US20080298544A1

US20080298544A1 - Genetic tuning of coefficients in a threat detection system

Info

Publication number: US20080298544A1
Application number: US12/129,439
Authority: US
Inventors: Peter Dugan
Original assignee: Lockheed Martin Corp
Current assignee: Lockheed Martin Corp
Priority date: 2007-05-29
Filing date: 2008-05-29
Publication date: 2008-12-04
Also published as: US20090052762A1; US20090003699A1; US20090055344A1; US8094874B2; US20090003651A1; US20090052622A1; US20090052732A1

Abstract

A system and method are presented for determining an optimized set of estimation coefficients for use in the gray scale conversion of measured intensity ratios derived from radiographic images of an object. Radiographic images for known materials may be obtained using different source energy levels. Measured training ratios for each known material may be determined intensity values derived from pairs of radiographic images. Standard attenuation data for each known material may also provided. A genetic algorithm may be used to obtain an optimized set of estimation coefficients for the known materials using initial candidate sets of estimation coefficients, the measured training ratios, and the standard attenuation data. The optimized set of estimation coefficients may be used in the gray scale conversion of measured ratios derived from radiographic images of unknown materials for the determination of the atomic number of the unknown materials.

Description

The present application claims the benefit of U.S. Provisional Patent Application No. 60/940,632, entitled “Threat Detection System”, filed May 29, 2007, which is hereby incorporated by reference in its entirety.
The present invention relates generally to the analysis of unknown materials by a threat detection system using radiographic images, and, more particularly, to the tuning of coefficients for use with radiographic images by a threat detection system.
Standard techniques using high-energy radiographic systems exist to determine or estimate atomic composition of a material. For example, two X-ray energy levels may be used to image an object of interest. The gray level intensity values measured for each of the two energy levels are used to compute a corresponding ratio. The ratio of the intensity values for an unknown material is compared against known materials. The known material with the closest ratio to that measured is used to estimate the unknown material's effective atomic number (Z_eff) of the unknown material. However, these radiographic systems may be prone to noise and other non-linear effects that can cause errors in Z_effdetermination, especially in high-Z materials. Elements with high-Z include special nuclear materials, such as plutonium and highly enriched uranium, as well as elements that would be extremely effective in shielding special nuclear materials from passive radiation detection techniques.
Using a radiographic system with only two radiographic source energy levels, two common problems can occur. First, insufficient penetration may occur when high-Z or high density materials do not allow enough energy to penetrate through the object of interest to a detector. Second, low-Z or low density materials may induce over-saturation, where little to no attenuation may occur at a particular radiographic source energy level. To overcome the problem of over-saturation, lower energies may be used, whereas higher energies may be used in cases of insufficient penetration. Higher energies may solve insufficient penetration issues but exacerbate over-saturation issues and vice versa. Thus, in dual energy systems, the solution for overcoming over-saturation issues may be at odds with the solution for overcoming insufficient penetration.
A multi-energy, multi-attenuation ratio system may help to alleviate these problems. In such an approach, more than two radiographic source energy levels are used to image an object of interest. The intensity values measured for each of the multiple energy levels are used to compute corresponding measured ratios. For example, if three energy levels (E₁, E₂, and E₃) are used, three different ratios (R₁₂, R₁₃, and R₂₃) may be determined from the intensity values in the respective images. These ratios for each unknown material can then be compared against like ratios obtained for known materials so as to determine the effective atomic number of the unknown material.
Whether using two energy levels or more than two energy levels, the resulting measured ratios are determined from intensity derived directly from the radiographic images. As material databases may be based on actual radiographic intensity values, the measured intensity values and the corresponding measured ratios can be converted from gray scale values to the corresponding photon intensity values using an appropriate conversion factor. However, gray level conversion is nonlinear across different materials and source energy levels. Further, the conversion factor may also depend upon the characteristics of the imaging system, including factors such as the dynamic range of the detector and the energy levels of the source. Thus, in determining the ratio of attenuation coefficients for a particular pair of energy levels directly from the images, an estimation coefficient, α, based on these conversion factors is desirable to account for the various nonlinearities in converting the resulting measured ratios.
Determining the estimation coefficient for converting the attenuation ratio from gray level to actual intensity can be done through experimental evaluation using various materials. However, for systems employing more than two energy levels, each measured ratio, R_j, has a corresponding estimation coefficient, thus complicating the ability to determine the attenuation coefficients through experimental evaluation. Embodiments of the present invention may address the above-mentioned problems and limitations, among other things.
An embodiment of the present invention can include a method for determining an optimized set of estimation coefficients. Each estimation coefficient may be used in the gray scale conversion of a respective measured ratio, which may be derived from radiographic images of an object. The method may include providing a set of known materials and obtaining a set of radiographic images for each known material. Each radiographic image of the set may be obtained using a different source energy level. A plurality of measure training ratios may be calculated for each known material from the respective set of radiographic images. An initial set of candidate sets of estimation coefficients may be provided. The method may also include providing accepted attenuation data for each known material. A plurality of standard attenuation ratios for each known material may be determined based on the respective accepted attenuation data. The plurality of standard attenuation ratios may correspond to the measured training ratios based on source energy levels. The method may also include employing a genetic algorithm to obtain the optimized set of estimation coefficients using the initial set of candidate sets of estimation coefficients, the plurality of measured training ratios, and the plurality of standard attenuation ratios. The genetic algorithm may determine a plurality of adjusted measured ratios based on the plurality of measured training ratios and the set of candidate sets of estimation coefficients. The genetic algorithm may also compare the adjusted measured ratios to respective standard attenuation ratios for each estimation coefficient. The genetic algorithm may mate and reproduce the candidate sets of estimation coefficients based on the comparison of the adjusted measured ratios and the respective standard attenuation ratios to arrive at a new set of candidate sets of estimation coefficients. Further, the genetic algorithm may repeat until a termination condition is satisfied.
Another embodiment may include a computer program product having a computer readable medium encoded with software instructions that cause the computer to perform the steps of calculating a plurality of measured training ratios for each material under test from a respective set of radiographic images and providing accepted attenuation data for each material under test. The steps can also include determining a plurality of standard attenuation ratios for each material based on respective accepted attenuation data. The plurality of standard attenuation ratios may correspond to the measured training ratios based on source energy levels. The steps may also include obtaining an optimized set of estimation coefficients for the materials under test from the plurality of measured training ratios and the plurality of standard attenuation ratios by using a genetic algorithm.
Another embodiment may include a system for determining an optimized set of estimation coefficients. The system may include an error evaluation module, which determines a set of adjusted measured ratios for a material based on a selected candidate set of estimation coefficients and a plurality of respective measured training ratios for the material. The error evaluation module may compare the set of adjusted measured ratios for the selected candidate set of estimation coefficients to a set of corresponding standard attenuation ratios for the material. The error evaluation module may also generate an output based on the comparison and determine if the selected candidate set of estimation coefficients satisfies a termination condition. The system may also include a genetic algorithm optimization module. The genetic algorithm optimization module may mate at least a portion of a plurality of candidate sets of estimation coefficients based on the output of the comparison module. The genetic algorithm optimization module may also generate a plurality of new candidate sets of estimation coefficients and output the plurality of new candidate sets of estimation coefficients. The error evaluation module may be configured to generate an output of the selected candidate set of estimation coefficients as the optimized set of estimation coefficients if the termination condition is satisfied.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an overview of an exemplary material domain imaging system incorporating a tuning module according to an exemplary embodiment.

