submitted papers

Simulated Radiance Profiles for Automating the Interpretation ofAirborne Passive Multi-Spectral Infrared Images

YUSUF SULUB* and GARY W. SMALL�Department of Chemistry and Optical Science and Technology Center, University of Iowa, Iowa City, Iowa 52242

Methodology is developed for simulating the radiance profiles acquired

from airborne passive multispectral infrared imaging measurements of

ground sources of volatile organic compounds (VOCs). The simulation

model allows the superposition of pure-component laboratory spectra of

VOCs onto spectral backgrounds that simulate those acquired during field

measurements conducted with a downward-looking infrared line scanner

mounted on an aircraft flying at an altitude of 2000–3000 ft (approxi-

mately 600–900 m). Wavelength selectivity in the line scanner is

accomplished through the use of a multichannel Hg:Cd:Te detector with

up to 16 integrated optical filters. These filters allow the detection of

absorption and emission signatures of VOCs superimposed on the

upwelling infrared background radiance within the instrumental field of

view (FOV). By combining simulated radiance profiles containing analyte

signatures with field-collected background signatures, supervised pattern

recognition methods can be employed to train automated classifiers for

use in detecting the signatures of VOCs during field measurements. The

targeted application for this methodology is the use of the imaging system

to detect releases of VOCs during emergency response scenarios. In the

work described here, the simulation model is combined with piecewise

linear discriminant analysis to build automated classifiers for detecting

ethanol and methanol. Field data collected during controlled releases of

ethanol, as well as during a methanol release from an industrial facility,

are used to evaluate the methodology.

Index Headings: Infrared imaging; Remote sensing; Simulation; Volatile

organic compounds; VOCs; Pattern recognition.

INTRODUCTION

Multi-spectral infrared (IR) remote sensing is a powerful toolfor measuring chemical species in the atmosphere and has beenutilized in a wide range of surveillance and target detectionapplications such as probing forest fires,1 weather forecasting,2

mineral identification,3 and investigating urban growth rates.4

An area of growing interest is the use of downward-lookingmulti-spectral IR imaging devices deployed on aircraft for thedetection of ground sources of volatile organic compounds(VOCs) released into the atmosphere.5,6 For example, theability to interrogate the site of a train derailment or chemicalplant accident remotely can be valuable to decision makersbefore deploying personnel to investigate a potentiallyhazardous accident site.

These imaging sensors collect the naturally occurring IRradiation emitted by objects or reflected from solar radiation.Because different materials absorb and reflect radiation atdifferent wavelengths distinct to their character, target speciescan be identified on the basis of their spectral radiancesignatures in the remotely sensed images. The upwellingradiation is further categorized to a range of wavelength bandsby coupling the elements of a multichannel detector with a setof bandpass optical filters. The output of this system is aradiance spectrum with points corresponding to the discretespectral band centers of the filters.

The high data rates obtained with imaging sensors motivatethe need for automated interpretation of the acquired images.Such interpretation tools are termed pattern recognitionmethods. For detecting chemical signatures within images,pattern recognition applications have mainly focused onapplying numerous supervised or unsupervised classificationalgorithms.5–8 Supervised methods require the selection oftraining samples that are used to compute a classification modelthat can recognize image pixels possessing the characteristicspectral signature of a target compound. The term ‘‘trainingsamples’’ refers to image pixels for which the presence orabsence of the target signature is known. By contrast,unsupervised techniques are used to search for naturalgroupings within the data and thus require no prior knowledgeof the classifications of the pixels. Interpreting or validating theresults of the unsupervised methods does require knowledge ofthe scene, however, and the unsupervised methods do not lendthemselves readily to the automated detection of targetsignatures.

Implementing pattern recognition techniques in a compounddetection application thus requires the collection of exampledata in which the target compound is both present and absent.This data collection effort can be time-consuming andexpensive under the best of circumstances. Moreover, if thetarget analyte is a toxic compound, it may not be possible torelease it into the atmosphere for the purpose of acquiring testdata for use in building the pattern recognition method.

These considerations motivate the development of patternrecognition classifiers that do not depend on the collection ofdata in which the target analytes are released into theenvironment. One strategy toward realizing this goal is to uselaboratory spectra of the analytes in conjunction withbackground data acquired in the field in which the analytesare not present. By acquiring a database of representative

Received 22 February 2008; accepted 25 July 2008.* Present address: Novartis Pharmaceuticals Corp., One Health Plaza, Bldg.

401/B244B, East Hanover, NJ 07936-1080.� Author to whom correspondence should be sent. E-mail: gary-small@uiowa.edu.

Volume 62, Number 10, 2008 APPLIED SPECTROSCOPY 10490003-7028/08/6210-1049$2.00/0

� 2008 Society for Applied Spectroscopy

background data over time, as well as a laboratory spectrallibrary of target analytes, classifiers could be constructed foruse with all target compounds without having to performcontrolled compound releases in the field. These classifierswould then be available for use in detecting the presence oftarget compounds during field data collections (e.g., at accidentsites). The key to implementing this approach, however, is aworkable strategy for combining laboratory spectra with fieldbackground data in a way that is compatible with therequirements of pattern recognition classifiers.

The objective of the work presented here is to develop asimulation approach based on a radiometric model to mimicanalyte-active multi-spectral radiance data. With these data,classifiers can be developed that enable the analyst to identifythe presence of target species within an image. Piecewise lineardiscriminant analysis9–14 (PLDA) is used to generate classifiersbased on training sets composed of simulated analyte-activedata and randomly picked analyte-inactive measurements frombackground images. These classifiers are subsequently testedwith field-collected imaging data with either ethanol ormethanol as the target analyte.

