Optical Engineering 45共10兲, 106401 共October 2006兲

Human-tracking systems using pyroelectric infrared detectors Mohan Shankar, MEMBER SPIE John B. Burchett Qi Hao Bob D. Guenther David J. Brady, MEMBER SPIE Duke University Fitzpatrick Institute for Photonics Durham, North Carolina 27708

Abstract. We design and develop a low-cost pyroelectric detectorbased IR motion-tracking system. We study the characteristics of the detector and the Fresnel lenses that are used to modulate the visibility of the detectors. We build sensor clusters in different configurations and demonstrate their use for human motion tracking. © 2006 Society of PhotoOptical Instrumentation Engineers. 关DOI: 10.1117/1.2360948兴

Subject terms: infrared; motion; tracking; lenses; detectors. Paper 050734R received Sep. 13, 2005; revised manuscript received Mar. 10, 2006; accepted for publication Mar. 31, 2006; published online Oct. 17, 2006.

1 Introduction Human motion tracking is primarily concerned with determining the existence and location of humans within certain regions of space. Conventional tracking implementations use IR 共Ref. 1兲 or regular video cameras,2 which stream and process large amounts of data to extract the position or identity of the person in the space. While low-false-positive biometric methods typically require close proximity and rely on the analysis of large amounts of high-resolution data, tracking systems, on the other hand, are designed to be distributed over larger areas and trade pinpoint accuracy for reduced sensory and computational requirements. Detection in the 8- to 10-␮m wavelength region has long been pursued. Thermistors and thermopiles have been used for temperature measurement. Although these components are relatively inexpensive, the circuitry to make them work is not and their response times and SNRs are far from what is desired for motion detection. The pyroelectric effect has been known for more than 24 centuries, but a firm understanding of the underlying physics has been developed only in modern times.3 Detection of human motion has been done by using pyroelectric detectors that are sensitive to changes in heat flux. These detectors are very attractive for heat detection because of their relatively low cost and they have been widely used in home/office lighting as well as security systems. Pyroelectric detectors have also been used for thermal imaging,4 guiding robots,5 radiometry,6 thermometers,7 etc. Motion-tracking arrays have been implemented to supplement video tracking8 as an alternative to expensive thermal cameras. Distributed IR sensor networks have begun to meet these needs, while being both cheap and easy to construct.9–11 An IR human-motiontracking system was demonstrated using a thermal imager with an array of 96 pyroelectric detectors.12 We designed and developed a low-cost IR sensor system that would have applications in biometric tracking and authentication. We use off-the-shelf components to minimize the cost and develop three configurations for the sensor clusters for different applications. We study the receiver response characteristics by modulating the visibility of a 0091-3286/2006/$22.00 © 2006 SPIE

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pyroelectric detector with Fresnel lens arrays and demonstrate the use of this sensor system in human motion tracking. 2 System Requirements We first discuss the requirements of the system for the tracking application. We start by analyzing humans as IR sources for tracking as well as listing the parameters of the humans that are of interest. Human bodies are very good IR sources. The temperature of a typical human body is about 37° C or 98° F. There is a constant heat exchange between the body and the environment due to the difference in their temperatures. The radiation characteristics of any object can be analyzed using the blackbody radiation curve governed by Planck’s law. For a typical human body, this curve is shown in Fig. 1. We can see that essentially all of the radiation is in the IR region with the peak radiation occurring at about 9.4 ␮m. The amount of power that the human body radiates within the wavelength range of interest is determined by integrating the blackbody radiation curve 共Fig. 1兲 over this range. The detector operates in the 5- to 14-␮m region; using typical values for the area of the human body, the power emitted from the body is estimated to be about 100 W in this wavelength range. This power is radiated isotropically and the amount of power available at a detector at a certain distance from the source depends on the distance as well as the area of the detector elements. IR detectors that are sensitive in the 10-␮m range would thus be able to detect humans at a fairly reasonable range. Other characteristics of interest include the velocity and the manner in which human motion occurs. Humans walk typically at a speed of 0.5 m / s and run at a speed of 3 m / s. Another attribute in walking or running is the swinging of the arms, which occurs at roughly the same rate as the walk or run. The sensor system must be able to track these events at the rate at which they occur. The system is designed to localize the position of a single person in a space as the person moves around. This is done using off-the-shelf components to minimize the cost of the system to enable deployment of hundreds of these in a space to perform human motion tracking.

