Patent Publication Number: US-2016231264-A1

Title: Remotely Classifying Materials Based on Complex Permittivity Features

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     Statement under MPEP 310. The U.S. government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of 0706D070-DI, 0707D070-DI, and 0708D070-DI, awarded by the Defense Advanced Research Projects Agency (DARPA). 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is generally directed to scanning items for concealed contraband, including but not limited to explosives, explosive precursors, and narcotics. 
     2. Background Art 
     Detection of contraband (such as, for example, explosives, explosive precursors, and narcotics) is a critical need of the U.S. Government (military, border control, and federal law enforcement), state and local law enforcement, and private security companies. Currently available systems for detecting contraband can be grouped into one of two categories: (i) residue-detection methods, which rely on physical residues or vapors to detect contraband; or (ii) nuclear-based methods, which use ionizing radiation to detect contraband. 
     Both the residue-detection methods and the nuclear-based methods have drawbacks. First, the residue-detection methods require access to a physical sample in order to detect contraband. Oftentimes, however, the contraband may be concealed, making residue detection difficult or impossible. For example, contraband that is odorless may be difficult to detect using residue-detection methods. Second, although nuclear-based methods do not require access to physical samples (like the residue-detection methods), the nuclear-based methods require ionizing (e.g., neutron) radiation, which can have deleterious effects on humans and/or the surrounding environment. Accordingly, nuclear-based methods are limited in their application by safety and cost considerations. 
     In addition to the residue-detection and nuclear-based methods, the food industry and the semiconductor industry use measurement methods based on the dielectric properties of materials to assess the quality of their respective products. Although the dielectric-based measurement methods do not have the same drawbacks as the residue-detection and nuclear-based methods, the dielectric-based measurement methods used by the food industry and the semiconductor industry are ill-suited for detecting contraband. Specifically, these dielectric-based measurement methods operate over very short ranges, have no imaging capability (e.g., are single voxel system), and are typically only used for sensing the presence of a single, targeted measurand (e.g., moisture content in cookies or purity of a pharmaceutical under manufacture). 
     For example, U.S. Pat. No. 7,280,940 to Goldfine et al., entitled “Segmented Field Dielectric Sensor Array for Material Characterization” (filed Mar. 7, 2006) (issued Oct. 9, 2007) describes representative measurement methods used for quality control in the semiconductor industry. Specifically, the &#39;940 patent is “directed toward the nondestructive detection and characterization of insulating or semiconductor materials . . . ” &#39;940 patent, col. 3 11. 31-33. According to the &#39;940 patent, electrodes are placed in very close proximity with a material under test (“MUT”) to generate a two-dimensional grid used to estimate electrical properties of the MUT. Like the conventional measurement methods used by the semiconductor industry discussed above, the &#39;940 patent teaches that the proximity, or “lift-off,” between the electrodes and the MUT is a very short range—on the order of a few millimeters to a few hundredths of a millimeter. 
     Given the foregoing, what is needed are methods, systems, and computer program products for remotely classifying materials based on complex permittivity features. The remote classification of materials could be used to identify contraband. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention meets the above-described needs by providing methods, systems, and computer-program products for remotely classifying materials based on complex permittivity features. In accordance with embodiments of the present invention, the remotely classified materials are used to identify contraband. 
     For example, an embodiment of the present invention provides a system for identifying materials. The system includes a first electrode, a second electrode, and a computing module. The first electrode is configured to generate an electric field. The second electrode is configured to sense interaction of the electric field with a container and any materials in the container and to provide a signal corresponding thereto. The computing module is configured to (i) convert the signal into one or more electrical parameters, (ii) classify the materials in the container based on the one or more electrical parameters, and (iii) identify at least one of the materials in the container based on the classifications. 
     Another embodiment of the present invention provides a method for identifying materials. The method includes several steps. First, an electric field is generated. Second, interaction of the electric field with a container and any materials in the container is sensed to provide a signal. Third, the signal is converted into one or more electrical parameters. Fourth, the materials in the container are classified based on the one or more electrical parameters. Then, at least one of the materials in the container is identified based on the classifications. 
     A further embodiment of the present invention provides a tangible computer-readable medium having stored thereon computer-executable instructions that, if executed by a device, cause the device to perform a method for identifying materials. The method includes several steps. First, a signal, sensed by an electrode, is converted into one or more electrical parameters, wherein the electrode is configured to sense interaction of an electric field with a container and any materials in the container. Second, the materials in the container are classified based on the one or more electrical parameters. Then, at least one of the materials in the container is identified based on the classifications. 
     Further features and advantages of the invention, as well as the structure and operation of various embodiments of the invention, are described in detail below with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES 
       The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the relevant art(s) to make and use the invention. 
         FIGS. 1A and 1B  depict example systems for remotely classifying materials based on electrical parameters. 
         FIG. 2  depicts the real and imaginary components of the complex diectric permittivity of a material as a function of the frequency of an electric field used to excite the material. 
         FIGS. 3A and 3B  depict example embodiments of systems for classifying materials included in an envelop. 
         FIGS. 4A-D  depict example data obtained from the systems of  FIGS. 3A and 3B . 
         FIG. 5  depicts example classification results obtained from the systems of  FIGS. 3A and 3B . 
         FIG. 6  depicts another example embodiment of a system for classifying materials included in a sample. 
         FIGS. 7A and 7B  depict example signatures for classifying materials included in a sample based on clustering of data points within a plot. 
         FIG. 8  depicts an example embodiment of a system for classifying materials included in an automobile. 
         FIGS. 9A and 9B  depict example data obtained from the system of  FIG. 8 . 
         FIGS. 10A-D  depict more example data obtained from the system of  FIG. 8 . 
         FIGS. 11A-D  depict still more example data obtained from the system of  FIG. 8 . 
         FIGS. 12 and 13  depict example signatures for classifying materials included in a sample based on clustering of data points within a plot. 
         FIG. 14  depicts example classification results obtained from the system of  FIG. 8 . 
         FIG. 15  depicts example computer system that may be used in accordance with embodiments of the present invention. 
     