EXPERIMENTAL

Instrumentation. An RS-800SG multi-spectral IR linescanner (Raytheon TI Systems, McKinney, TX) mounted in adownward-looking position in either a Douglas-Curtis 3 orAeroCommander 500B aircraft was used in this study. Withthis instrument, a rotating prism is used to sample a 608 field ofview (FOV) at 60 Hz as the aircraft flies. The upwelling groundradiance is directed onto the elements of a Hg:Cd:Te arraydetector to which optical interferences filters are bonded.

An across-track scanning mode was employed in which thescene is subdivided into a series of lines oriented perpendicular tothe direction of flight. Each line is scanned from one side of thescene to the other using the rotating prism. As the aircraft movesforward over the region of interest, successive scans build up atwo-dimensional image of the scene. This image is composed ofsamples and lines; the former represents the subdivision of eachscan line into individual pixels, while the latter corresponds to thenumber of scan lines acquired along the flight path.

The digital outputs of the detectors were converted to

radiance units through the use of two radiometric reference

sources whose radiance values were measured by employing a

transfer calibration using an external NIST traceable black-

body. The raw images were then registered to offset the

limitations of across-track scanning and errors related to pitch

and yaw of the aircraft.15

Procedures. Three sets of experiments were investigated in

this study. Experiment 1 was conducted in the winter and

involved controlled releases of ethanol (AAPER Alcohol and

Chemical Co., Shelbyville, KY). These releases made use of a

mobile plume generator (AeroSurvey, Inc., Manhattan, KS)

with stack dimensions of approximately 5 m high and 0.4 m

diameter at the exit flue. This setup was capable of achieving

flow rates and stack exit temperatures of up to 20 m/s and 300

8C, respectively. A total of seven flight passes (runs) were

made within the span of one day, with the aircraft flying at an

altitude of 2200 feet (670 m). Each flight path produced a 14-

channel image, with each channel corresponding to the readout

from a corresponding detector/filter combination.

Experiment 2 was performed in the summer near an airport

runway and involved similar controlled release conditions as

experiment 1 but with a wider stack diameter of approximately

TABLE I. Filter sets used for field experiments.

Channel

Experiment 1 Experiment 2 Experiment 3

Band Purpose Center (lm) Width (lm) Band purpose Center (lm) Width (lm) Band purpose Center (lm) Width (lm)

1 HCl 3.41 0.08 HCl 3.45 0.89 SO2 8.70 0.832 Backgrounda 3.91 2.60 Backgrounda 3.88 0.19 Backgrounda 9.29 0.343 Backgrounda 3.92 0.09 Backgrounda 4.22 0.11 CO2 9.45 0.094 Backgrounda 4.16 0.35 CO2 4.31 1.02 Methanol 9.67 0.725 CO2 4.22 0.41 Backgrounda 4.34 0.70 NH3 #1 10.38 0.226 NO 5.35 0.73 Backgrounda 4.36 0.74 SF6 10.57 0.407 Backgrounda 8.30 0.84 CO2 4.40 0.77 NH3 #2 10.72 0.218 SO2 8.80 0.97 NO 5.28 0.35 Backgrounda 11.23 2.679 Backgrounda 9.40 1.06 SO2 8.70 0.83

10 CO2 9.50 1.18 Backgrounda 9.29 0.3411 Backgrounda 10.50 1.27 CO2 9.45 0.0912 SF6 10.65 1.49 Methanol 9.67 0.7213 Backgrounda 10.91 2.60 NH3 #1 10.38 0.2214 Backgrounda 11.30 6.21 SF6 10.57 0.4015 NH3 #2 10.72 0.2116 Backgrounda 11.23 2.67

a Background filters were designed to characterize the infrared background radiance in the 8–12 and 3–5 lm spectral regions.

TABLE II. Summary of images from field experiments.

Experiment Run number Samples Lines Release

1 24 150 150 Ethanol1 26 150 150 Ethanol1 27 150 150 Ethanol1 28 150 150 Ethanol1 29 150 150 Ethanol1 31 150 150 Ethanol1 35 150 150 Ethanol2 2 550 550 Ethanol2 3 550 550 Ethanol3 1 635 783 Ammonia3 15 485 437 Carbon dioxide3 20 704 839 Methanol3 26 553 230 Methanol

1050 Volume 62, Number 10, 2008

0.8 m. Only two flight passes were performed in thisexperiment, each producing a 16-channel image.

Experiment 3 was performed in late spring at a chemicalfacility that produces formaldehyde, plasticizers, syntheticlubricants, nitrogen fertilizers, and pentaerythritol (PE). Thelatter is used in the manufacture of paints, resins, andexplosives. Methanol is a by-product in the PE production.Data collection spanned four days with the analyte of interestmethanol being released only on the last day. This release wasmade by purposely venting the methanol from an absorptioncolumn rather than directing it to a waste heat boiler as wouldoccur during normal operations. Images acquired in thisexperiment were composed of eight channels. Table I liststhe composition of the IR bandpass filters used in the threeexperiments, while Table II provides a summary of imagesfrom the field experiments.

Generation of Synthetic Data. A simulation approach wasemployed to synthesize values corresponding to imageradiance measurements for each experiment. This wasimplemented by use of Planck’s radiation law:

Li;j ¼ei;jc1

k5j exp

c2

kjTi

� �� 1

� � ð1Þ

In Eq. 1, Li,j is the spectral radiance in units of lW cm�2 sr�1

lm�1 for the ith pixel at the jth wavelength channel, ei,j is thecorresponding emissivity, kj is the center wavelength for the jthchannel (lm), Ti is the absolute radiant temperature of the ithpixel (K), c1 is the first radiation constant (1.19 3 1010 lW lm4

cm�2), and c2 is the second radiation constant (1.43 3 104 lm-K).

