-enery transmission modality is measured; the averae ray level in the forward-scatter modality is also measured. So each set of data is comprised by six ray levels:,,,,, and. 8 sets of those data are collected from three step wedes. Usin least-squareerror fittin method, the values of those constants are found to be =.8, =.3, and 3 =.6. iure 5.3- shows the comparison between the measured and the computed for some steps of a white plastic step wede. The errors in this case are very small. Equation works well with materials such as white plastics. What is particularly interestin is that this equation successfully predicted that the ray level decrease when the thickness of the object increases beyond a certain threshold. This prediction can be observed in iure Note: the larer the step number is, the thicker the overlapped reion.

23 Qian u Chapter 5. Determinin an Object s True Gray evels 5 5 Gray evel 5 5 Measured Computed Set Step Number number iure 5.3- Comparison between the measured ray level of the overlapped reion and the computed ray level of for some steps of a white plastic step wede in the forward scatter modality.

24 Qian u Chapter 5. Determinin an Object s True Gray evels 53 However, Equation does not work well with other materials. or some real-world objects that were tested, the computation error is reater than 5%. Some of the results are shown later in this section. There are many sources that miht contribute to this error. or example, the x-ray source is not an ideal parallel source. The detector eometry affects the collection of forward-scatter x-ray sinals. t was assumed that the fraction of the incident x-ray bein transmitted or forward scattered is constant. This may only be true in the first order approximation, but not in hiher orders. The noise of the forward scatter imaes is sinificantly larer than the transmission imaes. This may affect the precise computation of imae ray levels. The scattered radiation has a lower frequency than the transmission wavelenth and hence has less penetration power. Thus the fraction of a forward scattered sinal that is bein forward scattered should not be the same as the fraction of a transmitted sinal that is bein forward scattered. Unfortunately, there is no way that the first fraction can be directly measured or derived in the current experimental condition. One less perfect solution is to assume that those two fractions are the same. This assumption may have contributed sinificant amount of computation error to the overlap model. Due to the limitation of our equipment and fundin, it is difficult to quantify the amount of error that each of the above sources is likely to contribute. This forward scatter overlappin model can be further improved if one has the ability to determine the major source of error and to fix the model in that aspect. This mathematical model can also be improved if for different material or object thickness, different equations are used. However, refinin this model is beyond the scope of this research. t can be done if there is enouh fundin to support another 3 or 4 year of research. Usin Equation 5.3-4, the backround overlap effect can be eliminated thouh the computation may not be that accurate. Assume Obj is the object of interest, and Obj is the backround overlap object. Assume that the true transmission ray level of Obj is known; the true forward-scatter ray level of Obj is known; the forward-scatter

25 Qian u Chapter 5. Determinin an Object s True Gray evels 54 ray level of the overlapped reion is also known. The true transmission ray level of Obj can be computed usin Equation The true forward-scatter ray level of Obj can be computed as: = (5.3-4) + 3 The forward-scatter overlap model for case of the two-object-overlap problem can be derived in a similar manner. The mathematical model that results is: = (5.3-5) where =.8, =.3, and 3 =.6. The accuracy of this equation is the same as the accuracy of Equation y manipulatin this equation, the true forwardscatter ray level of Obj can be computed: = (5.3-6) + 3 Apparently, since Equation and are not very accurate in modelin forwardscatter overlap, the true ray levels computed usin Equation and are not very accurate either. Table 5.3- shows the computed true ray levels vs. the measured true ray levels for some objects of interest usin Equations and Column is the ray level of the overlapped reion formed by an object of interest and another backround object. Column is the measured true ray level of that object of interest. Column 3 is the computed true ray level of the objects of interest.

26 Qian u Chapter 5. Determinin an Object s True Gray evels 55 Table 5.3- Computed true ray levels of an object of interest vs. the measured true ray levels for some real-world objects in forward scatter modality ~ Errors % % % % % % % % % % % % % % % % % 8 3.6% % % %