    
    
     The features and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the corresponding reference number. 
     DETAILED DESCRIPTION OF THE INVENTION 
     I. Overview 
     The present invention is directed to remotely classifying materials based on complex permittivity features of the materials. In this document, references to “one embodiment,” “an embodiment,” “an example embodiment,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. 
     Embodiments of the present invention are directed to systems and methods for remotely detecting and classifying materials included in a container based on variations in electrical parameters (e.g., complex permittivity) of the materials. By remotely detecting and classifying materials, embodiments of the present invention may be used to detect contraband included in the container. 
     As used herein, the term “container” means a structure that holds or may be configured to hold goods, items, or materials. Example containers within the spirit and scope of the present invention may include, but are not limited to, an envelop, a jar, a box, a portable compartment (as may be used, for example, on a train, a ship, or a plane), a piece of luggage (such as, for example, a purse, a bag, a suitcase, a backpack, or the like), a vehicle (such as, for example, a train, a plane, or an automobile—including a car, a truck, a bus, and the like), or some other type of structure that holds or may be configured to hold goods, items, or materials. 
     As used herein, the term “contraband” means an illegal or prohibited good, item, or material. Examples of contraband may include, but are not limited to explosives, explosive precursors, narcotics, or some other type of illegal or prohibited good, item, or material. 
     The classification of materials and detection of contraband in accordance with embodiments of the present invention is based on dispersive properties of a material positioned relative to a driving electrode and one or more sensing electrodes. The driving electrode and the one or more sensing electrodes may be configured as opposing plate electrodes (as illustrated, for example, in  FIG. 1A ), a fringing-field sensor array (as illustrated, for example, in  FIG. 1B ), or a combination thereof. 
     For example,  FIG. 1A  depicts an example system  100  in which electrodes are configured as opposing plate electrodes. System  100  includes a driving electrode  102  and a sensing electrode  104  configured as two opposing plate electrodes, with a container  106  located in between. Although system  100  is illustrated to include only one driving electrode  102  and one sensing electrode  104 , it is to be appreciated that system  100  may include a plurality of driving electrodes and a plurality of sensing electrodes. In operation, driving electrode  102  is energized with a highly stable electric field. The electric field may have a single frequency (such as, for example, a sinusoidal waveform) or may have a plurality of frequencies (such as, for example, a substantially triangular waveform or a substantially square waveform). The electric field emanating from driving electrode  102  is distorted or modified by interstitial material included in container  106 . The degree of distortion or modification of the electric field is dependent upon the interstitial material&#39;s dielectric characteristics, as well as other factors, as explained in more detail below. Sensing electrode  104  measures voltage potential caused by the electric field. Based on the voltage potential, a computing module  110 —which is coupled to driving electrode  102  and sensing electrode  104 —derives electrical parameters of the interstitial material. The electrical parameters may include, for example, impedance, phase, the (complex) dielectric constant, or other electrical parameters. Based on these electrical parameters, the computing module  110  classifies the material(s) included in container  106  and identifies whether container  106  includes contraband. 