In order to calibrate the upwelling radiance incident on thesensor, a radiometric model of the scene was constructed.Figure 1 shows the key sources of radiances that were used inthe derivation of the radiometric model. When there is no

plume present in the scene, upwelling radiance is given by

LðkÞbackground ¼ satmLðkÞgr þ LðkÞatm ð2Þ

where L(k)background is the background radiance, satm is theatmospheric transmission, L(k)gr is the upwelling groundradiation, and L(katm) is the upwelling atmospheric radiation.The values of L(katm) and satm were obtained by use of theMODTRAN3 atmospheric model,16 while L(k)gr was calculat-ed using Eq. 1 for a specific range of temperatures andemissivities. Note that this equation ignores any downwellingsolar or atmospheric radiance that is reflected by the ground.

In the presence of a plume, the radiance incident on thesensor aperture may be described as

LðkÞpl ¼ sgassatmLðkÞgr þ ð1� sgassatmÞLðk; TatmÞBB ð3Þ

where L(k, Tatm)BB is the radiance equivalent to that of ablackbody at the temperature of the atmosphere and sgas is thetransmittance of the plume. This assumes that the plume andthe atmosphere are homogenous between the ground and thesensor. However, if the spatial cross-section of the plume issmall within the sensor FOV, the plume can be treated as adiscrete absorber or emitter separate from the atmosphere.Under this assumption, Eq. 3 simplifies to

LðkÞpl ¼ sgassatmLðkÞgr þ satmLðkÞgas þ LðkÞatm ð4Þ

where L(k)gas is the plume radiance. The three distinct terms inEq. 4 correspond to the ground radiance attenuated by theplume, the radiance emitted by the plume, and the atmosphericradiance, respectively. When there is no plume in the scene,sgas ¼ 1 and L(k)gas ¼ 0, and Eq. 4 simplifies to Eq. 2.

The output of the detector is a finite number of radiancevalues that correspond to filtering the incoming radiation,L(k)pl or L(k)background, and integrating the signals for each of

FIG. 1. Pictorial representation of the experimental setup illustrating the key sources of radiance incident on the sensor. The radiance and transmittance terms wereused to formulate a radiometric model that explains the resultant radiance incident on the sensor in the presence or absence of the plume cloud.

APPLIED SPECTROSCOPY 1051

the filters across the wavelength domain:

Rj ¼Z

kLðkÞFjðkÞ ð5Þ

In Eq. 5, Rj is the signal output for channel or filter j and Fj isthe spectral response of the optical system with respect to filterj. This term includes the bandpass response of the filter, thedetector responsivity in the filter bandpass, and the collectionefficiency of the optical system over the correspondingwavelength range.

Gaussian Plume Model. A Gaussian plume model17–19

based on Brigg’s equation for plume rise20 was employed inthis study to evaluate the downwind plume temperature andthus the radiance of the plume. This model is based on theanalogy that once a gaseous effluent exits the stack, its particleflow distribution is random and is assumed to be Gaussiandistributed. According to Brigg’s model, the plume height isgiven by

h ¼ h0 þ 3r0m2

mþ 3

� �x1=3 ð6Þ

where h is the height at the plume centerline, h0 is the stackheight, r0 is the stack radius, m is the ratio of the gas releasevelocity to the wind velocity, and x is the plume downwinddistance. The concentration of the plume at any distance awayfrom the stack exit can also be deduced in the form of aGaussian distribution:

C ¼ Q

2pryrzlexp � y2

2r2y

� �

3 exp �ðz� hÞ2

2r2z

" #þ exp �ðzþ hÞ2

2r2z

" #( )ð7Þ

In Eq. 7, Q is the source intensity (mass released per unit time),l is the mean wind speed, h is the plume centerline height, y isthe lateral distance from the centerline, z is the vertical distancefrom the ground, and ry, rz are the lateral and verticalcoefficients of dispersion, respectively. The dilution factor atany position within the plume can be computed as

D ¼ Q

Cpr20w

ð8Þ

where w is the vertical emission velocity. The temperature ofthe plume, Tpl, at any distance from the stack exit can beestimated using the stack exit temperature, Ts, dilution factor,D, and ambient air temperature, Ta.

21

Tpl ¼Ta

1þ Ta � Ts

Ts

1

D

ð9Þ

Data Analysis. All calculations involving generation ofsynthetic radiance data and K-means clustering were performedusing MATLAB (version 6.5, The Mathworks, Inc., Natick,MA) installed on a Dell Precision 450 workstation (DellComputer Corp., Austin, TX) operating under Red Hat Linux(Red Hat, Inc., Raleigh, NC). ENVI (version 3.4, ResearchSystems, Boulder, CO) installed on a Silicon Graphics Indigo2

IMPACT 10000 computer operating under Irix 6.5 (Silicon

Graphics Inc., Mountain View, CA) was used to view theimages. Piecewise linear discriminant analysis (PLDA) calcu-lations were performed on this system with original softwarewritten in FORTRAN 77. MODTRAN3 software (AFRL/VSBYB, Hanscom AFB, MA) was also run on this system.