27 Qian u Chapter 5. Determinin an Object s True Gray evels 56 Column 4 is the error of computation calculated usin the followin equation: ~ err = % (5.3-7) where ~ is the measured true ray level of the object of interest. y examinin Column 4 in Table 5.3-, one may find that althouh most computation errors are within %, but some of the computation errors are over %. The error is too lare for accurate true ray level computations. However, when the data in Column and the data in Column are carefully compared, one can easily see that the measured ray level at an overlapped reion is sinificantly different from the measured true ray level of the object of interest. The ray level at Column cannot be used to represent the true ray level of an object of interest. The computed true ray level shown at Column 3 is much closer to the measured true ray level shown at Column. Althouh the errors of this model are still too lare, the development of such a model represents a step forward. urther improvement to this model will not only benefit the true ray level computation, it will also directly contribute to the material characterization usin R- plane method. 5.4 ackscatter Overlap Models iure 5.4- shows the analysis model for case of the two-object-overlap problem, which is described in iure 5.-. Obj is closer to the x-ray source than Obj. The followin is a list of symbols used in the analysis model: The intensity of the backscattered sinal after The intensity of the backscattered sinal after a The intensity of the backscattered sinal after Obj. interacts with Obj. interacts with Obj. and interacts with

28 Qian u Chapter 5. Determinin an Object s True Gray evels 57 a The intensity of the backscattered sinal after a interacts with Obj. The intensity of the backscattered sinal of the overlapped reion. The assumption in this model is that reardless of the intensity and type of incident x-ray beam, the fractions of sinal bein transmitted and forward scattered by Obj remain constant; the fraction of sinal bein backscattered by Obj remain constant as well. The faction of sinal that is transmitted by Obj can be computed as. The faction of sinal that is forward scattered by Obj can be computed as. The fraction of sinal that is backscattered by Obj can be computed as. The backscatter process of two objects in an overlappin situation can be explained as follows. When the incident x-ray beam interacts with Obj, the sinal bein backscattered by Obj is ; the sinal bein transmitted is ; and the sinal bein forward scattered is. The incident x-ray to Obj is ( ) +. The sinal bein backscattered by Obj is a. a becomes the incident x-ray to Obj. The sinal bein transmitted and forward scattered is ( ) a +. a. So the total backscattered sinal is equal to Sinal a can be computed as the summation of a and a, where is the fraction of a that is bein transmitted by Obj, and bein forward scattered by Obj. is the fraction of a that is Sinal can be computed as ( ) a +, where ( ) + is the incident sinal to Obj, and is the fraction of sinal bein backscattered by Obj.

29 Qian u Chapter 5. Determinin an Object s True Gray evels 58 Obj a a Obj iure 5.4- Analysis model for backscatter modality when two objects are overlapped. This fiure shows the end view of Obj and Obj, where Obj is the object of interest, and is closer to the x-ray source than Obj.

30 Qian u Chapter 5. Determinin an Object s True Gray evels 59 Sinal, the backscatter sinal of the overlapped reion can be computed as the summation of ( ) a +. Now the mathematical model can be written as follows: = = = = β a a + a ( + ) + ( + ) ( ) + β + β ( ) 3 (5.4-) Due to system noise and some other factors, the results computed for the sinal backscattered by Obj need some calibration. and are the two constants used to calibrate the results. Row four of this equation is the expansion of row three. Equation 5.4- is then converted in the form of ray levels. The conversion factors c, c, and c are absorbed into,, and 3. The equation can then be written as: ( ) + ( ) = (5.4-) Usin a manner similar to both transmission and forward scatter model development, 8 sets of data were collected from the three step wedes. Each set of data contains 9 ray levels. or Obj, the ray levels include the true transmission ray level ; the true forward-scatter ray level ; and the true backscatter ray level. or Obj, the ray levels include the true transmission ray level ; the true forward-scatter ray level ; and the true backscatter ray level. or the overlapped reion, the ray levels include the true transmission ray level ; the true forward-scatter ray level ; and the true backscatter ray level. Usin this data the constants,,

31 Qian u Chapter 5. Determinin an Object s True Gray evels 6 and 3 can be determined usin a least-square method. They are found to be =.476, =-.639, and 3 =.38. iure 5.4- shows the comparison between the measured and the computed for some steps of a white plastic step wede. The errors in this case are extremely small; but this is not enerally true for many other objects that were tested. n some cases, Equation 5.4- has computation errors that are reater than %. Some of the computation results are shown later in this section. The sources of error are basic the same as in the forward-scatter modality. n addition, the computation of true ray level in backscatter modality relies on the knowlede of true ray level in forward scatter modality. Since no accurate true ray level in forward scatter modality can be calculated, the true ray level in backscatter modality cannot be accurate calculated. The solutions to improve this model are also the same as in the forward-scatter modality. Assume Obj is the object of interest, and Obj is its overlappin backround object. After manipulatin Equation 5.4-, the followin equation is used for compute the true backscatter ray level of Obj for case of the two-object-overlappin problem: ( + ) 3 = (5.4-3) Assume now Obj is further to the x-ray source than Obj. This is case of the twoobject-overlappin problem, as seen in iure 5.- (c). Usin similar manner, the equation for computin the true backscatter ray level of Obj can be derived. The equation is as follows: = (5.4-4) + + 3