       FIG. 1B  depicts an example system  150  in which driving electrode  102  and sensing electrode  104  are configured as a fringing-field sensor array. In this system  150 , driving electrode  102  and sensing electrode  104  are in a planar array with container  106  in a plane orthogonal to the plane of driving electrode  102  and sensing electrode  104 . Like system  100 , system  150  may include a plurality of driving electrodes  102  and a plurality of sensing electrodes  104 . As mentioned above, the electric field may have a single frequency or may have a plurality of frequencies. 
     In operation, driving electrode  102  generates a fringing electric field that interacts with container  106  (and any materials therein) and is then sensed by sensing electrode  104 . The distance between driving electrode  102  and sensing electrode  104  may be physically varied (e.g., increased) to vary (e.g., increase) the depth that the fringing electric field penetrates along the plane of container  106 . Alternatively, when the system includes a plurality of driving electrodes and a plurality of sensing electrodes, the distance between the driving electrodes and the sensing electrodes may be effectively varied (e.g., increased) by varying the electrodes that are energized to generate the electric field and by varying the electrodes that are selected to sense the electric field. So, rather than mechanically moving electrodes, embodiments of the present invention electronically switch between electrodes to effectively adjust the distance between the electrodes used to generate and/or sense the electric field. 
     Like system  100  of  FIG. 1A , system  150  includes computing module  110 , which derives electrical parameters of interstitial material that may be included in container  106 . In embodiments, both parallel-plate measurements of system  100  and fringing-field measurements of system  150  may be used to derive the electrical parameters of the interstitial materials, as the data produced by these two systems have different sensitivities. 
     The electrical parameter measurements provided by the parallel-plate configuration of system  100  and/or the fringing-field configuration of system  150  are processed by computing module  110 . Computing module  110  may implement any of a variety of classification algorithms. Multiple electrode combinations may be used to produce a map of dielectric properties and classification within different volume elements. The presence of sharp discontinuities in dielectric properties is a macro-indication that the test article may warrant further investigation, and classification based on known signatures for contraband substances may be conclusive. 
     In embodiments, for example, computing module  110  may implement linear discriminant analysis (LDA) to develop signatures for identifying contraband substances based on the electrical parameters. As explained in more detail below, LDA is a method for separating the electrical parameters into different clusters corresponding to the different types of materials that may be included in container  106 . 
     As mentioned above, the degree to which a material in container  106  distorts or modifies an applied electric field is dependent on dispersive properties of the material. The dispersive properties of a material can be understood, for example, in terms of the complex permittivity, which comprises a dielectric constant (relating the applied electric field to a displacement field within the material) and a frequency-dependent conductivity (relating the applied electric field to a current density within the material). The complex permittivity of a material can be represented mathematically as follows: 
       ∈*=∈′+ i∈″ 
 
     wherein ∈* is the complex permittivity, ∈′ is the dielectric constant or the real part of the complex permittivity, and ∈″ is the imaginary part of the complex permittivity. The imaginary part of the complex permittivity can be represented mathematically as follows: 
     
       
         
           
             
               ɛ 
               ″ 
             
             = 
             
               σ 
               
                 2 
                  
                 π 
                  
                 
                     
                 
                  
                 f 
               
             
           