FIG. 2 is a flowchart showing a process overview of an exemplary material domain imaging system.

FIG. 3 is a block diagram showing an overview of the tuning module according to an exemplary embodiment.

FIG. 4 is a flowchart showing a process overview of the tuning module according to an exemplary embodiment.

FIG. 5 is a flowchart showing a process detail of step 500 from FIG. 4.

FIG. 6 is a flowchart showing a process detail of step 600 from FIG. 4.

FIG. 7 is a flowchart showing a process detail of step 700 from FIG. 4.

FIG. 8 is a flowchart showing a process detail of step 800 from FIG. 4.

FIG. 9 is a flowchart showing a process detail of step 900 from FIG. 4.

DETAILED DESCRIPTION

The present invention is directed to tuning of coefficients for use with multiple radiographic images generated by a multi-energy approach.
Multiple energies are used to determine intensity ratios that are proportional to attenuation coefficient ratios. These intensity ratios can then be used to build a series of measured ratios. These measured ratios can then be used to build a series of adjusted measured ratios for use in a Z_effdetermination that may be more accurate than conventional methods.
Imaging of a material relies on the application of Beer's law. Beer's law equation can be stated using an arbitrary energy level k as,
I(k)=I _O(k)e ^−μ ^k ^t, (1)
where I(k) is the measured intensity of the radiation at energy level k, I_O(k) is the input intensity of the radiation at energy level k, μ_kis the linear attenuation coefficient of the material at energy level k, and t is the energy independent material thickness.
Experimentally, the linear attenuation coefficient depends on the material cross-section coefficient, σ. Since attenuation is energy dependent, each material has the basic regions of energy scatter, including photoelectric absorption σ_pe, coherent scatter σ_cs, incoherent scatter σ_is, and pair-wise production σ_pp. Each material has a material combined cross-sectional coefficient which depends on the sum of the individual cross-sections. For example,
σ=σ_pe+σ_cs+σ_is+σ_pp. (2)
The cross-sections and linear attenuation coefficients are related by:
$\begin{matrix} μ = \frac{σ N ρ}{A}, & (3) \end{matrix}$
where μ is the material linear attenuation coefficient, σ is the material combined cross-sectional coefficient, N is Avogadro's number, A is atomic weight, and ρ is density.
Using any two energies, denoted as x and y, the following intensity ratio may apply:
$\begin{matrix} R_{j} = \frac{\ln (\frac{I (x)}{I_{o} (x)})}{\ln (\frac{I (y)}{I_{o} (y)})} = \frac{μ_{x} t}{μ_{y} t} = \frac{μ_{x}}{μ_{y}}, & (4) \end{matrix}$
where R_jis the ratio of the logarithm of the respective intensity ratios and x and y represent the upper and lower energy levels. This expression eliminates the dependency on mass thickness. Thus, the R_jvalue may be compared against attenuation curves at the upper and lower energy levels for various materials to determine the Z_effof an unknown material.
Intensity values can be determined from measured radiographic images and used in the determination of a plurality of ratios for different pairs of radiographic source energy levels. Any number of energy levels in the X-ray regime may be used. For example, at least two energy levels and corresponding measured ratios can be used. In another example, four different energy levels and corresponding measured ratios can be used.

TABLE 1

Multi-Energy Attenuation Coefficient and Ratio Table

SourceEnergyLevels(1<2<3<4)	CorrespondingAttenuationCoefficients(μ_x, μ_y)	EnergyRegime	$R_{j} = \frac{\ln (\frac{I (x)}{I_{O} (x)})}{\ln (\frac{I (y)}{I_{O} (y)})} = \frac{µ_{x}}{µ_{y}}$

E₁, E₂	μ₁, μ₂	Low	R_i
E₁, E₃	μ₁, μ₃	Low-	R_ii
		Medium
E₁, E₄	μ₁, μ₄	Low-High	R_iii
E₂, E₃	μ₂, μ₃	Medium	R_iv
E₂, E₄	μ₂, μ₄	Medium-	R_v
		High
E₃, E₄	μ₃, μ₄	High	R_vi