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Fig. 1 Blackbody radiation curve of human body at 37° C. The peak emission wavelength is about 9.4 ␮m. About 52% of the power lies in the 5- to 14-␮m wavelength band, which corresponds to the wavelength range of detector sensitivity.

3 Pyroelectric Detectors Pyroelectric materials develop a charge in response to a change in temperature. Pyroelectric detectors are widely used in motion detection applications for home security and automation systems. These detectors are commonly available in single-, dual-, or quad-element versions. Pyroelectric detector arrays can also be obtained, but these are generally used for imaging applications. A single-element detector responds to any temperature changes in the environment and therefore must be thermally compensated to remove sensitivity to ambient temperature. Dual-element detectors have the inherent advantage that the output voltage is the difference between the voltages obtained from each of the elements of the detector, which subtracts out environmental effects. The pyroelectric detector converts incident thermal radiation into an electrical signal. This conversion takes place in three steps—the incident thermal radiation results in a change in temperature, altering the charge density on the electrodes. An electrical signal is generated by a preamplifier or impedance converter. The current generated by incident radiation is proportional to the change in temperature as well as the area of the detector elements.13 If i P represents the current flowing through the device on which an incident thermal radiation causes a temperature change ⌬T P, then dT P i P = pAs , dt

Since detection of human motion is of interest to us, pyroelectric detectors seem ideal since they respond only to changes in the heat flux that is associated with motion. This also helps to cancel out ambient fluctuations. The important characteristics of the pyroelectric detector that we used are summarized in Table 1. The power radiated by a human body is radiated isotropically and the power at the detector is a function of the area of the detecting elements as well as the distance between the source and the detector. The maximum range at which the sensor will work can be determined using the noise equivalent power 共NEP兲 value from Table 1. This parameter indicates the power level at which the SNR is 1, Table 1 Parameters of the PIR325 pyroelectric detector from Glolab Corporation.

共1兲

where p is the pyroelectric constant and depends on the material, and As is the area of the elements of the detector. Optical Engineering

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Parameter

Value

Sensitive area 共mm兲

2⫻1

Responsivity 共V/W兲

3300

Spectral response 共␮m兲

5–14

Noise equivalent power 共nW兲

0.96

Detectivity 共cm冑Hz/ W兲

1.5⫻ 108

Signal output 共mVp-p兲

3900

Response time 共ms兲

500

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Fig. 2 Experimental setup for sensor characterization. An incandescent bulb is used as a thermal source and a shutter/chopper is used to modulate the thermal input to the detector.

i.e., the minimum amount of power required to distinguish signal from the noise. The maximum range is determined to be about 100 m, using a detector having an NEP of 0.96 nW. This assumes ideal environmental conditions and noise-free circuits. The practical range would therefore be much less than this theoretical value. Another important parameter is the response time of the sensor to an input stimulus the sensor can respond to. The response time of this detector is about 500 ms, making it suitable for detecting human motion. By suitably modulating the visibility of these detectors using optics and ensuring that the limits of the detector in terms of response time or in noise performance are not reached, human motion can be detected over large areas. 3.1 Detector Characterization We use a dual-element, current-mode pyroelectric detector PIR325 obtained from Glolab Corporation.14 Using the experimental setup shown in Fig. 2, the step response and the field of view of the sensor was obtained. An incandescent bulb was used as the heat source with a shutter to modulate the heat flux on the pyroelectric detector. One of the elements was blocked to obtain the step response for a single element. The entire setup was thermally insulated. The response of the detector to a step input is plotted in Fig. 3. The equivalent electrical model of a pyroelectric detector consists of a capacitor in parallel with a resistor and a current source. Current flows through the circuit only when there is a change in thermal flux resulting in a change in the capacitance. The response can be approximated by two exponential waveforms due to the capacitive element present in the detector. The rise and fall of the signal voltage can be approximated by the following equation:

冋 冉 冊册 冉 冊

S = S0 1 − exp −

t ␶e

exp −

t , ␶t

3.2 Coded Aperture Arrays As shown in Fig. 5, pyroelectric detectors have an angular visibility of over 100 deg but any motion within this FOV does not create a significant change in the thermal flux, resulting in very little response. Detection is enhanced by