32 Qian u Chapter 5. Determinin an Object s True Gray evels 6 5 Gray evel 5 5 Measured Computed Set Number Step number iure 5.4- Comparison between the measured ray level of the overlapped reion and the computed ray level of for some steps of a white plastic step wede in the forward-scatter modality.

33 Qian u Chapter 5. Determinin an Object s True Gray evels 6 Since the mathematical overlap models for backscatter modality are not very accurate, the true backscatter ray levels that are computed usin Equation and are not very accurate either. Table 5.4- shows some computation results usin the backscatter overlappin models. Column is the measured ray level of the overlapped reion that is formed by an object of interest and its backround object. Column is the measured true ray level of an object of interest. Column 3 is the computed true ray level of an object of interest. Column 4 is the computation error that is calculated usin the followin equation: ~ err = % (5.4-5) where ~ is the measured true ray level of the object of interest. Most of the computation errors are over %. However, most of the errors may have been caused by not knowin the accurate true ray levels in forward scatter modality. t is author s belief that if the accurate true ray level in forward scatter modality can be computed, the error of the backscatter overlap model should be less than %. n summary, from Section 5. to Section 5.4, the discussion has focused on developin models for the two-object-overlap problems. There is a model for each sensin modality. Each model is first derived usin mathematical formulas with undefined constants. The values of those constants are then computed usin experimental data collected from the three step wedes. The accuracy of each model is then verified usin real-world objects. The transmission overlap models work quite precise. The forward scatter and backscatter overlap models need further refinement, since the scatter models are just a st order approximation. However, to refine those models is beyond the scope of this study; it can be done, but would take some considerable effort.

34 Qian u Chapter 5. Determinin an Object s True Gray evels 63 Table 5.4- Computed true ray levels of an object of interest vs. the measured true ray levels for some real-world objects in backscatter modality ~ Errors % % % % % % % % % % % % %

35 Qian u Chapter 5. Determinin an Object s True Gray evels The Alorithm for Determinin the Object s True Gray evels n this section, the alorithm for computin the true ray levels of an object of interest is discussed in detail. irst, a brief introduction is iven here as the backround to the alorithm development. As discussed earlier in Section 4.4, an object of interest Obj is more likely to be semented into several different reions in bl m, for example,, etc.; but Obj is more likely to be semented into one object in bl m Obj. bl m and bl m Obj are perfectly spatially reistered. f a reion in bl m have 7% of its pixels belonin to Obj, this reion should be part of Obj. Usin this method, and other reions that belon to Obj are identified and rouped. n other words, semented labeled components in bl m can be referred as reions, and each component is denoted by. Semented labeled components in bl m Obj can be referred as objects, and each component is denoted by Obj. or each reion, an object Obj can always be found where Obj. t is impossible to correctly resolve the overlap problem since one can never know from a -D imae whether overlap occurs or not. The principle of this alorithm is to apply some exterior criteria to the imae in order to determine the true ray level of an object of interest. The alorithm development is concentrated on the true ray level computation in the transmission modalities due to three important considerations. irst, the accuracy of the forward scatter and backscatter modalities still need some improvement, so it is impossible in the current situation to create an alorithm that can accurately calculate true ray levels in either of the scatter modality usin those models. Second and most importantly, if this alorithm works in the transmission modalities, just by usin more accurate scatter overlap models, the true ray levels can be easily computed in scatter modalities. Third, althouh the scatter data is missin, the dualenery transmission data computed usin this alorithm at least allows one to distinuish oranic materials from inoranic materials.