Table 1 shows an example of an application employing four different source energy levels. Four different source energy levels (E₁-E₄) are used to generate four different radiographic images of an object. E₁corresponds to the lowest X-ray source energy level. For example, E₁may be 1 MeV. E₄corresponds to the highest X-ray source energy level. For example, E₄may be 10 MeV. Measured intensity values I(x) for each energy level, x, are extracted from the corresponding radiographic images and used in the determination of each measured ratio, R_j. Source intensity values I_O(x) for each energy level are known from measurement conditions of the radiographic images and are also used in the determination of the measured ratios, R_j. Although only four source energy levels are discussed in detail with respect to Table 1, it is of course contemplated that more than four or less than four energy levels may be employed.
Ratios exist for various combinations of intensity values based on the different source energy levels. Therefore, it may be feasible that one could select between low, medium, or high energy ratios for estimating the effective atomic number of the material of the object to minimize errors due to saturation, noise, or insufficient penetration.
A family of attenuation curves for a group of materials with respect to X-ray energy is typically non-linear, with various ranges of polynomial order. Although the attenuation curves themselves are non-linear, the ratios from energy level to energy level can be modeled using linear methods. At least two energy solutions form a linear attenuation fit based on the ratio. Determining the atomic structure of a material can be based on comparing the slopes of the intensity values from radiographic images with those values of known materials residing in a database. The attenuation coefficient is proportional to measured X-ray intensities.
Radiographic imagers can use measured X-ray intensity to create a corresponding gray level picture, otherwise known as a radiographic image. The conversion from intensity to gray level can be defined by an inverse linear ratio, but the process of imaging various materials poses several non-linear settings. Despite the nonlinearity, ratios between the measured intensity values are approximately the same as ratios between the true material linear attenuation coefficients when adjusted for gray level conversion. In other words, an adjusted ratio of measured intensity values, as defined in equation (4), may be correlated with a similar ratio of known linear attenuation coefficients in determining the Z_effof an unknown material.
An adjusted measured ratio, R_M,j, can be determined from the equation:
R_M,j=α _jR_j
where R_jis the measured ratio of attenuation coefficients at two different source energy levels, α_jis an estimation coefficient corresponding to the particular two energy levels used in determining R_j, and j is a subscript referring to the particular pair of source energy levels. The estimation coefficient, α_j, can be determined from the mapping of the photon intensity values to a gray level value. Separate adjusted measured ratios, R_M, may be determined for each measured ratio, R, used. Alternately, the multiple separate measured ratios may be combined into a single vector. For example, using the set of ratios defined by Table 1, equation (5) would become:
R _M=α_i R _i î _i+α_ii R _ii î _ii+α_iii R _iii î _iii+α_iv R _iv î _iv+α_v R _v î _v+α_vi R _vi î _vi
wherein î_jrepresents a vector in n-space corresponding to attenuation coefficient R_j. The n-space may be a multi-dimensional space based on the number of energy levels employed or the number of measured ratios formed.
While it is contemplated that all radiographic images corresponding to different energy levels can be used in the determination of the Z_eff, it is also possible that only specific measured ratios of intensity values may be selected depending on the conditions associated with a particular energy level. For example, for a given energy level, an intensity value may not be applicable due to an over-saturation or non-penetration condition. Therefore, the measured energy ratios, R, using the intensity values for that particular energy level may be excluded from the calculation of the adjusted measured ratio, R_M,j. Alternately, the ratio R_M,jcorresponding to those conditions of over-saturation or non-penetration may be excluded from use in the determination of Z_eff.
FIG. 1 shows a block diagram of an overview of an exemplary material domain imaging system incorporating a tuning module according to an exemplary embodiment. The material domain imaging system as shown in FIG. 1 may be used in the estimation of Z_effof unknown materials as part of a threat analysis/detection system.
In a “testing” mode, a material domain imaging processor 100 may receive multiple radiographic images and other data as input and may output a multi-energy high Z-mapping for identification of threats. An image processor 108 may receive a set of radiographic images of an object of interest from radiographic imaging system 102 or another processor, system, or database. Each of the radiographic images may be taken at a different X-ray energy level. Each image may be processed by the image processor 108 to register the images, normalize the images, and remove any noise in the images.
The processed images may be sent to the Z_effprocessor 116. The Z_effprocessor 116 may extract corresponding intensity values from each pixel in each image. In an alternate embodiment, the Z_effprocessor 116 may only determine an intensity value for each pixel in each image that is within a region of interest. For determination of a region of interest, the images may be sent to an external analysis system, such as segmentation processor 114. Segmentation processor 114 may use, for example, edge boundary detection, texture based detection, or other region processing in order to determine boundaries within the images and to select a common region of interest for evaluation by the material domain imaging processor 100. The region of interest in each image may then be communicated to the Z_effprocessor 116 for determination of intensity values. The relevant pixels for subsequent processing may be limited to those pixels within the region of interest instead of the entirety of pixels in each image. Relevant pixels may also be selected based on penetration conditions (e.g., oversaturation, non-penetration). For example, like regions across the various registered images may be compared to determine penetration conditions.
After determination of the intensity values, the Z_effprocessor 116 may use the intensities to form a set of measured ratios, R_j, for the relevant pixels. The measured ratios, R_j, may be formed using the relation set forth in equation (4) above. Normalized intensity values from corresponding pixels in a pair of different radiographic images may also be used to form each measured ratio. Corresponding pixels may refer to pixels in different images which correspond to the same point or location on an imaged object. For example, the set of ratios for each pixel may take the form shown in Table 1.
The Z_effprocessor 116 may use estimation coefficients, α_j, with the set of measured ratios, R_j, to determine at least one adjusted measured ratio, R_M,j, for each relevant pixel. Separate adjusted measured ratios, R_M,j, may be determined for each energy ratio in the set or only for certain energy ratios within the set. Alternately, the multiple energy ratios may also be combined into a single measured ratio vector, R_m. The estimation coefficients may be provided by tuning module 110.
The relevant pixels may include, for example, a single pixel, all the pixels in the entire image, or just the pixels within a region of interest. In an alternative embodiment, relevant pixels may be selected based on penetration conditions (e.g., over-saturation, non-penetration, etc.). The material domain imaging processor 100 or a separate system may compare regions across various images to determine penetration conditions. The material domain imaging processor 100 or a separate system (i.e., segmentation processor 114 or context analysis system 106) may correlate regions with pixel values at a lower extreme of a photon intensity scale as regions of non-penetration, while regions with pixel values at an upper extreme of the photon intensity scale may be correlated as regions of over-saturation. The Z_effprocessor 116 may be configured to exclude these regions from the list of relevant pixels for further processing.
As described in more detail below, tuning module 110 can employ an algorithm for minimum error tuning of the estimation coefficients. In a system calibration process, tuning module 110 may determine a set of estimation coefficients, α, for use by the Z_effprocessor 116. In such a scenario, the material domain imaging processor 100 may be using in a “training” mode, so that tuning module 110 may optimize the set of estimation coefficients based on radiographic images of known materials received by processor 100. Accepted attenuation data may be input to the tuning module 110. The tuning module 110 may determine measured training ratios from radiographic images of a known material based on the output from the image processor 108. Using these attenuation ratios, the tuning module may optimize the value of the estimation coefficients so as to correspond to the accepted attenuation data. The accepted attenuation data may be data from public attenuation sources, such as the NIST public data source.