RESULTS AND DISCUSSION

Overview of Methodology. The goal of this research was todevelop automated pattern recognition classifiers for use indetecting ground sources of ethanol and methanol from multi-spectral IR imaging data collected from an aircraft platform. Toimplement the PLDA classifiers, a training set of knownanalyte-active and analyte-inactive patterns was required. Toovercome the complexity of performing controlled releases ofVOCs in the field for the purpose of acquiring training data, asimulation model was implemented in this work to generatesynthetic analyte-active patterns for use in training theclassifiers. To assemble the training set, these simulatedanalyte-active patterns were combined with field-collectedanalyte-inactive background patterns collected upwind of theground site being interrogated by the sensor. In this way, theclassifier could be tailored to the site being investigated withoutrequiring any special data collection. In the actual implemen-tation of this methodology to a real site monitoring application,the simulation model would be applied and dedicatedclassifiers would be trained separately for each site beingmonitored.

Data Simulation and Preprocessing. Simulation parame-ters were obtained using recorded meteorological conditions inconjunction with stack dimensions and the Gaussian plumemodel.17–19 This model is only designed to explain emissionphenomena. However, downwind from the stack exit the plumeis expected to equilibrate with the surrounding atmosphere andthus exhibit a lower temperature with respect to the ground.This results in the occurrence of an absorption phenomenon(i.e., a net absorption by the plume of the upwelling groundradiance) and thus should be included into the simulation by

FIG. 2. Absorbance spectra for ethanol (solid line) and methanol (dashed line)at 2 cm�1 point spacing taken from the Nicolet-Aldrich vapor-phase IRdatabase (Thermo Electron Corp., Madison, WI). The spectral values wereconverted to transmittance measurements and input into the simulationalgorithm.

1052 Volume 62, Number 10, 2008

having the temperature of the plume be lower than the

temperature of the ground. To capture the variation in the

background radiance, the emissivity of the ground was also

varied. Atmospheric transmittance estimates were obtained

using MODTRAN3.

The transmittance values for ethanol and methanol needed in

Eqs. 3 and 4 were obtained by scaling their respective laboratory

spectra in Fig. 2 to mimic variations in the transmittance of theanalyte within the FOV. This calculation does not requireabsolute absorptivities of the compounds because a quantitativemodel is not being constructed (i.e., no attempt is being made toestimate analyte concentrations in the measured data). All that isrequired is a span of transmittance values. For experiments 1, 2,and 3, the transmittance ranges used in constructing thesimulated data were 0.01–0.9, 0.1–0.9, and 0.0005–0.1,respectively. These ranges were selected to span the expectedmethanol signal strengths in the measured data.

Using Eqs. 3–5, simulated data for each experiment werecomputed for the set of temperatures and emissivity valueslisted in Table III. The integral expression in Eq. 5 wasapproximated using the trapezoidal rule22 in conjunction withthe experimentally measured responses of the optical filters.Polynomial interpolation was used to equalize the samplingpoints between the filter spectra and the laboratory spectra ofethanol and methanol. The output of the simulation was a set ofsampled signals corresponding to the band centers of theoptical filters.

As described by Eq. 1, radiance measurements from thesurface of the earth encode both temperature and emissivityinformation. Variations of the latter encode the chemicalinformation that allows a target species to be detected. Atemperature and emissivity separation algorithm known as thealpha residual method was implemented in this work to helpsuppress temperature contributions in the radiance datameasured by the sensor.5,6,23,24 The importance of suppressingtemperature effects was assessed by performing separateanalyses with both raw and alpha residual data.

Instrumental Effects. Figure 3 shows a comparison of theradiance values between actual (Fig. 3A) and simulated plumepixels (Fig. 3B) in experiment 1. Visual inspection reveals thatalthough the spectral radiance profiles look similar, thesimulated measurements exhibit elevated values. This impliesthat the simulation protocol did not incorporate sufficientinformation pertaining to the measured data. In particular,factors related to the instrumental response such as theefficiency of the optical system and the spectral responsivitiesof the detector elements have not been incorporated into thesimulation.

To probe this deficiency in the simulation methodology, theresponse of a blackbody measurement at a fixed temperature(75 8C) collected each day was compared to one calculatedusing Planck’s function. The same disparity was seen in theseprofiles, confirming that the instrumental response wasresponsible for this difference. To incorporate this informationinto the simulation, a scaling or attenuation factor was obtainedby computing the ratio of the measured to the calculatedblackbody measurements. This factor was used to weight thesimulated radiance measurements in each channel. Figure 4

TABLE III. Simulation parameters for field experiments.

Exp. Temp. air (K) Temp. plume (K) Ground emissivity No. of patterns (active, inactivea) Channels used for PLDAb

1 280–282 (277–280)c 295–330 0.90–1 3640, 3654 3, 5, 7, 9, 102 305–309 (299–301)c 310–350 0.85–1 3360, 3000 3, 5, 7, 9, 11–163 295–300 (280–289)c 300–320 0.80–1 7000, 3000 1–8

a Analyte-inactive patterns taken from runs 35, 2, and 20 in experiments 1, 2, and 3, respectively.b The number and combination of channels were evaluated via the divergence index feature selection algorithm.c Values in parentheses reflect absorption signals.

FIG. 3. Comparison of radiance spectra extracted from (A) experimentallymeasured imaging data corresponding to plume pixels and (B) syntheticradiance values with respect to data in experiment 1.

APPLIED SPECTROSCOPY 1053

displays the profile of the simulated scaled radiance values,which now look similar to the measured values in Fig. 3A.

Parameter Determinations for Simulation of All Exper-iments. Separate sets of parameters were used in simulatingdata for the three field experiments on the basis of knowledgeof the characteristics of the measurement site. This procedureassumes that in the real-world implementation of thismethodology, similar basic knowledge of the measurementcharacteristics and environmental conditions will be available.