36 Qian u Chapter 5. Determinin an Object s True Gray evels 65 Knowin only the models for eliminatin the backround effects will not allow one to correctly compute the true ray levels of an object of interest. This is because the luae inspection problem overlappin situations are typically quite complex. One such example is iven in iure n iure 5.5- (a), two reions are observed in a -D x-ray imae. Those two reions may be formed by two objects that are placed side-byside as seen in iure 5.5- (b) or by two objects that are overlapped as seen in iure 5.5- (c). ein able to correctly interpret such kinds of scenarios is crucial towards the computation of true ray levels of an object of interest. Another example is that in a ba imae, an object of interest is often surrounded by many neihborin reions. ein able to determine the correct neihborin reion that represents the backround object is another problem that needs to be correctly resolved. The methods that are used to revolve those issues are discussed in this section. These methods are implemented in the procedure true_l(). The principle of computin true ray levels is to find a special neihborin reion to an object of interest, and use this neihborin reion s ray level information to compute the true ray level of the object of interest. This special reion is a reion that is most likely to be part of the object that overlaps with the object of interest. As discussed in Section 4.3, objects in a ba can enerally be classified into two cateories: textile objects and solid objects. Textile objects are objects without constant shape. Solid objects are objects with constant shape. Explosives includin plastic explosives are considered as solid objects. Consequently, the objects of interest for this imae-processin system are solid objects. Now usin these concepts, the typical object layout in a ba is analyzed. Problems that miht prevent the computation of the true ray levels of an object are identified. Solutions to those problems are presented.

37 Qian u Chapter 5. Determinin an Object s True Gray evels 66 (a) Obj Obj Obj (b) (c) Obj iure 5.5- nterpretation of an imae scenario. The imae scenario shows in a) in a one-view imae may be interpreted as two objects are placed side by side as seen in b), or Obj is the backround object of Obj as seen in c).

38 Qian u Chapter 5. Determinin an Object s True Gray evels 67 The typical object layout in luae is shown in iure The left drawin in this fiure is the side view of a ba, and the riht drawins represent end views of the ba. The side view is the view from which the AS&E system would collect imaes. The end view is the view that one may observe from the travelin direction of the ba; the end view is used to illustrate the overlappin situations. n a ba, the ba covers or sides always appear. So every object of interest will be at least overlap with those ba covers. n most cases, people stuff their luae with towels, socks, and clothes, all of which are textile objects. So an object of interest will also overlap with these textile objects as well. However, when solid objects overlap with textile objects, in many cases, the textile objects will not sinificantly contribute to the overlapped reions. They may cause or 3 ray level variations. Consider that the noise of the system may cause up to 7 ray level variations, those effects caused by textile objects can enerally be inored. n case 3, an object of interest is overlapped with another solid object. The development of true_l() is based on handlin the object layouts shown in this. The inputs to routine true_l() are four perfectly reistered imaes: m Smth, H m Smth, bl m, and bl m Obj. or convenience, the labeled components in reions and the labeled components in bl m Obj are called objects. bl m are called Since explosives are considered as solid objects, and solid objects are usually semented into reions larer than 4 pixels in pixels are considered by true_l(). bl m, only reions with size larer than 4 Symbol Obj always represents the object of interest. n a low-enery transmission imae, a reion of interest, where Obj, may represent a situation where an object of interest Obj only overlaps with the ba covers and other textile objects, as seen in case of iure n this case,, the true ray level of Obj can be determined if the overlap effects caused by the ba covers and the textile objects are removed.

39 Qian u Chapter 5. Determinin an Object s True Gray evels 68 container cover textile objects solid objects 3 END VEW SDE VEW solid objects 3 iure 5.5- llustration of commonly seen object layout in a ba. The left raph is a side view imae, and the riht three raphs are three typical object layouts. ayout type one is when only some textile objects appear at a reion. ayout type two is that a solid object is overlapped with some textile objects. ayout type three is that a solid object is overlapped with some other solid objects, and those solid objects are overlapped with some textile objects.