In the “testing” mode, the resulting adjusted measured ratios, R_M,j, can be output from the Z_effprocessor 116 to the material assignment module 118. The material assignment module 118 can compare the adjusted measured ratios to a material attenuation database from dynamic material attenuation (DMA) module 112. Alternately, the Z_effprocessor 116 may send the measured ratios, R_j, to the material assignment module 118. In such a scenario, material assignment module 118 would use the estimation coefficients and the measured ratios to form the adjusted measured ratios, R_M,j, for comparison to the material attenuation database. In either embodiment, the material assignment module 118 may assign a Z_effvalue to each relevant pixel or to a region of pixels based on the comparison.
In an exemplary embodiment, the DMA module 112 may be a processor that uses configurable settings to dynamically create a densely populated attenuation ratio lookup table with variable resolution in both the energy scale and the effective atomic number (Z_eff) scale. The DMA module 112 can be used for the two or more energies used in the radiographic images for determining Z_effvalues. Sparse attenuation data from public sources for any material (liquid, solid, gas) can be stored on a disk using a standard format. Alternately, accepted attenuation data (i.e., attenuation coefficients) may be input to the DMA module 112 from accepted attenuation database 104. Accepted attenuation data may also be provided by an integrated database, a memory device, or a separate system or processor. The accepted attenuation data may be data from public attenuation sources, such as the NIST public data source. The attenuation data can be created using a variety of scattering approaches, such as coherent, incoherent, photoelectric, pairwise production nuclear field, pairwise production electric field, total scatter with coherent, and total scatter without coherent. A user may select the materials used to create the attenuation lookup table, such as water, peroxide, lead, carbon, etc. Using the attenuation data, the attenuation lookup table may be created as a function of the X-ray energy level and the Z_effof the material.
Material assignment module 118 may include a plurality of independent material assignment algorithms. Each material assignment algorithm may employ a different methodology or use different measured ratios for comparison to the same attenuation database to generate a set of candidate Z_effvalues for each relevant pixel. Each material assignment algorithm can also assign a confidence value to the candidate Z_effvalues.
The set of candidate Z_effvalues may be sent to the Z_effprocessor 116. The Z_effprocessor 116 may compare the confidence values for each Z_effvalue in the set and may select the Z_effvalue for each relevant pixel with the highest associated confidence value. The result can be a Z_effimage with each pixel having an assigned Z_effvalue with the highest confidence. In an exemplary embodiment, the Z_effprocessor 116 may output the result to external analysis system, such as context analysis system 106, for evaluation of regions of non-penetration or over-saturation for inclusion in the final processor output. For example, context analysis system 106 may use a-priori information, in the way of configuration data, to assist in identifying non-penetrable and false alarm cases.
The result from the Z_effprocessor 116 can be sent to a color image assignment module 120. The color image assignment module 120 can map a color scale to a range of corresponding Z_effvalues. Thus, each relevant pixel may be assigned a color based on the assigned Z_effvalue, thereby creating a color image of the object. This color image can be output from the material domain imaging processor 100 to threat decision processor 124. In addition, the color image and Z_effvalues may be further processed by a threat assignment module 122. The Z_effvalue for each pixel can be compared with a threat threshold by the threat assignment module 122 to determine regions where the threshold is exceeded, i.e., those regions where a threat exists. These regions and associated confidence values may be output from the material domain imaging processor 100 to the threat decision processor 124 for further processing or integrated decision making.
FIG. 2 shows a process flow for an exemplary method of material domain image processing. The process begins at step 200 and advances to step 202. In step 202, a set of estimation coefficients is obtained. The set of estimation coefficients may be a set of optimized or tuned estimation coefficients, α_j, for use with corresponding measured ratios, R_j. As described herein, a genetic algorithm employing minimum error tuning may be used to optimize a set of estimation coefficients such that measured training ratios derived from radiographic images of a known material correspond to accepted attenuation data. The technique for determining the optimized set of estimation coefficients will be discussed in more detail below.
The process may proceed to step 204, where radiographic images of an object may be obtained. Each radiographic image may be obtained at a different radiographic source energy level. For example, at least two independent radiographic source energy levels can be used. In another example, four radiographic source energy levels can be used to generate four independent radiographic images of an object. The number of energies may be determined by insufficient penetration and/or over-saturation conditions measured. The process may continue to step 206.
In step 206, an intensity value may be extracted for each relevant pixel in each radiographic image. The relevant pixels may be the pixels within a designated region of interest or all pixels within each image. At step 208, the intensity values may be used to create a set of measured ratios, R_j, for each relevant pixel based on the different images, with each image corresponding to a different radiographic source energy level. For example, the set of measured ratios, R_j, for each pixel may take the form shown in Table 1. At step 210, a set of adjusted measured ratios, R_M,j, for each relevant pixel can be determined. Each measured ratio can be based on the product of an estimation coefficient, α_j, with a corresponding measured ratio, R_j, from step 208. Separate adjusted measured ratios, R_M,j, may be determined for each measured ratio, R_j, in the set or only for certain pairs of source energy levels. Proceeding to step 212, the resulting set of measured ratios, R_M,j, may be compared to standard attenuation ratios, R_T,j, built using a material attenuation database. The process may then advance to step 214, wherein results of the comparison in step 212 can be used to determine the Z_efffor each relevant pixel. The process may advance from step 214 to end at step 216.
In the determination of the intensity values and the corresponding measured ratios from the radiographic images, the conversion from intensity to gray level can be defined by an inverse linear ratio. An adjusted measured ratio, R_M,j, for each material can be determined from equation (5) above. The estimation coefficient, α_j, can be determined from the mapping of the photon intensity values to a gray level value. Although conversion from gray level to intensity can be defined by an inverse linear ratio for a particular ratio (and corresponding pair of energy levels) and a particular material, gray level mapping for the estimation coefficient is nonlinear across different material and different energy levels. Thus, in order to determine a set of estimation coefficients that yields sufficient results for most energy levels and materials of interest, a genetic algorithm may be employed in an exemplary embodiment for minimum error tuning so as to optimize the set of estimation coefficients, α_j. In such an approach, known calibration materials may be analyzed using a radiographic imaging system at multiple energy levels to determine a set of measured attenuation ratios. The results may be compared to accepted attenuation curves. Using the accepted attenuation curves, a series of standard attenuation ratios, R_T,j, may be computed. For example, known materials may be imaged by the radiographic system at different energy levels. These images may then be used to form a series of measured training ratios, R_TR,j. The measured training ratios, R_TR,jare formed in a similar manner as the formation of the measured ratios, R_j, except the materials imaged for the measured training ratios, R_TR,j, are known. Thus, the measured training ratios, R_TR,j, may be formed using the relation set forth in equation (4) above. There may exist a set of estimation coefficients, α_j, that satisfies:
R _M,j=α_j *R _TR,j ≈R _T,j (7)
Accordingly, each estimation coefficient of the set may be optimized to minimize a difference between the adjusted measured ratio for each pair of source energy levels and the standard attenuation ratio at the same pair of source energy levels. For example, an error, ε, may be defined as the difference between the standard ratio, R_T,j, for a given material and energy level j and the product of the estimation coefficient, α_j, and the measured training ratio, R_TR,j, for a selected material:
ε=|R _T,j −R _M,j |=|R _T,j−α_j *R _TR,j| (8)
The set of estimation coefficients, α_j, can then be optimized to solve for the minimum error condition for all materials using a genetic algorithm. Note that the above error determination may be biased or weighted so as to favor certain materials or certain source energy level pairs in the optimization of the estimation coefficients. For example, equation (8) could be rewritten as:
ε_i,j =|R _T,i,j−α_j *R _TR,i,j*β_i,j|, (9)
where the subscript i refers to the selected material, the subscript j refers to the selected pair of source energy levels, and β is a material dependent weighting factor. By judicious selection of β, the optimization process may be preferentially weighted toward a particular material or subset of materials.
The optimization process can employ genetic optimization rules. Standard genetic optimization techniques may be used, such as those described in “Genetic Algorithms in Search, Optimization, and Machine Learning” (David Goldberg, 1989), which is hereby incorporated by reference in its entirety. A differential cost surface may also be constructed based on the ratios of the gray values for the various materials under test, the accepted attenuation values for each material, and the number of energies used in the determination. This cost surface may then be minimized to determine an optimized set of estimation coefficients. The optimized set of estimation coefficients may then be used by the material domain imaging system 100 in subsequent evaluations of unknown materials.
An overview of the tuning module 110 for determining the set of estimation coefficients is shown FIG. 3. In a training process, radiographic images may be taken at multiple source energy levels of a set of known materials. The radiographic image data 302 may be input to the tuning module 110. From the image data 302, image processing module 306 may extract intensity values from each radiographic image of each known material. For example, an intensity value for each pixel representing the known material in each radiographic image may be determined by image processing module 306. The module 306 may output these intensity values to measured ratio module 310. Measured ratio module 310 may form a set of measured training ratios, R_TR,j, for each material. Intensity values from corresponding pixels in a pair of different radiographic images may be used to form each ratio. For example, the set of measured ratios for each material may take the form shown in Table 1. Although the image processing module 306 and the measured training ratio module 310 are shown separately, it is also contemplated that modules 306 and 310 may be formed as a single module.
Standard attenuation data 304 may also be provided to the tuning module 110. The standard attenuation data for each known material may be derived from publicly available data sources. For example, the data may be provided from NIST public attenuation data sources. The standard attenuation data may be in the form of accepted intensity data of known materials at various source energy levels. For example, the standard attenuation data may be provided to the tuning module 110 by DMA module 112. Optional standard attenuation coefficient module 308 may use this accepted intensity data to form a plurality of standard attenuation coefficients for each known material. For example, a standard attenuation coefficient, μ_T, may be determined for each known material. In an alternate embodiment, the standard attenuation data 304 may be in the form of accepted attenuation coefficients of known materials at various source energy levels. In such a case, standard attenuation coefficient module 308 may be omitted. Standard attenuation coefficients may be provided to standard ratio module 312. Standard ratio module 312 may form a set of standard ratios, R_T,j, for each known material. For example, the set of standard ratios for each known material may take the form shown in Table 1. Although the standard attenuation coefficient module 308 and the standard ratio module 312 are shown separately, it is also contemplated that modules 308 and 312 may be formed as a single module.
Once the set of measured training ratios, R_TR,j, and the set of standard ratios, R_T,j, for each material have been determined by modules 310 and 312, respectively, the sets are provided as input to tuning engine 326. Tuning engine 326 may employ a genetic algorithm with minimum error tuning to optimize estimation coefficients such that measured training ratios, R_TR,j, derived from radiographic images for each known material correspond to accepted attenuation data.
An initialization module 314 may be provided in tuning module 110. The initialization module 314 may be configured to initialize a set of candidate sets of estimation coefficients, α. Initialization module 314 may also provide initial ranges for desired source energy ranges or Z_effranges for optimization of the estimation coefficients, as well as information regarding material ROI and genetic algorithm settings. Each candidate set includes an estimation coefficient that directly corresponds to the pair of energy levels used in the determination of one of the ratios. In other words, each ratio in the set of measured attenuation ratios has a corresponding estimation coefficient in the candidate set of estimation coefficients. For example, for the set of ratios shown in Table 1, there may be six corresponding estimation coefficients, i.e. α_i, α_ii, α_iii, α_iv, α_v, and α_vi, in each candidate set of estimation coefficients. This initial set of candidate sets may be provided to tuning engine 326 for use in the determination of the optimized set of estimation coefficients. The initial set of candidate sets of estimation coefficients may be determined in any manner known in the art. For example, the initial set of candidate sets of estimation coefficients may be randomly assigned. In an alternative embodiment, the initial set of candidate sets of estimation coefficients may be predetermined and stored in initialization module 314. Although shown separately, initialization module 314 may be integrated with the tuning engine 326.
Tuning engine 326 may have an error evaluation module 328 and a genetic algorithm optimization module 322. Error evaluation module 328 may include an adjusted measured attenuation ratio module 316, a comparison module 318, and an error-checking module 320. Although modules 316, 318, and 320 are shown as separate modules, the functions of the three modules may be integrated into fewer than three modules. For example, the functions of modules 316, 318, and 320 may be performed by a single module of the error evaluation module 328.
The adjusted measured ratio module 316 of the error evaluation module 328 may accept as inputs the set of measured training ratios, R_TR,j, and the initial set of candidate sets of estimation coefficients, α_j. A set of adjusted measured ratios, R_M,j, may be determined by the adjusted measured attenuation ratio module 316 based on the set of measured training ratios, R_TR,j, and each initial set of candidate sets of estimation coefficients, α_j. For example, for each candidate set, the set of adjusted measured ratios may be determined using equation (5) above. For each estimation coefficient of the candidate sets, the adjusted measured ratio, R_M,j, is compared with respective standard ratios, R_T,j, by comparison module 318. Similar to equation (4) above, the standard ratio, R_T,j, can be expressed as:
$\begin{matrix} R_{T, j} = \frac{μ_{x}}{μ_{y}} . & (10) \end{matrix}$
In an exemplary embodiment, this comparison may take the form of a difference calculation between the adjusted measured ratio, R_M,j, and the corresponding standard ratio, R_T,j, as per equation (8). The comparison may then be passed to error-checking module 320. Error-checking module 320 may determine if a termination condition has been met. If a termination condition is not met, the error-checking module 320 may be configured to pass the set of candidate sets of estimation coefficients and the comparison from comparison module 318 to the genetic algorithm optimization module 322.
Genetic algorithm optimization module 322 may be configured to perform an evolutionary recombination of the set of candidate sets to determine a new set of candidate sets of estimation coefficient. For example, the candidate sets of estimation coefficients from error-checking module 320 may be ranked according to the comparison by comparison module 318. Those candidate sets of estimation coefficients resulting in adjusted measured ratios closer to the respective standard attenuation ratios may be ranked higher. Based on the ranking, the candidate sets may be selectively recombined or reproduced. Accepted techniques for recombination may be employed, such as those described in “Genetic Algorithms in Search, Optimization, and Machine Learning.”