共2兲

where S0 represents the steady state response of the sensor. We can see that the response is governed by two time constants, ␶e and ␶t, which are termed the electrical time constant and the thermal time constant, respectively. The frequency response of the detector thus resembles a bandpass filter 共Fig. 4兲. The upper cutoff frequency is related to the electrical time constant ␶e and controls how fast the detector can respond to an input stimulus. The lower cutoff frequency is related to the thermal time constant ␶t and controls the lowest frequency of the input stimulus that the detector can respond to. For the detectors that we used in Optical Engineering

all our work, we found the values of ␶t and ␶e to correspond to 0.7 and 2 Hz, respectively. The field of view 共FOV兲 of the detector was determined using the same setup as in Fig. 2. The detector was rotated about its axis, keeping the source fixed. A polar plot representing the result is shown in Fig. 5. The signature difference between the a single- and dual-element design is that the two elements are connected in series opposition, and their signals are subtracted. This creates a region of insensitivity in the middle of the FOV shown in Fig. 5, corresponding to the region of overlap of the visibility of both the elements of the detector. The response of the sensor with respect to distance was determined by using a hot soldering iron, modulating the sensor’s visibility with an optical chopper. By setting the sensor at different distances, we plot the falloff in the magnitude of the sensor response with distance versus the expected 1 / r2 dependence in Fig. 6.

Fig. 3 Detector response to step input. The step is applied at time t0 = 1.8 s.

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Fig. 4 Frequency response of the pyroelectric detector. The lower and upper cutoff frequencies are 0.7 and 2 Hz, respectively.

creating boundaries in space between distinct regions of visibility so that a large response is obtained when the boundaries are crossed. This illustrates the concept of multiplexed sensing and this has many advantages over conventional sensing systems.15,16 Coded apertures provide multiplexed sensing by using a coded mask to create visibility patterns in space. This concept has been used to demonstrate human motion tracking with pyroelectric detectors over a 2-D grid.17 The resolution with a coded mask is increased by decreasing the aperture size of the mask element. This, however, limits the amount of energy that reaches the detector. A trade-off thus exists between the resolution of the system and the SNR that can be achieved. The response of the detector depends on the incident time-varying power collected by the detector, which in turn depends on the area of the elements of the detector. Since

the detector elements have a small area 共2 mm2兲, the amount of power collected is a very small fraction of the incident power. This situation is further worsened with the use of coded apertures since the collection area is now reduced to the area of each mask element, which is a small fraction of the area of the detector element. Fresnel lens

Fig. 5 Polar plot of response of the dual-element pyroelectric detector. Each lobe corresponds to the visibility region of one of the elements of the detector and the two lobes are separated by a region of low sensitivity because of the overlap in the sensitivity regions of both lobes and the resulting difference signal.

Fig. 6 Characteristics of the response of the dual-element pyroelectric detector with distance 共from the sensor to the heat source兲 plotted along with the 1 / r2 plot for comparison. Since the incident power on the detector falls off as the inverse square of the distance from source to detector, the response follows a similar trend.

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Fig. 7 Beams formed by a single lens on a lens array. The two beams correspond to each of the elements in a dual-element detector and the gap between them is due to the region of insensitivity of the detector 共Fig. 5兲.

Fig. 9 Characterization of field of view of the Fresnel lens array; A is the beamwidth, 3 deg, of one of the beams of the lens array. At 6 m, this width is 31 cm. The angular separation between the beams of adjacent lenses 共B兲 is 2 deg. The beam separation within a single lens is 1 deg 共C兲. The lens array has an FOV 共D兲 of 88 deg 共top view兲 and a lateral FOV of 12 deg 共side view兲.

arrays provide the advantages of increased collection efficiency as well as multiplexed sensing and this will be discussed in detail. 4 Fresnel Lens Arrays for Visibility Modulation Fresnel lenses are very good energy collectors and are being used extensively for various applications—magnifying lenses, projectors, car head lights, etc. These lenses are constructed from a conventional lens by dividing the curve into right circular cylindrical segments and translating each segment to the plano side of the lens, creating grooves. They can be molded out of inexpensive plastics with the desired

Fig. 8 Signal obtained from detector from one lens with person moving 共a兲 in the one direction and 共b兲 in the opposite direction. The polarity of the response is reversed when moving in the opposite direction.