Radiance values for experiments 1 and 2 were determinedusing Eqs. 4 and 3, respectively. The justification of whichequation to use was made on the basis of the release conditionsfor each experiment. This is primarily determined by the stackdimension, whereby the wider the stack, the higher theresulting elution volume. The elution volume directly relatesto the plume cross-sectional area. In an attempt to capture thevariation of the background during the airborne measurements,the emissivity values were varied between 0.85 and 1 for thesimulated data.

Because of the complexity of the background radianceemanating from the chemical plant in experiment 3, thesimulation of active plume radiance measurements required theuse of Eq. 3. To be compatible with a wider range ofbackgrounds, the emissivity was varied between 0.80 and 1 forthe simulated data generated for use with experiment 3. Withthe lack of a specific stack dimension in this case, thetemperature of the plume could not be estimated with theGaussian plume model. The average monthly temperature ofthe site was obtained from meteorological records, while thetemperature of the plume was estimated on the basis ofcomparing simulated radiance data obtained from severaltemperature range sets and actual radiance spectra from plumepixels within the vicinity of the release site. In addition,principal component (PC) score plots25 were used to furtherjustify these parameters.

Figure 5 displays score plots based on the first and secondPCs (Fig. 5A) and second and third PCs (Fig. 5B) computedfrom the simulated analyte-active, measured analyte-active,and measured analyte-inactive radiance values from run 2 inexperiment 3 using all 8 channels. Measured analyte-activepixels were selected from the vicinity of the release site, while

measured analyte-inactive pixels were selected from a regionthat was away from the release site in the upwind direction.

The significant overlap among the data groups observed inthe scores of the first two principal components (Fig. 5A)suggests that the major background components are verysimilar across both the simulated and measured data, as well asthe analyte-active and analyte-inactive data. When the scoresalong the second and third PCs (Fig. 5B) are considered,discrimination between the analyte-active and analyte-inactiveobservations is observed, specifically due to the informationprovided by the third PC. By comparing the locations of thethree data groups in this plot, we see a similarity between thesimulated and measured analyte-active data, as well as a similarorientation of these groups with respect to the analyte-inactivedata. This was considered a promising result if the proposedsimulation protocol was to succeed in correctly classifyingplume pixels in the measured imaging data.

FIG. 4. Simulated radiance values corresponding to experiment 1 attenuatedwith a scaling term to incorporate the instrumental response function.

FIG. 5. (A) Principal component (PC) score plot illustrating the data spacespanned by the analyte-active simulated (dots), analyte-active measured (opencircles), and analyte-inactive measured (þ) data from experiment 3. Scoresalong the first (PC1) and second (PC2) PCs are plotted. The significant overlapbetween the analyte-active and analyte-inactive measured data indicates thesimilarity in the background signatures of the corresponding image pixels. (B)Plot of the scores along the second (PC2) and third (PC3) PCs. The plotsymbols are the same as in panel A. The analyte-active and analyte-inactivesubgroups have greater separation in the higher PCs. This plot also shows thatthe simulated data occupy a region in the PC space that is close to and orientedin the same direction as the actual active measurements.

1054 Volume 62, Number 10, 2008

The addition of random noise was also investigated as a wayto add realism to the simulated data but was found to be notbeneficial. This was due to the inclusion of enough variancefrom the temperature and emissivity ranges used to encode thebackground radiance.

Feature Selection. To evaluate which subset of channelsprovided the best discrimination between the analyte-active andanalyte-inactive plume pixels, a feature selection algorithmknown as the divergence index26,27 was implemented. Thedivergence index is an indicator of the degree of separationbetween the classes and is given by

D ¼ 1

2tr ðRa � RbÞðRa � RbÞ�1h i

þ 1

2tr ðR�1

a � R�1b Þðla � lbÞðla � lbÞ�1

h ið10Þ

where D is the divergence index, and R and l are thecovariance matrices and means for the patterns of classes a andb, respectively. Implementation of this scheme in allexperiments involved choosing analyte-active pixels withinthe vicinity of the release site and analyte-inactive pixels from aregion far away from the release locale in the upwind direction.For experiments 1 and 2, 66 (replicated to 6600) and 27(replicated to 3645) analyte-active pixels obtained from all theruns were used in conjunction with 6000 and 3500 analyte-inactive pixels obtained from runs 35 and 2, respectively. Forexperiment 3, the measured analyte-active and analyte-inactivepixels for the PC score plot illustration in Fig. 5 were used.Using all possible combinations of taking 3 to 14 channels at atime, the divergence index was calculated. The optimalcombination of features for experiment 1 was the set ofchannels 3, 5, 7, 9, and 10. Similar investigations conducted forexperiments 2 and 3 revealed channels 3, 5, 7, 9, 11, 12, 13, 14,15, and 16 and 1, 2, 3, 4, 5, 6, 7, and 8, respectively, as beingoptimal with respect to separating the analyte-active andanalyte-inactive pixels.

Development of Classifiers for Plume Detection. Once thesimulated radiance values were computed, radiance valuescorresponding to analyte-inactive pixels from one particularrun were used to augment the simulated values to generate a setof training patterns. The inactive pixels were selected fromregions of the image where plume pixels were known to beabsent to a certain degree of accuracy. For example, areas awayfrom the location of emission stacks and in the upwinddirection were determined to be viable choices for selectinganalyte-inactive pixels. Simulated analyte-active and measuredanalyte-inactive patterns used for training in all threeexperiments are listed in Table III. Analyte-inactive patternsfor each experiment were randomly selected from pixels in theregions of the image judged to be free of analyte-active pixels.