         
       
     
     wherein σ is the conductivity of the material and f is the frequency of the applied electric field. 
       FIG. 2  depicts a schematic plot of the real part (∈′) and the imaginary part (∈″) of the complex permittivity of a material as a function of the frequency of the applied electric field. At optical frequencies (or wavelengths), molecular vibration and rotation of molecules and inter atomic bonds lead to the detailed structure observed in infrared spectroscopy. At extremely low excitation frequencies (e.g., 1 Hz to 500,000 Hz), polarized dipoles re-align to neutralize the effect of the applied field. This re-alignment of dipoles occurs to a varying extent for different materials and gives rise to changes in the complex permittivity of materials. These changes over a span of frequencies form a signature that can be exploited for material identification. The significant dispersion of dielectric properties of materials occurs at both the extremely low end of the spectra and in the millimeter wave and higher region. Some embodiments of the present invention operate at extremely low frequencies (ELF), while other embodiments operate in the millimeter and Terahertz range. 
     For illustrative purposes, and not limitation, three embodiments are described below in which the container respectively comprises an envelop, a jar, and an automobile. It is to be appreciated, however, that other forms of containers may be used without deviating from the spirit and scope of the present invention. 
     II. Example Embodiment for Classifying Materials Included in an Envelop 
       FIGS. 3A and 3B  respectively illustrate an example parallel-plate system  300  and an example fringing-field system  350  for classifying materials included in an envelop  306 . Using system  300 , system  350 , or a combination thereof, contraband included within envelop  306  may be detected. 
     Referring to  FIG. 3A , system  300  includes a driving electrode  302 , a sensing electrode  304 , and a computing module  310  coupled to each electrode. Driving electrode  302  and sensing electrode  304  are arranged as opposing plate electrodes. In an embodiment, the separation between driving electrode  302  and sensing electrode  304  is approximately 15 millimeters, and the measurement surface is approximately 6.5 inches by approximately 9.74 inches. 
     Referring to  FIG. 3B , system  350  includes a driving electrode  352 , a sensing electrode  354 , and computing module  310  coupled to each electrode. In system  350  driving electrode  352  and sensing electrode  354  are arranged as a fringing-field array. 
     In both system  300  and system  350 , driving electrodes  302 ,  352  respectively generate an electric field that interacts with envelop  306  and any materials included therein. The interaction of the electric field with envelop  306  and any materials therein distorts the electric field. Sensing electrodes  304 ,  354  sense the distorted electric field to provide a signal. Computing module  310  receives the signal and derives electrical parameters of the materials included in envelop  306 . For example, computing module  310  may derive data as illustrated in  FIGS. 4A-4D . 
     Based on such data, computing module  310  classifies materials included in envelop  306 . In embodiments, computing module  310  classifies the materials based on linear discriminant analysis (LDA), which is a mathematical technique for identifying a subspace in which data has the largest variance. In this way, the data of the electrical parameters of the materials can potentially be organized in clusters, wherein each cluster of data corresponds to a different material included in envelop  306 . LDA is described in more detail below. 
       FIG. 5  illustrates example results from an experiment to classify materials using a system like the ones shown in  FIGS. 3A and 3B . In  FIG. 5 , the materials listed on the rows represent materials that were included in envelop  306 . The materials listed on the columns represents the classifications made by computing module  310 . So, for example, computing module  310  correctly identified air nine times; in contrast, computing module  310  correctly identified potassium chlorate only three times and incorrectly identified potassium chlorate two times (once as potassium nitrate and once as sodium bicarbonate). 
     III. Example Embodiment for Classifying Materials Included in a Jar 
       FIG. 6  illustrates an example system  600  for classifying materials included in a jar. Referring to  FIG. 6 , system  600  includes a driving electrode  652 , a sensing electrode  654 , a motor driver  610 , and a platform  606 . Driving electrode  652  and sensing electrode  654  are positioned along a first (e.g., transverse) arm of aluminum segment  630 . Platform  606  is configured to hold a jar (or other test object) and is coupled to a non-conductive linkage  620 . Non-conductive linkage is configured to move along a second (e.g., longitudinal) arm of aluminum segment  630  and a non-conductive segment  640  that is in a line with the second arm of aluminum segment  630 . Motor driver  610  is configured to: (1) cause driving electrode  652  and sensing electrode  654  to move along the first (e.g., transverse) segment of aluminum segment  630 , thereby adjusting the distance between driving electrode  652  and sensing electrode  654 ; and/or (2) cause non-conductive linkage  620  to move along the second (e.g., longitudinal) arm of aluminum segment  630 , thereby adjusting the distance between a sample positioned on platform  606  and driving electrode  652  and sensing electrode  654 . Motor driver  610  is coupled to a computing module (not shown), which is configured to send commands to motor driver  610  and to process data from sensing electrode  654 . 
     The computing module may implement one or more methods for classifying materials included in a sample positioned on platform  606 . For example, the computing module may implement a Bayesian-classification method. The computing module may then compute, for example, the Bhattacharyya distance between materials included in the sample. In general, the Bhattacharyya distance measures the similarity of two discrete probability distributions. In this context, the Bhattacharyya distance may be used as a measure for assessing the performance of the Bayesian-classification method. Table 1 includes the Bhattacharyya distance for a classifying various materials included in a sample. Assuming equal prior probabilities for two probability distributions, the Bhattacharyya distance, B, bounds the Bayes error (i.e., error&lt;exp(−B)). This means that B&gt;10 gives an error rate lower than 2e-5, B&gt;5 gives an error rate lower than 0.3%, and B&gt;2 gives an error rate lower than 6.8%. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Material A 
                 Material B 
                 Material C 
                 Material D 
                 Material E 
                 Material F 
                 Material G 
                 Material H 
                 Material I 
                 Material J 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Material A 
                 0 
                 607 
                 2342 
                 3.89 
                 442 
                 3067 
                 3668 
                 4042 
                 1603 
                 1076 
               