For example, a portion of the candidate sets of estimation coefficients, may be selected based on selection criteria to thereby form an old generation. The selected candidate sets may then be reproduced. In a mating step, members of the old generation may be divided to form parents. Traits from the parent estimation coefficients may be crossed-over by selecting points in their chromosomes for combination to form a new estimation coefficient population. Random chromosomes in the new estimation coefficient population may be mutated by selective modification. Mutation and cross-over may occur, for example, at the bit level. The final new set of candidate sets may then be provided to the adjusted measured ratio module 315 for subsequent processing.
In another example, a portion of the candidate sets that are ranked highest may be selectively recombined to produce a new set of candidate sets of estimation coefficients. In the recombination, a mutation may be provided within the set of candidate sets of estimation coefficients. For example, random values may be inserted into candidate sets of estimation coefficients prior to or after recombination. The ranking and/or recombination of at least a portion of the set of candidate sets of estimation coefficients may also be biased or weighted to favor one or a particular subset of materials over other materials of the set of known materials. For example, the ranking may be weighted to favor estimation coefficients that have low error value with respect to a subset of materials. This subset may include materials of particular interest in threat detection systems, such as high atomic number materials and/or special nuclear materials. The new set of candidate sets may then be provided to the adjusted measured ratio module 316, where the process of the tuning engine 326 may be repeated until stopped by error checking module 320.
If a termination condition is met, the error-checking module 320 may be configured to pass a selected set of candidate sets of estimation coefficients along output 324. In an exemplary embodiment, the selected set may be the candidate set of estimation coefficients with the highest ranking. In an alternate embodiment, the selected set may be the candidate set of estimation coefficients meeting a minimum error condition. The termination condition may be a threshold value for the amount of processing time or the number of iterations of and/or generations in the process of the tuning engine 326. In an alternate embodiment, the termination condition may be a candidate set meeting the minimum error condition. This minimum error condition may be when the minimum error for each material, as calculated by equation (8), for a candidate set of estimation coefficients reaches a minimum value.
FIGS. 4-9 show a process 400 of the tuning module 110 according to an exemplary embodiment. FIG. 4 shows an overview of the process 400, with FIGS. 5-9 showing process step details referred to in FIG. 4. The process 400 begins at step 402 and advances to process 500. In process 500, standard ratios, R_T,j, are determined for each material of a set of materials under test. With reference to FIG. 5, process 500 begins with step 502 and advances to step 504. In step 504, a material from the set of materials under test is selected. Process 500 advances to step 506, wherein standard attenuation data at different source energy levels is obtained. The standard attenuation data for each material under test may be derived from publicly available data sources. For example, the data may be provided from NIST public attenuation data sources. In an exemplary embodiment, the standard attenuation data may be in the form of accepted intensity data of known materials at various source energy levels. Process 500 advances to step 508 where accepted intensity data is used to form a plurality of standard attenuation coefficients. For example, a standard attenuation coefficient, μ_T, may be determined for each known material. Proceeding to step 510, a set of attenuation ratios, R_T, for each material under test is formed. Process 500 then advances to step 512. In step 512, the process checks if all materials of the set of materials under test have been evaluated. If all the materials have not been evaluated, process 500 advances to step 504 where a new material from the set of materials under test is selected. Process 500 then repeats steps 504-512 until all materials are evaluated. Once all materials are evaluated, the process advances to step 514. In step 514, the plurality of standard attenuation ratios for each material under test are output for use by other process steps in process 400. Process 500 ends at step 516.
Referring again to FIG. 4, process 400 advances from process 500 to process 600. In process 600, measured training ratios, R_TR,j, are determined for each known material under test. With reference to FIG. 6, process 600 begins at step 602 and advances to step 604. At step 604, a material from the set of materials under test is selected. Process 600 advances to step 606. At step 606, radiographic images may be taken at multiple source energy levels for each material of the set of materials under test. Alternatively, multiple materials may be simultaneously imaged at different energy levels, with the process 600 configured to separately address each material in the images by defining, for example, separate regions of interest for each material under test in the image.
Process 600 advances to step 608 where intensity values are extracted from the radiographic images. For example, an intensity value for each pixel in a region of interest in the image of the material under test may be determined. Proceeding to step 610, a set of measured training ratios, R_TR,j, for each material under test is formed. Intensity values from corresponding pixels in a pair of different radiographic images may be used to form each ratio. For example, the set of ratios for each material may take the form shown in Table 1. Process 600 then advances to step 612. In step 612, it is checked if all materials of a set of materials under test have been evaluated. If all the materials have not been evaluated, process 600 advances to step 604 where a new material from the set of materials under test is selected. Process 600 then repeats steps 604-612 until all materials are evaluated. Note that if multiple materials are included in a single set of radiographic images, process 600 may be configured, for example, to evaluate the next region of interest containing the next material under test in lieu of obtaining additional radiographic images. Once all materials are evaluated, process 600 advances to step 614. In step 614, the plurality of measured training ratios, R_TR,j, for each material are output for use by other process steps. Process 600 ends at step 616.
Referring again to FIG. 4, process 400 advances from process 600 to step 404. In step 404, a set of candidate sets of estimation coefficients, α_j, is initialized. Each candidate set may include an estimation coefficient that directly corresponds to the pair of source energy levels used in the determination of one of the measured training ratios, R_TR,j. For example, for the set of ratios shown in Table 1, there may be six corresponding estimation coefficients, i.e. α_i, α_ii, α_iii, α_iv, α_v, and α_vi. The initial set of candidate sets of estimation coefficients may be determined in any manner known in the art. For example, the initial set of candidate sets of estimation coefficients may be randomly assigned. Alternately, the initial set of candidate sets of estimation coefficients may be predetermined. In another example, the initial set may be pseudo-randomly assigned or chosen using a “best-guess” starting point.
Process 400 then advances to process 700. In process 700, a set of adjusted measured ratios, R_M,j, is determined for each candidate set of estimation coefficients, α_j, for each material under test. With reference to FIG. 7, process 700 begins at step 702 and advances to step 704. At step 704, one set of the candidate sets of estimation coefficients, α_j.may be selected. Process 700 advances to step 706. At step 706, a material from the set of materials under test may be selected. Proceeding to step 708, a set of adjusted measured ratios, R_M, may be determined based on the selected candidate set of estimation coefficients, α_j, and the set of measured training ratios, R_TR,j. For example, for each estimation coefficient, α_j, of the selected candidate set, the set of adjusted measured ratios may be determined using equation (5).
Process 700 may then advance to step 710. At step 710, one ratio in the set of adjusted measured ratios is selected. Proceeding to step 712, the selected adjusted measured ratio, R_M,j, is then compared to a respective standard ratio, R_T,j. This comparison may take the form of a difference calculation between the selected adjusted measured ratio, R_M,j, and the respective standard ratio, R_T,j, as per equation (8). Note that the respective standard ratio, R_T,j, for the material may be determined using the same pair of source energy levels as the selected adjusted measured ratio, R_M,j.