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Fig. 10 Signal from a detector when a person walks at a distance of 2 m from sensor cluster. Each of the pairs of positive and negative peaks corresponds to crossing of one lenslet’s FOV.

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Shankar et al.: Human-tracking systems… Table 2 Summary of the characteristics of the Fresnel lens array obtained from Frensel Technologies 共Fig. 9兲. Parameter

Value

FOV of lens array 共D兲

88 deg

FOV of each beam formed by one lens 共A兲

3 deg

Angular separation between two beams from each lens 共C兲

1 deg

Angular separation between beams of adjacent lenses 共B兲

2 deg

Lateral angular spread

12 deg

Transmittance of lens in IR

⬇75%

Fig. 12 Ceiling mounted sensor cluster with eight detectors, all designed to be mounted at a height of 6 m from the floor, looking down to track motion in the space.

transmission characteristics 共for the required wavelength range兲, making the system thin, lightweight, and inexpensive. Furthermore, lens arrays are easily built by stacking them in different orientations to suit each application. Fresnel lens arrays and pyroelectric detectors are commonly used in motion detection applications for intrusion detection as well as home/office automation and security systems. To aid in the sensing of motion, Fresnel lens arrays are designed so that the visible space is divided into zones. Detection is enhanced by creating distinct regions of visibility. Each of the lenses on the array creates a single cone of visibility to the detector, depending on the focal length and the size of the detector elements. However, with a dualelement pyroelectric detector, the cone of visibility is divided into two distinct zones, corresponding to each of the lobes in Fig. 5, as illustrated in Fig. 7. The response obtained when crossing one beam is exactly the opposite of that obtained by crossing the other. For the sake of convenience, we designate the beam that results in a rise and then fall in the detector response as a person enters into it as positive 共+兲 and the other beam as negative 共−兲. The order of occurrence of these beams depends on the path direction. This visibility pattern can be considered to have four

Fig. 11 Radial sensor module with eight detectors with Fresnel lens arrays arranged around a circle. These sensor modules are designed to be placed raised from the ground by 1 m and look radially in all directions to track motion.

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boundaries—the leading and trailing edges of the 共+兲 and the 共−兲 beams. The detector responds to crossing of each of these boundaries, depending on the direction of motion. 5 Characterization of Fresnel Lens Array We use the Animal alley array, AA0.9GIT1, a commercially available lens array obtained from Fresnel Technologies Inc.18 The material of the lens is such that it has suitable transmission in the 5- to 10-␮m wavelength range. The detector response observed from one lens aperture with one person walking across it is a positive and negative peak, as shown in Fig. 8共a兲. This response is essentially what is obtained when the four boundaries, as already discussed, have been crossed. When the person moves in the opposite direction, the response is exactly the same but with opposite polarity, as shown in Fig. 8共b兲. This gives information about the direction of motion of the source, assuming that the orientation of the detector is previously known. The FOV of the Fresnel lens array was characterized using a hot soldering iron as a source of heat that closely approximates a point source. The sensor was mounted on a rotation stage and an optical chopper was used to modulate the input heat flux to the detector. The sensor was rotated about the detector axis and the FOV of lens array was char-

Fig. 13 Sensor cluster with detectors arranged to be along a sphere with any desired orientation.

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Fig. 14 Two radial sensor modules used to capture data with a person walking along the path indicated. The sensor’s FOVs are indicated by the dotted lines. The data obtained from the sensors are used to estimate the angular position, as shown in Fig. 15.

acterized. This is illustrated in Fig. 9 and a summary of the different parameters of this lens array are shown in Table 2.

enclosed space. We also analyzed the spectral content of the raw sensor signal to classify people and their actions.19