               
                 Material B 
                 607 
                 0 
                 610 
                 563 
                 482 
                 1050 
                 1325 
                 1664 
                 345 
                 234 
               
               
                 Material C 
                 2342 
                 610 
                 0 
                 2273 
                 1821 
                 501 
                 476 
                 818 
                 465 
                 760 
               
               
                 Material D 
                 3.89 
                 563 
                 2273 
                 0 
                 451 
                 2984 
                 3551 
                 3951 
                 1551 
                 1041 
               
               
                 Material E 
                 442 
                 482 
                 1821 
                 451 
                 0 
                 1753 
                 2471 
                 2416 
                 715 
                 332 
               
               
                 Material F 
                 3067 
                 1050 
                 501 
                 2984 
                 1753 
                 0 
                 114 
                 71 
                 243 
                 570 
               
               
                 Material G 
                 3668 
                 1325 
                 476 
                 3551 
                 2471 
                 114 
                 0 
                 147 
                 538 
                 994 
               
               
                 Material H 
                 4042 
                 1664 
                 818 
                 3951 
                 2416 
                 71 
                 147 
                 0 
                 558 
                 996 
               
               
                 Material I 
                 1603 
                 345 
                 465 
                 1551 
                 715 
                 243 
                 538 
                 558 
                 0 
                 74 
               
               
                 Material J 
                 1076 
                 234 
                 760 
                 1041 
                 332 
                 570 
                 994 
                 996 
                 74 
                 0 
               
               
                   
               
            
           
         
       
     
     System  600  can be used to collect various data used to classify materials included in a container positioned on platform  606 . In operation, driving electrode  652  generates an electric field. Sensing electrode  654  senses distortions in the electric field based on the interaction of the electric field with the container (and materials therein) positioned on platform  606 . Data regarding the distortion of the electric field is collected by a computing module (not shown). Data may be collected for various frequencies of the electric field generated by driving electrode  652 , for various distances between driving electrode  652  and sensing electrode  654 , and/or for various distances between platform  606  and the first (e.g., transverse) arm of segment  630 . 
     From the data of the distortion of the electric field, the computing module can derive electrical parameters of the materials included in the container. For example, the computing module may derive the complex permittivity of the materials as a function of frequency. In embodiments, the data of the electrical parameters is organized into multi-dimensional vectors. The multi-dimensional vectors are projected into a lower-dimensional subspace using LDA. Importantly, the data may be grouped into distinct clusters in the lower-dimensional subspace, wherein the distinct clusters represent distinct materials included in the container. In this way, each cluster may serve as a signature for classifying the materials included in the container. 
     To further illustrate how computing module may classify materials, example data collected from system  600  is presented below. It is to be appreciated, however, that this example data is presented for illustrative purposes only, and not limitation. In this example data, five classes of materials were tested: air, salt, sugar, starch, and flour. The data was taken from a fixed distance (i.e., the separation between the materials and the first (e.g., transverse) arm of segment  630  was fixed). Twenty samples of air, salt, and starch and seventy samples of sugar and flour were used. The computing module derived the complex impedance of the samples taken at six different frequencies, resulting in 12-dimensional sample vectors (6 real components and 6 imaginary components). The mean air signature was subtracted from all the data. The 12-dimensional sample vectors were projected into a two-dimensional subspace using Fisher LDA. 
       FIGS. 7A and 7B  illustrate example plots of the data when projected into the two-dimensional subspace using Fisher LDA. In particular,  FIG. 7A  illustrates the clustering of the data when the distance between the samples and the electrodes remains fixed; whereas  FIG. 7B  illustrates the clustering of the data when the distance between the samples and the electrodes varies. As illustrated in  FIG. 7A , the data falls into four distinct clusters corresponding to the four classes of materials (other than air) included in the container: salt, sugar, starch, and flour. Accordingly, the clustering serves as a signature for classifying materials. 
     The Bhattacharyya distance for classifying various materials using system  600  of  FIG. 6  are illustrated below in Table 2 and Table 3. As mentioned above, the Bhattacharyya distance measures the similarity of two discrete probability distributions. Table 2 illustrates the Bhattacharyya distances when the distance between the samples and the electrodes was in a first range of distances, and Table 3 illustrates the Bhattacharyya distances when the distance between the samples and the electrodes was in a second range of distances. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Bhattacharyya distances for 16 cm to 26 cm range 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Starch 
                 Flour 
                 Salt 
                 Sugar 
                 Water 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Starch 
                 0 
                 3.1 
                 1.7 
                 1.0 
                 2.4 
               
