wavelet-rx anomaly detection for dual-band forward-looking infrared imagery

Wavelet-RX anomaly detection for dual-bandforward-looking infrared imagery

Asif Mehmood* and Nasser M. NasrabadiU.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783, USA

*Corresponding author: [email protected]

Received 17 March 2010; revised 8 July 2010; accepted 14 July 2010;posted 16 July 2010 (Doc. ID 125589); published 18 August 2010

This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-lookinginfrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. Theproposed approach, called the wavelet-RX (Reed–Xiaoli) algorithm, consists of a combination of atwo-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called theRX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decomposethe input image into uniform subbands. A subband-image cube is formed by concatenating togethera number of significant subbands (high-energy subbands). The RX algorithm is then applied to the sub-band-image cube obtained from a wavelet decomposition of the LWor MW sensor data. In the case of thedual band, the RX algorithm is applied to a subband-image cube constructed by concatenating togetherthe high-energy subbands of the LWand MW subband-image cubes. Experimental results are presentedfor the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detectinganomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor.The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector forboth single-band and dual-band FLIR sensors. © 2010 Optical Society of AmericaOCIS codes: 100.5010, 100.4994, 100.3008.

1. Introduction

Anomaly detectors are pattern recognition schemesthat are used to detect objects and might be of inter-est for bothmilitary and civilian applications. Almostall anomaly detectors attempt to locate anythingthat looks different from its neighborhood, spatiallyor spectrally. In spatial anomaly detection algo-rithms, pixels that have significantly different signa-tures from their neighboring background (clutter)pixels are identified as spatial anomalies. Similarly,in spectral anomalies, pixels that have significantspectral dissimilarities with their neighborhood(background spectral clutter) are recognized as spec-tral anomalies. Anomaly detection is one of the mostwidely used techniques applied to much sensor data,such as hyperspectral imagery [1,2], synthetic aper-

ture radar (SAR) [3], and forward-looking infrared(FLIR) imagery [4,5].

Detection and identification of targets can bethought of as a two-stage process. In the first stage,an anomaly detector identifies either spatial or spec-tral, or both spatial and spectral (joint) anomalies inthe image or data under consideration. The secondstage determines whether there is a real target ora false alarm. The second stage can be accomplishedby using target computer-aided design (CAD) modelsfrom a library [6] or by using predetermined targettemplates [7].

Detection of targets in the FLIR imagery is a dif-ficult problem because of the variability of the ap-pearance of targets due to atmospheric conditions,background, and the thermodynamic state of the tar-gets [8]. Furthermore, most of the time, the back-ground forms similar shapes to those of the actualtargets, and the targets could be partially obscured.In the FLIR images, potential target locations areusually obtained by finding high-contrast local

0003-6935/10/244621-12$15.00/0© 2010 Optical Society of America

20 August 2010 / Vol. 49, No. 24 / APPLIED OPTICS 4621

regions using a dual-window approach, consisting ofa target-size inner window and a slightly larger outerwindow. Burton and Benning [9] presented an eva-luation of some target-detection methods based on adouble-window filter for single-band IR imagery.This double-window filter is based on the contrastbetween the target and its immediate background(dual-window approach). It consists of two rectangu-lar windows in which the inner window surroundsthe target and the outer window contains back-ground. In Ref. [6], a probe-based approach combinedwith image CAD models is used to detect and recog-nize targets in LWFLIR imagery. In Ref. [5], a target-detection algorithm is presented that achievesclutter rejection by using multiple observations ofthe same target scene of a single-band FLIR imagery.The major disadvantage with the above techniques isthat they exploit spatial information only to detecttargets and do not take into consideration the spatialfrequency information.

A number of detection techniques have also beendeveloped in the literature for dual-band FLIR ima-gery and multisensor data. Chan et al. [10] proposeda neural-based clutter rejecter for a dual-band FLIRsensor, which consisted of an eigenspace transforma-tion of concatenated dual-band data, followed by asimple multilayer perceptron. In Ref. [1], a multisen-sor target-detection technique is proposed that in-corporates multiple imaging sensors at differentspectral ranges, such as the visible, near-infrared,and far-infrared bands.

In this paper, the Reed–Xiaoli (RX) [11] anomalydetection algorithm is combined with a 2D discretewavelet transform (DWT) [12] to perform target de-tection on dual-band (LW and MW) FLIR imagery.The RX detection algorithm is a multivariate con-stant false alarm rate (CFAR) detection algorithmand is derived as a generalized likelihood ratio test(GLRT) used for detecting anomalies given a singleband or multiple band images.

In the proposed method, called the wavelet-RX al-gorithm, each input image is wavelet decomposeduniformly into B equal subbands. All the subbandsobtained using decomposition are rearranged intoa subband-image cube such that the first band repre-sents the baseband and the subsequent bandsrepresent the higher frequency subbands. The high-frequency subbands are sorted (based on their en-ergy contents) before concatenation, and a numberof high-frequency subbands with insignificant energyare discarded. Each pixel in the cube now contains allthe spatial frequency information at a particular lo-cation. Now the RX algorithm, which is mainly usedin hyperspectral anomaly detection, is applied to thiscube using a dual-window approach.