The PLDA method5,6,9–14,28 was then applied to the trainingpatterns to compute the classifier. This is a mathematicaltechnique used to form multiple linear boundaries or surfacescalled discriminants within the data space. Patterns can beclassified on the basis of their orientation with respect to theseseparating boundaries. The implementation of the PLDAalgorithm in this work was based on generating discriminantsthat yielded discriminant scores with values greater than zerofor analyte-active pixels or less than zero for analyte-inactivepixels. The training set composed of simulated active andmeasured inactive radiance measurements was used to optimizethe placement of the linear surfaces or classifiers in the

multidimensional data space. For experiments 1, 2, and 3, theclassifiers required only a single discriminant function and100% separation of the analyte-active and analyte-inactive dataclasses was achieved. Discriminants generated during thetraining procedure were subsequently used to classify andpredict image pixels in all the measured runs for the threeexperiments.

Representation of Classification Results. The output ofthis classification methodology is a numerical count indicatingthe number of analyte-active and analyte-inactive pixels withinan image. It is hard to judge the authenticity of these results,however, since there is no spatial information accompanyingthem. Moreover, a reference number of analyte-active pixelsfor each image is needed in order to report the results accordingto the conventional values of false positive and false negativeclassification rates.

To represent the results in an image format, discriminantscores generated during prediction with values less than andgreater than zero were linearly mapped onto a scale between 0and 18.5 and 44.5 and 63, respectively. Mapping these valuesonto a standard color map ranging from 0 to 63 produces adiscriminant score image with pixels having colors rangingfrom dark to light blue representing analyte-inactive pixels andyellow to red representing analyte-active pixels.5 The inherentcolor ranges for each class represent the magnitude of thediscriminant score in both the positive and negative domains.For instance, higher positive values are represented by a moreintense red color, while lower negative values are characterizedby an intense blue color.

For the analyte-inactive class, variations in the colorintensities are primarily a function of differences in emissivityamong the various materials comprising the scene. When theclassifiers are based on the raw radiance values, temperaturedifferences will also affect the magnitudes of the discriminantscores. When the classifier is based on alpha residual values,this temperature effect is suppressed. For the analyte-activeclass, the color intensity will be a function of analyteconcentration and the plume dimension along the optical pathof the sensor, with higher values of both of these parameterstranslating to higher intensity red colors in the image. Thetemperature differential between the analyte plume and the IRbackground will also affect the color intensity, with a highertemperature differential producing colors more toward the redlimit of the color map. When the alpha residual data are used tobuild the classifier, this temperature effect will be suppressed.

Figure 6A is an aerial photograph for the site of experiment1. The release site was bare ground terrain and in addition tothe stack, there were other objects such as a propane tank,calibration panels of known emissivity, and a wind sock.Figure 6B is a discriminant score image plot for run 35 inexperiment 1. The classifier was based on the raw radiancedata. This image shows a clear distinction between pixelswithin the vicinity of the stack and all other pixels within theimage.

Figure 7A is an RGB image plot corresponding to run 3 inexperiment 2 produced by channels centered at 9.29, 9.45, and9.67 lm. Based on the location of the stack, the white traildepicts the profile of the ethanol plume. Implementing thesame analysis as experiment 1 produced a discriminant scoreimage in Fig. 7B that clearly discerns plume pixels from therest of the image.

Figure 8A is an RGB image plot corresponding to alpha

APPLIED SPECTROSCOPY 1055

residual data from run 20 in experiment 3. Raw radiance valuesgave poor prediction results because of the complexity of thebackground and thus alpha residuals were computed from allthe data in experiment 3 prior to data analysis. The methanolreleases emanated from the PE plant whose location isindicated by the circle in Fig. 8A. Employing the optimizedclassifier from training and mapping the resultant discriminantscores onto the aforementioned color map scale generated thediscriminant score image in Fig. 8B for run 20. Pixels classifiedas active were located around the PE plant with a trace thatextended diagonally from this location. Similar results wereobtained with run 26.

The robustness of this classification scheme was evaluatedby using the same optimized discriminant to predict theexistence of methanol pixels in runs 1 and 15 collected ondifferent days that are known to contain no methanol releases.

The discriminant score image for run 1 in Fig. 9 shows thesuccess of this classification scheme, with only a few pixelslocated far away from the expected methanol plume locationexhibiting false alarms. Similar results were obtained for run15. The results in Figs. 8B and 9 confirm that the classifier isdetecting methanol on the basis of its chemical signature ratherthan on some artifact of the background. The false alarms thatdo occur correspond to background signatures that were notadequately represented in the training data. While beingoptimized, the discriminant function was thus not forced todiscriminate these signatures from the signatures of back-ground pixels that also contained low levels of methanol.

In an effort to establish a reference number of active pixelsfor each run in all the experiments, the K-means clusteringalgorithm was employed.5,6 The basis of this approach is theassumption that the radiance profiles of the plume pixels aredifferent from the non-plume pixels and will hence clustertogether. Inputs to the K-means algorithm corresponding to thenumber of iterations and clusters were selected on the basis oftrial and error. The output of this algorithm is an indexindicating the cluster membership of each pixel.

The total number of plume pixels was obtained from the sumof the pixels corresponding to a cluster of a particular indexthat coincided with the stack or plume trace location. Using thisas a reference number for a particular run, the following figure

FIG. 7. (A) RGB image plot of alpha residual data from run 3 in experiment 2.The white trace indicated by the red circle corresponds to the stack location. (B)Discriminant score image of the same scene (run 3) preprocessed with alpharesidual analysis using a classifier generated from synthetic analyte-active andmeasured analyte-inactive radiance signals. Pixels with orange-to-red pigmentsare predicted as analyte-active.