6 Signal Analysis When a person walks across the FOV of a single Fresnel lens, a positive and negative peak is obtained from the detector 共Fig. 8兲. Thus, motion across the FOV of a lens array results in a series of positive and negative pulses. The sensor response obtained when a person walks across the FOV of one lens array at a distance of 2 m from the sensor is shown in Fig. 10. From this plot, certain information about the motion can be inferred. The presence of a person is obvious from the signal obtained from the detector. The direction of motion relative to the sensor can be inferred if the orientation of the sensor is known. The angular velocity of the source could also be determined if we assume that the person walks across the detector FOV at the same speed without changing the direction of motion. With reference to Fig. 9 and Table 2, it can be seen that the angular range traversed in the time between two adjacent positive or negative peaks is 9 deg or 0.15 rad 共2A + B + C兲. Knowing this range, the angular velocity can be determined from the sensor response by looking up the time between two adjacent peaks. For example, from Fig. 10, the angular velocity can be calculated to be 0.15 rad/ s and assuming the source moving at a constant velocity at a distance of 2 m across the FOV, the linear velocity is determined to be 0.31 m / s. With one detector and lens array, the direction and the velocity of the source can be estimated. Using multiple detectors and lens arrays having overlapping FOVs and different orientations, human motion can be tracked over an

7 Sensor System Hardware The signal conditioning involves filtering the sensor signal followed by amplification and digitization. We use a bandpass filter to restrict the signal between the frequency band 1 to 100 Hz. The amplification of the signal is provided by two stages, with a maximum gain of 40,000. An extra input to the second-stage amplifier was provided to adjust the dc offset after the first amplification. The amplifier board handles eight channels simultaneously, corresponding to the number of detectors used in each sensor module. With the optimal gain settings, the maximum distance over which detection is achieved is about 12 m for a typical human source. The Texas Instruments MSP430F149 was selected for our platform to handle digital sampling, processing, and transmission/collection of the data. It runs at 20 MHz and contains 64 K of total onboard memory, available either for programming instructions or data storage. It features a C language compiler for easy programming, and uses memory-mapped registers that facilitate the control of an onboard 12-bit, eight-channel analog-to-digital converter 共ADC兲 and a universal asynchronous receiver/transmitter 共UART兲 serial interface. The sampling frequency of the ADC is about 166 Hz, well above the frequency of the human motion being tracked. Each microcontroller is augmented by a TRF6901 daughter board that controls a twomode dual-antenna radio transmitter that provides us the facility to transmit data from each of the sensor clusters through a wireless or via serial communication.

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Fig. 15 Interpreted data from each of the sensor nodes indicating angular position of the target with time. With the spatial locations of these clusters known, the angular position is used to obtain a trajectory of the motion.

The three different sensor configurations designed are shown in Figs. 11–13. In one configuration, the detectors and lens arrays were arranged around a circle to provide a full 360-deg visibility. This system has potential applications in monitoring the periphery of military installations. A single cluster of eight detectors 共Fig. 11兲 could be used to coarsely identify the direction of motion and with the help of more than one cluster, the resolution of the tracking system would be improved. Another configuration is the ceiling mount type 共Fig. 12兲, which monitors the space by looking at boundary crossings across the cells created by the lens array. We are currently developing the third configuration that uses a single Fresnel lens per detector. A sensor cluster is being developed with the detectors arranged along a sphere with any desired orientation, as shown in Fig. 13. Each detector on the cluster would monitor a small spatial region and motion can be tracked using information from multiple sensors on the cluster as well as from other clusters. The sensor support structure for holding the lens array as well as the pyroelectric detector were designed in a CAD program and fabricated with a rapid prototyping machine to provide an easy mechanism for mounting the multiple lenses on each platform while enabling us to experiment with different lens orientations. Important aspects from the sensor deployment are communications and synchronization. Data from each of the nodes must be collected and processed in real time, and this must be done in the most efficient way possible—to miniOptical Engineering

mize both energy consumption and computation cost. Each node on the network is assigned a unique ID to be able to identify it. Each of the transceivers in the sensor modules are programmed to transmit at a unique frequency between 888 and 928 Mhz at programmable transmission data rates from 19 to 76 K bits/ s. The data packet contains the source ID, the destination ID, and a checksum field for error detection. 8 Human Tracking We demonstrate human motion tracking using two radial type of sensors 共Fig. 11兲. Each of these sensor nodes 共slaves兲 transmit data to a central receiver 共master兲, which aggregates all the data and sends it to a host computer for processing or display. The tracking strategy for distributed sensors includes event detection, event registration, motion inference, and trajectory smoothing. In this implementation, the event detection is done in the embedded microcontroller of the slave sensor node. The master node synchronizes the events registered by the different slave nodes and implements a hidden Markov model to register and smooth the received event data. A bandpass sine filter is used for event detection and signal digitization. Motion inference is done by converting the data received from each sensor node into angular displacements. The angular information obtained relative to each node is then converted to Cartesian coordinates using a grid approximation to display the