Process 700 may then advance to step 714, where it is determined if all of the adjusted measured ratios, R_M,j, in the set of adjusted measured ratios have been selected. If not, process steps 710 through 714 are thus repeated. If all adjusted measured ratios, R_M,j, in the set have been selected, process 700 advances to step 716. In step 716, it is determined if all of the materials of the set of materials under test have been selected. If not, process steps 706 through 716 are thus repeated. If all materials in the set of materials under test have been selected, process 700 advances to step 718. In step 718, it is determined if all of the candidate sets of estimation coefficients have been selected. If not, process steps 704 through 718 may be repeated. If all candidate sets have been selected, process 700 advances to step 720. In step 720, the results of comparison step 712 for each candidate set may be output for use by other process steps in process 400. Process 700 then ends at step 722.
Referring again to FIG. 4, process 400 advances from process 700 to step 406. In step 406, it is determined if a termination condition is satisfied. If a termination condition is not satisfied, process 400 advances to process 800. In process 800, the set of candidate sets of estimation coefficients are optimized using evolutionary recombination techniques to determine a new set of candidate sets of estimation coefficients. An exemplary embodiment of process 800 is shown in FIG. 8.
Process 800 begins at step 802 and advances to step 804. At step 804, the candidate set of estimation coefficients, α_j, may be selected based on a selection criteria, which may include an error value with respect to the standard ratio, R_T,j. This selected set forms the old generation or population. Proceeding to step 806, the candidate set is reproduced based on selecting coefficients from the old generation. Proceeding to step 808, mating occurs by dividing the selected parents of the old estimation coefficient population. In step 810, parent traits are crossed-over by selecting a point in the parent chromosomes, for example, at the bit level. Parents may then be combined at the selected points to form a new estimation coefficient population. The process may then advance to step 812 wherein random chromosomes of parent estimation coefficients in the new coefficient estimation population are mutated, for example, at the bit level. Proceeding to step 814, the new population of candidate sets of estimation coefficients may be output. The process 800 may end at step 816.
Alternately, the candidate sets of estimation coefficients may be ranked according to the results of the comparison of the adjusted measured ratios with the respective standard attenuation ratios output from process 700. Those candidate sets of estimation coefficients resulting in adjusted measured ratios closer to the respective standard attenuation ratios may be ranked higher. Based on the ranking, a portion of the set of candidate sets of estimation coefficients may be selected for recombination. A mutation may be provided. This mutation may take the form of random values randomly substituted for certain estimation coefficients in the candidate sets. The selected portion of the set of candidate sets may be recombined so as to produce a new set of candidate sets of estimation coefficients. Evolutionary techniques for recombination may be employed, such as those described in “Genetic Algorithms in Search, Optimization, and Machine Learning.” The ranking and/or recombination of at least a portion of the set of candidate sets of estimation coefficients may also be biased or weighted to favor one or a particular subset of materials over other materials of the set of known materials. For example, the ranking may be weighted to favor estimation coefficients that have low error value with respect to a subset of materials. This subset may include materials of particular interest in threat detection systems, such as high atomic number materials and/or special nuclear materials.
Process 400 may then advance from process 800 to process 700, so as to repeat process 700, step 406, and process 800 until a termination condition is met. The termination condition may be a threshold value for the amount of processing time or the number of iterations and/or generations within process 400 or within process 800. In an alternate embodiment, the termination condition may be a candidate set meeting a minimum error condition. This minimum error condition may be when the minimum error for each material under test, as calculated by equation (3), for a candidate set of estimation coefficients reaches a minimum value.
If step 406 determines that a termination condition is met, the process 400 advances to process 900. In process 900, the optimized set of estimation coefficients may be selected and outputted. With reference to FIG. 9, process 900 begins with step 902 and advances to step 904. In step 904, a candidate set of estimation coefficients is selected from the set of candidate sets. Various criteria may be used for the selection of the candidate set from the set of candidate sets. In an exemplary embodiment, the selected set may be the candidate set of estimation coefficients with the highest ranking. In an alternate embodiment, the selected set may be the candidate set of estimation coefficients meeting the minimum error condition. After selection of a particular candidate set, the process 900 advances to step 906, wherein the selected candidate set of estimation coefficients is output for use by another system, such as a material domain imaging system 100. Process 900 may then advance to and terminate at step 908. After process 900, process 400 may terminate at step 408.
It should be appreciated that the steps of the present invention may be repeated in whole or in part in order to perform the contemplated determination of an optimized set of estimation coefficients. Further, it should be appreciated that the steps mentioned above may be performed on a single or distributed processor. Also, the processes, modules, and units described in the various figures of the embodiments above may be distributed across multiple computers or systems or may be co-located in a single processor or system.
Embodiments of the method, system, and computer program product for determining an optimized set of estimation coefficients, may be implemented on a general-purpose computer, a special-purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit element, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmed logic circuit such as a PLD, PLA, FPGA, PAL, or the like. In general, any process capable of implementing the functions or steps described herein can be used to implement embodiments of the method, system, or computer program product for determining an optimized set of estimation coefficients.
Furthermore, embodiments of the disclosed method, system, and computer program product for determining an optimized set of estimation coefficients may be readily implemented, fully or partially, in software using, for example, object or object-oriented software development environments that provide portable source code that can be used on a variety of computer platforms. Alternatively, embodiments of the disclosed method, system, and computer program product for determining an optimized set of estimation coefficients can be implemented partially or fully in hardware using, for example, standard logic circuits or a VLSI design. Other hardware or software can be used to implement embodiments depending on the speed and/or efficiency requirements of the systems, the particular function, and/or particular software or hardware system, microprocessor, or microcomputer being utilized. Embodiments of the method, system, and computer program product for determining an optimized set of estimation coefficients can be implemented in hardware and/or software using any known or later developed systems or structures, devices and/or software by those of ordinary skill in the applicable art from the function description provided herein and with a general basic knowledge of the computer, radiographic, and evolutionary optimization arts.
Moreover, embodiments of the disclosed method, system, and computer program product for determining an optimized set of estimation coefficients can be implemented in software executed on a programmed general purpose computer, a special purpose computer, a microprocessor, or the like. Also, the method for determining an optimized set of estimation coefficients of this invention can be implemented as a program embedded on a personal computer such as a JAVA® or CGI script, as a resource residing on a server or image processing workstation, as a routine embedded in a dedicated processing system, or the like. The method and system can also be implemented by physically incorporating the method for determining an optimized set of estimation coefficients into a software and/or hardware system, such as the hardware and software systems of multi-energy radiographic inspection systems.
It is, therefore, apparent that there is provided, in accordance with the present invention, a method, computer system, and computer program product for determining an optimized set of estimation coefficients. While this invention has been described in conjunction with a number of embodiments, it is evident that many alternatives, modifications and variations would be or are apparent to those of ordinary skill in the applicable arts. Accordingly, Applicant intends to embrace all such alternatives, modifications, equivalents and variations that are within the spirit and scope of this invention.