FIG. 6. (A) Aerial photograph of the scene interrogated in experiment 1. Inaddition to the stack, there were a pair of calibration panels, a propane tank, anda wind sock. (B) Discriminant score image plot of unprocessed run 35 (ethanolrelease) obtained from a classifier generated from synthetic analyte-active andmeasured analyte-inactive radiance measurements. The orange-to-red pixelswithin the vicinity of the stack are classified as ethanol pixels.

1056 Volume 62, Number 10, 2008

of merit was computed:

Percent False Alarm ¼ Isim � Imatch

Iclust inact3 100 ð11Þ

In Eq. 11, Imatch corresponds to the number of pixels predictedto be analyte-active using both the PLDA classifier and K-means clustering, Iclust_inact indicates the number of pixelsclustered as analyte-inactive by K-means clustering, and Isim isthe number of pixels predicted as analyte-active using thePLDA classifier.

The results for all the runs in all three experiments aretabulated in Table IV. The false alarm rates were satisfactorily

low, especially bearing in mind that no experimentallymeasured analyte-active pixels were required during training.One point to note in evaluating these results, however, is thatplume pixels corresponding to very weak analyte signal levelsmay cluster with the non-plume pixels and therefore not berecognized. Thus, Iclust_inact in the denominator of Eq. 11 willtend to be high. The false alarm rates computed by Eq. 11 willtherefore be optimistic estimates.

To use spatial information to minimize false positives, aneighborhood rule was also applied to the discriminant scoreimages. This rule proposes that analyte-active plume pixelsshould be clustered spatially. Stated differently, single pixelsclassified as analyte-active but which are primarily surroundedby analyte-inactive pixels are most probably false positives.This classification rule was implemented by requiring that if apixel is predicted as analyte-active, then four of its neighboringeight pixels must also be analyte-active. This cleans up thediscriminant score images considerably, as shown in Figs. 10Aand 10B for runs 20 and 1, respectively. This reduction in theFIG. 8. (A) Image plot of run 20 in experiment 3. Red, green, and blue

components of the image correspond to spectral channels centered at 9.67,11.23, and 10.57 lm, respectively. The source of methanol is indicated by thecircle. The plume is observed as the blue-green pixels originating in the circleand trailing to the upper right. (B) Discriminant score image of the same scene(run 20) preprocessed with alpha residual analysis using a classifier generatedfrom synthetic analyte-active and measured analyte-inactive radiance signals.Pixels with orange-to-red pigments are predicted as analyte-active.

FIG. 9. Discriminant score image of run 1 from experiment 3 (no methanolrelease) generated by using a classifier trained with alpha residuals computedfrom synthetic analyte-active and measured analyte-inactive data.

TABLE IV. False detection rates.

Exp.Runno.

% Falsedetection raw

radiance

% Falsedetection alpha

residual

% Falsedetection alpharesidual-NNb

1 35 0.00 0.00 0.001 31 0.00 0.00 0.001 29 0.05 0.05 0.001 28 0.04 0.04 0.001 27 0.01 0.01 0.001 26 0.04 0.04 0.001 24 0.03 0.03 0.002 2 0.01 0.00 0.002 3 0.01 0.00 0.003 20 n/a 0.30 0.003 26 n/a 0.34 0.003a 15 n/a 0.00 0.003a 1 n/a 0.00 0.00

a Runs where no analyte was released.b False detection rates after application of nearest-neighbor (NN) rule.

APPLIED SPECTROSCOPY 1057

number of false positives does come at the cost of losing somediscrete analyte-active pixels, however. Under conditions inwhich the plume is highly dispersed (e.g., high winds), the useof the neighborhood rule may be problematic.

CONCLUSION

Results in these studies have demonstrated the capability toincorporate simulation in remote sensing imaging with an aimto forego the need to collect a representative image of actualanalyte releases. Classifiers generated from simulated radiancespectra mimicking measured radiance measurements per-formed well in predicting actual analyte-active pixels with acorresponding false positive rate between 0 and 0.3%. Resultsfor all three experiments were excellent. The performance ofthe methodology with the data from experiment 3 wasparticularly encouraging given that this was not a controlledrelease but rather an output from an industrial process.

Furthermore, this experiment is the best representation of whatto expect after an industrial accident with toxic gaseouseffluents escaping into the atmosphere.

The use of a simulation model to generate analyte-activedata for the pattern recognition analysis also helps to eliminatethe possibility that the discrimination between analyte-activeand analyte-inactive data is being performed on the basis ofdata artifacts. Previous studies in which training data sets wereassembled purely on the basis of clustering analysis andknowledge of the scene suffered from the disadvantage that noconfirmed chemical signature was observed in the analyte-active patterns.5,6 With the simulation model used here, thediscriminating signature must arise from the infrared spectralrepresentation of the target analyte.

The sources of error in the current method are related to theadequacy of the radiance model used to construct the simulatedtraining data, as well as the suitability of the backgrounds usedto define the analyte-inactive class. As noted previously, thelinear discriminant functions that comprise the PLDA classifierdefine a separating boundary in the data space. Inadequacies inthe training data cause this separating boundary to bepositioned incorrectly, resulting in either missed detections orfalse alarms.