               
                   
                 Flour 
                 3.1 
                 0 
                 3.2 
                 5.0 
                 7.1 
               
               
                   
                 Salt 
                 1.7 
                 3.2 
                 0 
                 4.3 
                 6.8 
               
               
                   
                 Sugar 
                 1.0 
                 5.0 
                 4.3 
                 0 
                 1.7 
               
               
                   
                 Water 
                 2.4 
                 7.1 
                 6.8 
                 1.7 
                 0 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Bhattacharyya distances for 50 cm to 80 cm range 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Starch 
                 Flour 
                 Salt 
                 Sugar 
                 Water 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Starch 
                 0 
                 0.66 
                 0.49 
                 0.52 
                 3.8 
               
               
                   
                 Flour 
                 0.66 
                 0 
                 0.46 
                 0.36 
                 3.5 
               
               
                   
                 Salt 
                 0.49 
                 0.46 
                 0 
                 0.53 
                 4.0 
               
               
                   
                 Sugar 
                 0.52 
                 0.36 
                 0.53 
                 0 
                 3.8 
               
               
                   
                 Water 
                 3.8 
                 3.5 
                 4.0 
                 3.8 
                 0 
               
               
                   
                   
               
            
           
         
       
     
     IV. Example Embodiment for Classifying Materials Included in an Automobile 
       FIG. 8  depicts an example system  800  for classifying materials included in an automobile  801 . System  800  includes a driving electrode  802  mounted on a linear guide  814  and a sensing electrode  804  mounted on a linear guide  824 . Driving electrode  802  and sensing electrode  804  are coupled to a computing module  810 , which sends instructions to and receives data from driving electrode  802  and/or sensing electrode  824 . Computing module  810  is also coupled to motors  812  and  816 . Motor  812  is configured to cause driving electrode  802  to move along linear guide  814 , and motor  816  is configured to cause sensing electrode  804  to move along linear guide  824 . 
     System  800  may be used, for example, to detect contraband (e.g., explosives, explosive precursors, and/or narcotics) included in automobile  801 . In operation, driving electrode  802  generates an electric field, and sensing electrode  804  senses distortions in the electric field after the electric field interacts with materials in the automobile  801 , in a similar manner to the embodiments described above. And, like the embodiments discussed above, computing module  810  classifies the materials included in automobile  801  based on electrical parameters of the materials derived from the distortions of the electric field. 
     To further illustrate how system  800  may be used to detect the presence of contraband, example data collected from system  800  is presented below. It is to be appreciated, however, that this example data is presented for illustrative purposes only, and not limitation. In this example, several different types of explosive materials and several different types of relatively benign materials were tested. Data were taken over a fairly broad frequency range from approximately 10 Hz to 40 kHz. The higher frequencies were measured first. The spacing between driving electrode  802  and sensing electrode  804  was fixed. Each sample vector is 12 dimensional (including 6 real components and 6 imaginary components). 
       FIGS. 9A and 9B  illustrate example pre-measurement signatures obtained by system  800 . Specifically,  FIG. 9A  illustrates pre-measured signatures of the capacitance of the various materials as a function of the frequency of the applied electric field, and  FIG. 9B  illustrates pre-measured signatures of the phase of the various materials as a function of the frequency of the applied electric field. 