Recently, wavelet-based approaches are being em-ployed extensively in target detection [13,14]. In Ref.[13], the most recent target-detection methods usingwavelets are reviewed by illustrating different ideasof using wavelet coefficients as a tool for target-back-ground separation. In Ref. [15], a wavelet-based joint

transform correlation is developed based on the ideaof composite filters [7]. A composite filter for eachclass of target is constructed from the wavelet fea-tures. Riley and Devaney [16] exploited multiresolu-tion analysis (MRA) to perform anomaly detectionusing a model-based approach, sequentially begin-ning at coarsest scale (low resolution) and proceedingto finer scale as needed. MRA is achieved by waveletdecomposition of an image that deals with the repre-sentation and analysis of images at more than oneresolution. But the approach discussed in Ref [16]employs only one subband at a time and does notfully exploit the information frommultiple subbands.In Ref. [17], target detection is performed by calcu-lating co-occurrence matrix features from detailedDWT subbands of nonoverlapping, but adjacent sub-blocks. The subbands with maximum co-occurrencematrix feature values are considered target seedpoints for a region-growing algorithm.

Recent developments also include those of Zhangand Desai [18], who have presented a target segmen-tation algorithm incorporating the multiresolutionanalysis of images and their probability density func-tions (PDFs) with a Bayes classifier. Sadjadi [19] hasdeveloped a clustering algorithm to segment targetsfrom clutter using a multiresolution texture-basedmethodology, again incorporating the PDFs of wave-let decomposition subbands. Wavelet methods em-ploying subband concatenation have also receiveda considerable amount of attention for object detec-tion and recovery. In Ref. [20], a supervised linearclassifier is applied to feature vectors comprised ofsamples taken from the subbands of an undecimatedwavelet transform. Other researchers [14,21] havealso used feature vectors from concatenation of thewavelet transform coefficients or concatenation ofwindowed subband energies and applied them asinputs to a classifier, or to a Euclidean distance mea-sure for detection.

In some previous studies, wavelet transforms, inconjunction with the RX algorithm, have been usedfor anomaly detection. Reed and Yu [22] proposed amultispectral object detection using the hierarchicalwavelet decomposition and applied to multispectralSAR imagery. They developed a robust adaptiveGLRT for detecting low observable target patternby combining target spectral, orientation, and scalefeatures. The algorithm developed in Ref. [22] is ap-plied to two concatenated SAR bands and, sequen-tially, a target decision is made at each waveletdecomposition scale. In Ref. [23], the RX algorithmis extended to detect anomalies within the waveletcoefficients of a single band imagery, and it is shownthat the detection performance of this algorithm ishigher than that of the CFAR algorithm for anoma-lies in a correlated noise background.

Most of the anomaly detection methods in thewavelet domain discussed above are different fromthe framework we have employed in this paper.To the best of our knowledge, no one has used theRX algorithm on concatenated uniformly wavelet

4622 APPLIED OPTICS / Vol. 49, No. 24 / 20 August 2010

decomposed subbands as applied to dual-band FLIRdenoted as LWþMW FLIR imagery. Furthermore,we have evaluated our proposed algorithm on a largedatabase, which has not been done previously.

In our proposed wavelet-RX algorithm, the dual-window approach is applied to the subband-imagecube obtained from LW, MW, or LWþMW data. Thedual-window approach consists of two windows cen-tered at each test pixel in order to create two disjointregions, an inner window region (IWR) and an outerwindow region (OWR), as shown in Fig. 4. The sizes ofthe IWR and OWR are set according to the approxi-mate size of the biggest target in the database. It isassumed that the length of the longest target andthe height of the tallest target in the database areknown. An approximate target size is predeterminedvia prior knowledge of the range and field of view(FOV) information. In some schemes, only the rangeto the center of the FOVand the depression angle areknown, so that a flat earth approximation providesthe best estimate. The range can be obtained accu-rately by use of a laser range finder or other activesource or a digital map. Accurate range informationcan also be obtained from the altimeters or fromthe passive means. In the RX algorithm, the back-ground clutter is represented as amultivariate Gaus-sian distribution with a covariance matrix, which iscalculated from the pixels in the OWR of a dual-win-dow approach. Therefore, the size of the OWR is setsuch that a meaningful covariance matrix (nonsingu-lar) for the RX algorithm can be evaluated. The RXalgorithm is applied to a cube consisting of only thesignificant concatenated subbands. TheRXalgorithmon the concatenated wavelet subbands will take theadvantage of intercorrelation between the subbands,as well as the correlation between the dual-bandFLIR imagery. Furthermore, we have also discardedsome of the high-frequency (noninformative) sub-bands that are corrupted by the sensor noise.

This paper is organized as follows: Section 2 brieflydescribes DWT and its application to FLIR imagery;Section 3 explains anomaly detection algorithmssuch as CFAR and RX, along with the wavelet-RXand joint wavelet-RX; Section 4 presents the resultsand analysis; and Section 5 concludes this paper.