40 Qian u Chapter 5. Determinin an Object s True Gray evels 69 One valid assumption is that the overlappin effects caused by the ba covers are the same everywhere in a ba. f the reion where only ba covers are found, the ray level of this reion can then be used to remove the effects caused by the ba covers. Denote this reion as Cover, and the ray level of this reion as Cover. Cover should be the brihtest reion in a low-enery transmission imae. Knowin the averae ray level of reion,, and the true ray level of Obj, Cover, the true ray level of Obj, can then be computed usin Equation This computation basically inores the effects caused by the textile objects that are inserted between the solid objects and the ba covers., However, besides overlappin with the ba covers and other textile objects, the reion of interest may also be formed by Obj overlappin with another solid object Obj besides those ba covers and some textile objects as seen in case 3 of iure To compute the true ray level of Obj,, and the ray level of a neihborin reion needs to know. Reion is the reion that belons to Obj. Part of Obj overlaps with the object of interest Obj that forms ; part of Obj only overlaps with the ba covers and some textile objects that forms. Reion should be one of the neihborin reions of. t is very difficult to determine which neihborin reion of is. Some of the neihborin reions are eliminated from the candidate list because they cannot be. Reion should always be brihter than because Obj, where Obj, forms the reion of. n the transmission modality, an overlapped reion should always be darker than the object that forms this reion. So if a neihborin reion is darker than reion, it should be eliminated from the candidate list. Reion should also have some percentae of common boundaries with. f the common boundary between a candidate reion and is less than 5% of the perimeter of, it is also unlikely that this reion is a candidate for. Hence it should be eliminated from the candidate list. n addition, the candidate true ray level computed usin Cover is also added to the list. After reion elimination usin these conditions, the number of

41 Qian u Chapter 5. Determinin an Object s True Gray evels 7 candidate reions should be around to 4. A list of candidate true ray levels of is computed usin and the ray levels of those candidate neihborin reions. As we know that Obj. The next oal is to find the true ray level of Obj. All reions, for example,, etc., that belon to Obj can be found usin the method mentioned at the beinnin of this section. After all such reions have been identified, a list of candidate true ray levels for Obj is created. t includes all the candidate true ray levels of all the reions that belon to Obj. The true ray level Obj is the candidate ray level that occurs with the hihest frequency in the list. n hih-enery transmission modality, the procedure for determinin the true ray level of Obj, H, is exactly the same as in low-enery transmission modality. Note: the brihtest reion in the low-enery transmission imae should also be the brihtest reion in the hih-enery transmission imae. Althouh this alorithm was not implemented in the forward scatter and backscatter modalities, the procedure for determinin the true ray levels of Obj, and, are no different than in either the low- or hih-enery transmission modality. Once those scatter models are refined, this alorithm can easily be modified to handle the computation in all four sensin modalities. The complete procedure in transmission modalities is described as follows: Procedure true_l(). Compute the size and boundary lenth of each reion in bl m.. or each reion in bl m, compute the averae ray level of its correspondin reion in 3. ind the brihtest reion of m Smth. m Smth that is at least 4 pixel in size.

42 Qian u Chapter 5. Determinin an Object s True Gray evels 7 4. or a reion in bl m, use the brihtest reion toether with all selected neihbors of to compute a list of possible true ray levels for in lowenery transmission modality. A selected neihbor should be brihter than ; and the common boundary between the neihbor and should be reater than 5% of the perimeter of. 5. Repeat step 4 for all reions in 6. or an object Obj in reions in bl m. Obj m with at least 4 pixels in size, determine all the bl m that belon to Obj. 7. The candidate true ray levels for an object Obj in candidate true ray levels of reions that belon to Obj. Obj m include all the 8. The true ray level for an object Obj in Obj m is the one that occurs the most frequent in the candidate list. 9. Repeat step 6 to 8 for all objects in Obj m.. Repeat step to 9 to compute the true ray levels for all reions in H m Smth. Procedure true_l() reports a list of solid objects alon with their true ray levels in lowand hih-enery transmission modalities. A typical report format is as follows: Object Number True ray level in m Smth True ray level in H m Smth Note that the object number refers to the label used in Obj m.

43 Qian u Chapter 5. Determinin an Object s True Gray evels Chapter Summary n this chapter, the development of the module for determinin an object s true ray levels is discussed. The development of this module was done in two staes. At the first stae, overlap models are developed for each of the different sensin modalities. The hih-enery and low-enery overlap models are quite precise in determinin an object s true ray levels. Althouh the forward-scatter and backscatter overlap models have not achieved the needed computation precision, they have sinificantly improved one s ability to compute the true ray levels in those two sensin modalities. urther improvement to those two models can be done with enouh fundin and additional research time. An alorithm is developed for computin the true ray levels of an object of interest for the luae inspection problem. This alorithm uses the overlap models and concepts like textile and solid objects in performin its analysis. The true ray level computation is focused on the transmission modalities. Once the scatter overlap models are refined, they can be easily added to the alorithm for computin true ray levels in those scatter modalities.