We envision the application of this methodology ingenerating classifiers in near real-time for use in interrogatinga scene that may contain a chemical release. With theavailability of a spectral library of toxic industrial chemicals,the simulation model can be applied quickly to generateradiance spectra that mimic the background conditions of thecurrent scene. By collecting background data upwind of thetargeted site, the training set can be assembled and the classifiercomputed. Each of these computational tasks can be performedwithin several minutes, thereby providing classifiers tuned tothe current scene and environmental conditions.

Areas of future work include an evaluation of othersupervised pattern recognition approaches for use in thisapplication and the incorporation of a quantitative or semi-quantitative component to the results. The PLDA method wasused here as a standard linear discriminant technique and onewith which we have extensive experience. Other supervisedclassification methods may be equally or better suited to thisapplication, however.

Including a quantitative component in the results wouldgreatly aid decision makers in the event of a chemical detectionin a hazardous monitoring application. For example, is theconcentration above a threshold required for initiating anevacuation? Making precise quantitative determinations withpassive infrared measurements is difficult, although we haverecently made some progress in this area with passive Fouriertransform infrared data.29 A key question in adding aquantitative component to the image analysis application iswhether the current imaging system has enough spectralchannels to allow the analyte information to be quantified inthe presence of a complex background.

Implementing a quantitative or semi-quantitative analysiswould require knowledge of the plume concentrations andthicknesses associated with the measurements used to developand test the method. An acknowledged limitation of the currentwork is a lack of such knowledge for the plumes viewed by theimager during experiments 1, 2, and 3. Because of thislimitation, we are unable to estimate limits of detection for

FIG. 10. Discriminant score images of (A) run 20 and (B) run 1 in experiment3 after implementation of the neighborhood rule. This procedure eliminatesisolated analyte-active pixels in both images. The classifier used was based onalpha residuals computed from the radiance values.

1058 Volume 62, Number 10, 2008

ethanol and methanol in the context of our current patternrecognition detection algorithm.

1. F. Sunar and C. Ozkan, Int. J. Remote. Sens. 22, 2265 (2001).2. E. Morin, W. F. Krajewski, and D. C. Goodrich, J. Hydrometeorol. 4, 782

(2003).3. M. J. Abrams, R. Ashley, L. C. Rowan, A. F. H. Goetz, and A. B. Kahle,

Geology 5, 713 (1977).4. J. R. Jensen, Introductory digital image processing: a remote sensing

perspective (Prentice-Hall, Inc., Upper Saddle River, NJ, 1986), 2nd ed.5. L. Zhang and G. Small, Appl. Spectrosc. 56, 1082 (2002).6. M. J. Wabomba, Y. Sulub, and G. W. Small, Appl. Spectrosc. 61, 349

(2007).7. J. A. Saghri and A. G. Tescher, J. Imag. Sci. Technol. 46, 575 (2002).8. J. Wang and W. Li, Int. J. Remote. Sens. 21, 4129 (2003).9. R. E. Shaffer and G. W. Small, Chemom. Intell. Lab. Syst. 32, 95 (1996).

10. R. E. Shaffer and G. W. Small, Anal. Chim. Acta 331, 157 (1996).11. A. S. Bangalore, G. W. Small, R. J. Combs, R. B. Knapp, R. S. Kroutil, C.

A. Traynor, and J. D. Ko, Anal. Chem. 69, 118 (1997).12. F. W. Koehler, G. W. Small, R. J. Comb, R. B. Knapp, and R. T. Kroutil,

Vib. Spectrosc. 27, 97 (2001).13. M. J. Wabomba and G. W. Small, Anal. Chem. 75, 2018 (2003).14. T. Tarumi, G. W. Small, R. J. Combs, and R. T. Kroutil, Appl. Spectrosc.

57, 1432 (2003).15. R. W. Zywicki, Proc. SPIE-Int. Soc. Opt. Eng. 3557, 237 (1999).

16. A. Berk, L. S. Bernstein, and D. C. Robertson, A Moderate ResolutionModel for LOWTRAN 7 (Geophysics Laboratory-Airforce SystemsCommand, Burlington, 1989).

17. D. McCready, ‘‘Predicting Plume Temperature for Potential WorkerExposure in a Downwind Elevated Platform’’, in 92nd Air & WasteManage. Assoc. Conference, 1999, p. 3432.

18. S. D. Kuo, J. R. Schott, and C. Y. Chang, Opt. Eng. 39, 1047 (1999).19. J. Halitsky, JAPCA J. Air Waste Manage. 39, 856 (1989).20. G. A. Briggs, JAPCA J. Air Waste Manage. 15, 433 (1965).21. The DIRSIG User’s Manual (Rochester Institute of Technology, Ro-

chester, NY, 2006).22. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling,

Numerical Recipes: The Art of Scientific Computing (CambridgeUniversity Press, Cambridge, UK, 1986).

23. P. S. Kealy and S. J. Hook, IEEE Trans. Geosci. Remote Sens. 31, 1155(1993).

24. Z. Li, F. Becker, M. P. Stoll, and Z. Wan, Remote Sens. Environ. 69, 197(1999).

25. S. Wold, K. Esbensen, and P. Geladi, Chemom. Intell. Lab. Syst. 2, 37(1987).

26. T. Kavzoglu and M. P. Mather, Int. J. Remote. Sens. 23, 2919 (2002).27. D. A. Landgrebe, Signal Theory Methods in Multispectral Remote Sensing

(Wiley-Interscience, Hoboken, NJ, 2003).28. G. W. Small, S. E. Carpenter, and T. F. Kaltenbach, Anal. Chim. Acta 246,

85 (1991).29. Y. Sulub and G. W. Small, Analyst (Cambridge, U.K.) 132, 330 (2007).

APPLIED SPECTROSCOPY 1059