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Fig. 16 Human motion tracking using ceiling sensors modeled as line sensors. The lines are obtained by mounting the ceiling version of the sensor clusters at a height of 6 m from the ground. These lines can be arranged arbitrarily to create boundaries in the space. The sensor system plots the estimate of the position 共black dots兲 based on the sequence of lines crossed.

trajectory of the target. Using a two-sensor-node setup 共Fig. 14兲, Fig. 15 demonstrates the tracking of a single person with a person walking across the FOV of both nodes. A detailed description of the setup, including the simulated and experimental results can be found in Ref. 20. Another approach uses each sensor as a tripwire, treating each sensor’s visibility region as a planar slice.21 Sensor clusters 共ceiling type兲 are mounted on the ceiling at a height of 6 m, looking down, their plane of visibility projecting to a boundary line on the floor below. The 2-D floor space is decomposed into polygonal regions by splitting an initial polygon with each sensor boundary line. Each polygon represents a spatial resolution element; a hot source moving within the region will not trigger any sensors. If a source moves between adjacent regions, the sensor whose line forms the boundary will be triggered. We model this system as a neighborhood graph, where vertices in the graph correspond to polygon regions 共themselves a collection of spatial vertices兲, and connecting edges correspond to sensor lines. Tracking is accomplished Optical Engineering

by recognizing that motion within the space corresponds to sequences of sensor triggers 共as their lines are crossed兲; by recognizing sequences we can determine the path of sources present in the space. We demonstrate tracking of a single person walking in the space, and a snapshot of the estimated position of the person is shown in Fig. 16. Each line represents the visibility of one sensor, as mapped on the floor, and black dots correspond to the position of the person as estimated by the sensor system. The lines joining these dots are drawn to represent the trajectory of motion of the person. 9 Conclusions We designed and developed a low-cost sensor cluster for tracking human motion using off-the-shelf components. The sensor system can detect human motion over large areas at distances of over 12 m. Pyroelectric detectors are inexpensive and most commonly found in motion detectors in security or home automation systems. Fresnel lens arrays

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Shankar et al.: Human-tracking systems… Mohan Shankar received his BS degree in electronics and communications engineering in 2002 from National Institute of Technology Karnataka, India, in 2002 and his MS degree in electrical and computer engineering in 2004 from Duke University, Durham, North Carolina, where he is also currently pursuing his PhD degree.

are made of inexpensive plastics and can easily be molded to implement the desired spatial segmentations. We characterized the behavior of the dual-element pyroelectric detector as well as the Fresnel lens array. The data obtained from the sensor enables us to extract velocity information as well as the direction of motion. By using multiple sensor clusters in different orientations, we demonstrated human motion tracking. Acknowledgments The authors would like to acknowledge the Army Research Office for supporting this work through Grant No. DAAD19-03-1-0352.

John B. Burchett received his PhD degree in December 2005 from the Electrical and Computer Engineering Department at Duke University, Durham, North Carolina. His research interests include software development for low-cost biometric sensor networks for human tracking.