     In addition to the pre-measurement signatures, system  800  may be used to obtain data used to derive electrical parameters of materials included in automobile  801 . For example,  FIGS. 10A-D  illustrate plots of electrical parameters of the various materials as a function of the frequency of the applied electric field when the electrodes are at a first fixed position. Similarly,  FIGS. 11A-D  illustrates plots of electrical parameters of the various materials as a function of the frequency of the applied electric field when the electrodes are at a second fixed position. Specifically,  FIGS. 10A and 11A  depict plots of the gain of the electric field as a function of frequency;  FIGS. 10B and 11B  depict plots of the capacitance of the various materials as a function of frequency;  FIGS. 10C and 11C  depict plots of the phase of the electric field as a function of frequency; and  FIGS. 10D  and  11 D depict plots of the conductance of the various materials as a function of frequency. 
     Computing module  810  may implement one or more methods to classify the materials in automobile  801 . For example, according to a first example method, computing module  810  compares normalized blind measurements with the normalized pre-measured signatures illustrated in  FIGS. 9A and 9B . According to this method, computing module  810  calculates the deviation between the normalized blind measurements of capacitance and the pre-measurement signatures of capacitance (which are illustrated in  FIG. 9A ). Based on this method, the pre-measured sample with the smallest absolute value deviation to the unknown sample is identified as a match. 
     According to a second example method, computing module  810  computes a Bayesian-classification method. The performance of the Bayesian-classification method can be assessed using the Bhattacharyya distance. As mentioned above, the Bhattacharyya distance measures the similarity of two discrete probability distributions and may be used to measure the separability of classes in a classification. The Bhattacharyya distances for the above-mentioned example materials are presented below in Table 4. Assuming equal prior probabilities for two probability distributions, the Bhattacharyya distance, B, bounds the Bayes error (i.e., error&lt;exp(−B)). This means that B&gt;10 gives an error rate lower than 2e-5, B&gt;5 gives an error rate lower than 0.3%, and B&gt;2 gives an error rate lower than 6.8%. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Bhattacharyya distances for example materials tested 
               
               
                 using the system of FIG. 8 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Material A 
                 Material B 
                 Material C 
                 Material D 
                 Material E 
                 Material F 
                 Material G 
                 Material H 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Material A 
                 0 
                 35.63 
                 277.70 
                 32.60 
                 5.11 
                 35.57 
                 37.52 
                 221.69 
               
               
                 Material B 
                 35.63 
                 0 
                 120.80 
                 1.72 
                 48.60 
                 1.59 
                 1.67 
                 84.03 
               
               
                 Material C 
                 277.70 
                 120.80 
                 0 
                 125.50 
                 309.93 
                 118.38 
                 116.59 
                 5.04 
               
               
                 Material D 
                 32.60 
                 1.72 
                 125.50 
                 0 
                 46.93 
                 1.27 
                 0.59 
                 87.80 
               
               
                 Material E 
                 5.11 
                 48.60 
                 309.93 
                 46.93 
                 0 
                 49.39 
                 52.66 
                 252.50 
               
               
                 Material F 
                 35.57 
                 1.59 
                 118.38 
                 1.27 
                 49.39 
                 0 
                 1.10 
                 82.51 
               
               
                 Material G 
                 37.52 
                 1.67 
                 116.59 
                 0.59 
                 52.66 
                 1.10 
                 0 
                 80.22 
               
               
                 Material H 
                 221.69 
                 84.03 
                 5.04 
                 87.80 
                 252.50 
                 82.51 
                 80.22 
                 0 
               
               
                   
               
            
           
         
       
     