Claims

1. A method for determining an optimized set of estimation coefficients, each estimation coefficient usable in a gray scale conversion of a respective measured ratio derived from radiographic images of an object, the method comprising:

(a) providing a set of known materials;

(b) obtaining a set of multiple radiographic images for each said known material, each radiographic image of the set obtained using a different source energy level;

(c) calculating a plurality of measured training ratios for each said known material from the respective set of multiple radiographic images;

(d) providing an initial set of candidate sets of estimation coefficients;

(e) providing accepted attenuation data for each said known material;

(f) determining a plurality of standard attenuation ratios for each said known material based on the respective accepted attenuation data, the plurality of standard attenuation ratios corresponding to the measured training ratios based on source energy levels; and

(g) employing a genetic algorithm to obtain the optimized set of estimation coefficients using the initial set of candidate sets of estimation coefficients, the plurality of measured training ratios, and the plurality of standard attenuation ratios,

wherein the genetic algorithm determines a plurality of adjusted measured ratios based on the plurality of measured training ratios and the set of candidate sets of estimation coefficients,

the genetic algorithm compares the adjusted measured ratios to respective standard attenuation ratios for each estimation coefficient,

the genetic algorithm reproduces and mates the candidate sets of estimation coefficients based on the comparison of the adjusted measured ratios and the respective standard attenuation ratios to arrive at a new set of candidate sets of estimation coefficients, and

the genetic algorithm repeats until a termination condition is satisfied; and

(h) outputting the optimized set of estimation coefficients.

2. The method according to claim 1, wherein said termination condition includes a condition when a particular candidate set of estimation coefficients satisfies a minimum error condition for all materials of the set of known materials.

3. The method according to claim 1, wherein said termination condition includes at least one of an amount of time for operation of the genetic algorithm and a number of generations produced by the genetic algorithm.

4. The method according to claim 1, wherein the optimized set of estimation coefficients is used in the determination of an effective atomic number of an unknown material based on radiographic images at different source energy levels of said unknown material.

5. The method according to claim 1, wherein the initial set of candidate sets of estimation coefficients is randomly chosen.

6. The method according to claim 1, wherein said genetic algorithm is weighted so as to emphasize a particular subset of the set of known materials.

7. The method according to claim 6, wherein the particular subset comprises at least one of a high atomic number material and a special nuclear material.

8. The method according to claim 1, further comprising using the optimized set of estimation coefficients in the gray scale conversion.

9. A computer program product comprising:

a computer readable medium encoded with software instructions that, when executed by a computer, cause the computer to perform the steps of:

(a) calculating a plurality of measured training ratios for each material of a set of materials under test from a respective set of radiographic images;

(b) providing accepted attenuation data for each said material of the set of materials under test;

(c) determining a plurality of standard attenuation ratios for each said material based on respective accepted attenuation data, the plurality of standard attenuation ratios corresponding to the measured training ratios based on source energy levels; and

(d) obtaining an optimized set of estimation coefficients for the set of materials under test from the plurality of measured training ratios and the plurality of standard attenuation ratios by using a genetic algorithm.

10. The computer program product according to claim 9, wherein the genetic algorithm includes:

determining a plurality of adjusted measured ratios based on the plurality of measured training ratios and a set of candidate sets of estimation coefficients, comparing the adjusted measured ratios to respective standard attenuation ratios for each said estimation coefficient,

reproducing and mating the candidate sets of estimation coefficients based on the comparing of the adjusted measured ratios and the respective standard attenuation ratios to arrive at a new set of candidate sets of estimation coefficients, and

repeating the determining of the plurality of adjusted measured ratios, the comparing, and the reproducing and mating until a termination condition is satisfied.

11. The computer program product according to claim 10, wherein said termination condition includes a condition when a particular candidate set of estimation coefficients satisfies a minimum error condition for all materials of the set of materials under test, an amount of time for operation of the genetic algorithm, or a number of generations produced by the genetic algorithm.

12. The computer program product according to claim 10, wherein the genetic algorithm is configured to provide at least one mutation in each new set of candidate sets of estimation coefficients, each mutation comprising a randomly modified estimation coefficient.

13. The computer program product according to claim 9, wherein the steps further include outputting the optimized set of estimation coefficients.

14. The computer program product according to claim 9, wherein the optimized set of estimation coefficients is used in the determination of an effective atomic number of an unknown material based on radiographic images at different source energy levels of the unknown material.

15. A system for determining an optimized set of estimation coefficients comprising:

an error evaluation module configured to determine a set of adjusted measured ratios for a material based on a selected candidate set of estimation coefficients and a plurality of respective measured training ratios for the material, compare the set of adjusted measured ratios for the selected candidate set of estimation coefficients to a set of corresponding standard attenuation ratios for the material, generate an output based on the comparison, and determine if the selected candidate set of estimation coefficients satisfies a termination condition; and

a genetic algorithm optimization module configured to reproduce at least a portion of a plurality of candidate sets of estimation coefficients based on the output of the comparison module so as to generate a plurality of new candidate sets of estimation coefficients and outputs the plurality of new candidate sets of estimation coefficients,

wherein the error evaluation module is configured to output the selected candidate set of estimation coefficients as the optimized set of estimation coefficients if the termination condition is satisfied.

16. The system of claim 15, wherein the termination condition includes a minimum error condition for the selected candidate set of estimation coefficients for various materials.

17. The system of claim 15, wherein the measured training ratios are determined from a plurality of radiographic images of a material, each radiographic image generated using a different source energy level, and the standard attenuation ratios are derived from accepted attenuation data from public data sources.

18. The system of claim 15, wherein said genetic algorithm optimization module is configured to provide at least one mutation in the plurality of candidate sets of estimation coefficients, each mutation comprising a randomly modified estimation coefficient.

19. The system of claim 15, wherein said genetic algorithm optimization module is configured to emphasize a particular subset of materials by biasing the comparison.

20. The system of claim 19, wherein the particular subset comprises at least one of a high atomic number material and a special nuclear material.