References 1. F. Xu and K. Fujimura, “Pedestrian detection and tracking with night vision,” in Proc. IEEE Intelligent Vehicle Symp. 共2002兲. 2. R. Bodor, B. Jackson, and N. Papanikolopoulos, “Vision-based human tracking and activity recognition,” in Proc. 11th Mediterranean Conf. on Control and Automation 共2003兲. 3. S. B. Lang, “Pyroelectricity: from ancient curiosity to modern imaging tool,” Phys. Today 58共8兲, 31–36 共2005兲. 4. R. W. Astheimer and F. Schwarz, “Thermal imaging using pyroelectric detectors,” Appl. Opt. 7共9兲, 1687–1696 共1968兲. 5. D. Cima, Using Lithium Tantalate Pyroelectric Detectors in Robotics Applications, Eltec Instruments, Inc., Daytona Beach, FL 共Oct. 1994兲. 6. M. M. Pradhan and R. K. Garg, “Pyroelectric null detector for absolute radiometry,” Appl. Opt. 21, 4456–4458 共Dec. 1982兲. 7. C. F. Tsai and M. S. Young, “Pyroelectric infrared sensor-based thermometer for monitoring indoor objects,” Rev. Sci. Instrum. 74, 5267– 5273 共Dec. 2003兲. 8. G. D. Jones, M. A. Hodgetts, R. E. Allsop, N. Sumpter, and M. A. Vincencio-Silva, “A novel approach for surveillance using visual and thermal images,” in DERA/IEE Workshop on Intelligent Sensor Processing, pp. 911–919 共2001兲. 9. S. de Vlaam, “Object tracking in a multi sensor network,” Master’s thesis, Delft University of Technology, the Hague 共2004兲. 10. S. D. Feller, E. Cull, D. Kowalski, K. Farlow, J. Burchett, J. Adleman, C. Lin, and D. J. Brady, “Tracking and imaging humans on heterogeneous infrared sensor array for tactical applications,” Proc. SPIE Vol. 4708, pp. 212–221 共2002兲. 11. A. Armitage, T. D. Binnie, J. Kerridge, and L. Lei, “Measuring pedestrian trajectories using a pyroelectric differential infrared detector,” in 12 Sensors and Their Applications, Limerick, Ireland 共2003兲. 12. P. C. Hobbs, “A $ 10 thermal infrared imager,” Proc. SPIE 4563, 42–51 共2001兲. 13. Infratec, “Application Note—Pyroelectric detectors,” http:// www.infratec.de/sensorik/. 14. Glolab Corporation, “Infrared parts manual,” http://www.glolab.com/ pirparts/infrared.html. 15. D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21共7兲, 1140–1147 共2004兲. 16. D. J. Brady, “Multiplex sensors and the constant radiance therorem,” Opt. Lett. 27共1兲, 16–18 共2002兲. 17. U. Gopinathan, D. J. Brady, and N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express 11共18兲, 2142– 2152 共2003兲. 18. Fresnel Technologies Inc., http://www.fresneltech.com/arrays.html. 19. J. Burchett, M. Shankar, A. B. Hamza, B. D. Guenther, N. P. Pitsianis, and D. J. Brady, “Lightweight biometric detection system for human classification using pyroelectric infrared detectors,” Appl. Opt. 45共13兲, 3031–3037 共2006兲. 20. Q. Hao, D. J. Brady, B. D. Guenther, J. B. Burchett, M. Shankar, and S. D. Feller, “Human tracking with wireless distributed radial pyroelectric sensors,” IEEE Sens. J. 共in press兲. 21. J. Burchett, M. Shankar, B. D. Guenther, and D. J. Brady, “Sequence recognition algorithm for lightweight single person tracking using pyroelectric infrared boundary detectors,” IEEE Sens. J. 共in press兲.

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Qi Hao received his Ph.D degree from Duke University in 2006 and his B. Eng. and M. Eng. degrees from Shanghai Jiao Tong University, China, in 1994 and 1997, respectively, all in electrical engineering. He worked at Shanghai Electric Tool Research Institute from 1997 to 1998 in developing CAD software and optimization algorithms. From 1998 to 2001 he worked at the Data Storage Institute of Singapore on self-tuning robust control of HDD servo systems. Currently, he is a post-doctoral scholar of the Center for Visualization and Virtual Environments at the University of Kentucky. His research interests include wireless sensor systems for multiple human tracking and identification. Bob D. Guenther received his BS degree in physics and mathematics from Baylor University, Texas, in 1960 and his MS and PhD degrees from University of Missouri in 1963 and 1968, respectively. He is currently an adjunct professor with the departments of Physics and Electrical and Computer Engineering at Duke University, Durham, North Carolina.

David J. Brady is the Addy Family Professor of Electrical and Computer Engineering in the Pratt School of Engineering at Duke University. Brady joined the Duke faculty in 2001 and directed the Fitzpatrick Institute for Photonics from 2001–2005. He currently leads the Duke Imaging and Spectroscopy Program 共www.disp.duke.edu兲. He was on the faculty of the University of Illinois from 1990–2001. He received his Ph.D. and M.S. degrees in applied physics from California Institute of Technology and a B.A. in physics and mathematics from Macalester College.

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