     According to a third example method, computing module  810  implements LDA to find a linear combination of features that best separates the classes of materials included in automobile  801 . For example,  FIG. 12  illustrates the results of LDA implemented on the above-mentioned materials, wherein the horizontal and vertical dimensions in the plot of  FIG. 12  represent the best cross-section of a 7-dimensional space.  FIG. 13  illustrates the horizontal and vertical dimensions of  FIG. 12  proportionally mapped to a third dimension to show an equivalent cluster density (which is not to be confused with separability). 
     According to a fourth example method, computing module  810  implements a partial least squares fit. Unlike a conventional least squares fit, a partial least squares fit is well-suited for blind tests, but requires extensive preliminary measurements prior to material identification. According to a partial least squares fit, prediction functions are extracted from cross-product matrices involving both a response variable, Y, and an independent variable, X. Compared to a conventional least squares fit, calibrations in a partial least squares fit are generally more robust, provided that the calibration set accurately reflects the range of variability expected in unknown samples. 
       FIG. 14  illustrates example results obtained from a partial least squares fit. It is to be appreciated that these results are intended for illustrative purposes only, and not limitation. In  FIG. 14 , the rows show what the true measurements are, and the columns show what computing module  810  concluded the material is. 
     V. Example Computer System 
     Various aspects of the present invention—such as the computing modules described herein—can be implemented by software, firmware, hardware, or a combination thereof.  FIG. 15  illustrates an example computer system  1500  in which an embodiment of the present invention, or portions thereof, can be implemented as computer-readable code. Various embodiments of the invention are described in terms of this example computer system  1500 . After reading this description, it will become apparent to a person skilled in the relevant art how to implement the invention using other computer systems and/or computer architectures. 
     Computer system  1500  includes one or more processors, such as processor  1504 . Processor  1504  can be a special purpose or a general purpose processor. Processor  1504  is connected to a communication infrastructure  1506  (for example, a bus or network). Computer system  1500  may also include a graphics processing system  1502  for rendering images to an associated display  1530 . 
     Computer system  1500  also includes a main memory  1508 , preferably random access memory (RAM), and may also include a secondary memory  1510 . Secondary memory  1510  may include, for example, a hard disk drive  1512  and/or a removable storage drive  1514 . Removable storage drive  1514  may comprise a floppy disk drive, a magnetic tape drive, an optical disk drive, a flash memory, or the like. The removable storage drive  1514  reads from and/or writes to a removable storage unit  1518  in a well known manner. Removable storage unit  1518  may comprise a floppy disk, magnetic tape, optical disk, etc. which is read by and written to by removable storage drive  1514 . As will be appreciated by persons skilled in the relevant art(s), removable storage unit  1518  includes a computer usable storage medium having stored therein computer software and/or data. 
     In alternative implementations, secondary memory  1510  may include other similar means for allowing computer programs or other instructions to be loaded into computer system  1500 . Such means may include, for example, a removable storage unit  1522  and an interface  1520 . Examples of such means may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an EPROM, or PROM) and associated socket, and other removable storage units  1522  and interfaces  1520  which allow software and data to be transferred from the removable storage unit  1522  to computer system  1500 . 
     Computer system  1500  may also include a communications interface  1524 . Communications interface  1524  allows software and data to be transferred between computer system  1500  and external devices. Communications interface  1524  may include a modem, a network interface (such as an Ethernet card), a communications port, a PCMCIA slot and card, or the like. Software and data transferred via communications interface  1524  are in the form of signals  1528  which may be electronic, electromagnetic, optical, or other signals capable of being received by communications interface  1524 . These signals  1528  are provided to communications interface  1524  via a communications path  1526 . Communications path  1526  carries signals  1528  and may be implemented using wire or cable, fiber optics, a phone line, a cellular phone link, an RF link or other communications channels. 
     Computer programs (also called computer control logic) are stored in main memory  1508  and/or secondary memory  1510 . Computer programs may also be received via communications interface  1524 . Such computer programs, when executed, enable computer system  1500  to implement embodiments of the present invention as discussed herein, such as the computing modules. In particular, the computer programs, when executed, enable processor  1504  to implement the methods of embodiments of the present invention, including the methods implemented by the computing modules. Accordingly, such computer programs represent controllers of the computer system  1500 . Where the invention is implemented using software, the software may be stored in a computer program product and loaded into computer system  1500  using removable storage drive  1514 , interface  1520 , hard drive  1512  or communications interface  1524 . 
     VI. Conclusion 
     Set forth above are example systems, methods, and computer-program products for remotely classifying materials based on complex permittivity features. While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. 
     It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary embodiments of the present invention as contemplated by the inventor(s), and thus, are not intended to limit the present invention and the appended claims in any way. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.