2. Discrete Wavelet Transform

In order to apply wavelet decompositions to images,2D extensions of wavelets are required. This can beachieved by using separable or nonseparable wave-lets. In most applications, it is common to employseparable filters. A separable filter implies that filter-ing canbeperformed in onedimension (rows) followedby filtering in another dimension (columns). A 2Dwavelet transform can be computed with a separableextension of the one-dimensional (1D) decompositionalgorithm.We first convolve the rows of the image un-der consideration with a 1D filter (decimation acrosscolumns), retain every other column, convolve the col-umns of the resulting image with another 1D filter,and retain every other row (decimation across rows).The advantages of the separable filter approach arethat it is conceptually simple, easy to extend tomulti-ple dimensions, and computationally efficient, rela-tive to its nonseparable counterpart [24,25].

The wavelet decomposition used in this paper isthe uniform wavelet decomposition, and it is com-puted with successive low-pass and high-pass filter-ing of the image. The filter bank representation ofthe wavelet uniform decomposition employing a se-parable approach is shown in Fig. 1. As can be seenin Fig. 1, the separable filters are first applied in onedimension (e.g., vertically) and then in the other di-mension (e.g., horizontally) to an image f ðm;nÞ. Thewavelet filters used in this paper are Haar filtersbecause Haar filters are the simplest orthogonal fil-ters and are compactly supported [12]. The advan-tage attributed to Haar filters is that they can beefficiently calculated and provide a lot of flexibility.

Fig. 1. (Color online) Wavelet filter bank for one-level image decomposition.


In Fig. 1, the outputs at the first stage are denoted byaðm;nÞ, DVðm;nÞ, DHðm;nÞ, and DDðm;nÞ and repre-sent the low-passed approximation, vertical detail,horizontal detail, and diagonal detail of the input im-age, respectively. Only one iteration of the waveletfilter bank is shown in Fig. 1. Further levels of thedecomposition filter bank can be obtained simplyby repeating the process.

Figure 2(a) shows a one-level wavelet decomposi-tion, and Fig. 2(b) shows a two-level uniform waveletdecomposition. The low-pass filtering (LPF) isrepresented by “L,” and high-pass filtering (HPF) isrepresented by “H.” At each level, the HPF producesdetail information and the LPF produces coarseapproximation.

We have performed a three-level wavelet decom-position of the FLIR image shown in Fig. 8 andobtained 64 uniform subbands, as shown in Fig. 3.Figure 3(a) depicts the uniform wavelet decomposi-tion of a LW image with 64 equal subbands, andFig. 3(b) represents the uniform wavelet decomposi-tion of a MW image with 64 equal subbands. If welook at Fig. 3(a) or Fig. 3(b), we can see that the sizeof each subband is 1=8 of the original image in eachdimension because we have performed a three-leveldecomposition with decimation. The subimage in thetop left corner is the coarsest approximation of theoriginal image and is obtained by performing LPFconsecutively, and the subimage in the bottom rightcorner is obtained by successive HPF and representsthe finest detail for the image under consideration.The remaining 62 subbands are obtained by the com-bination of LPF and HPF.

Note that decimation is performed in each dimen-sion after each filtering operation in order to reducethe overall number of samples. The advantage of dec-imation is that the computational cost to performanomaly detection is drastically reduced. However,if the target size is very small, then decimationcan be detrimental. Therefore, as we are dealing withtargets of significant sizes, decimation does not dis-tort target information and it serves our purpose ofreducing the computational cost for detecting tar-gets. However, if the input image contains targetsof smaller sizes, then the decimation during waveletdecomposition will distort targets’ information and

targets may not be detected. In fact, the proposedwavelet-RX algorithm can also be applied to smalltargets by using undecimated wavelet subbands[26], but the computational cost will obviously in-crease. Furthermore, we uniformly decompose anddecimate each image separately; therefore, we arenot concerned about destroying the translationalinvariance requirement [27].

3. Anomaly Detection Algorithms

Anomaly detection is an important problem that hasbeen investigated within diverse research areas andapplication domains. Many anomaly detection tech-niques have been specifically developed for certainapplication domains, while others are more generic.In this paper, our focus is on CFAR- and RX-basedmethods in wavelet domain and their applicationto single-band and dual-band FLIR imagery.

A. CFAR

The CFAR detection benchmark is an example ofdata-dependent processing designed to find targets

Fig. 2. (Color online) Wavelet uniform decomposition of (a) onelevel and (b) two levels.

Fig. 3. Uniform three-level wavelet decomposition of (a) LWimage and (b) MW image.


in an environment of varying background clutter.The CFAR algorithm computes the difference be-tween an input pixel at a given location and its sur-rounding neighbors weighted by the variance of thebackground clutter. In this algorithm, the variance ofthe background clutter is considered either un-known, or it is computed from the data using adual-window approach. This algorithm can be math-ematically expressed as

δCFARðrijÞ ¼ ðrij − μÞTσ−1ðrij − μÞ; ð1Þ

where rij represents the pixel under considerationlocated at the center of IWR, μ represents the esti-mated mean from the pixels within the OWR, andσ is the variance of the pixels within the OWR.The extension of Eq. (1) to multivariate data is ex-plained in the following section for both the concate-nated dual-band FLIR data and its wavelettransformed version.

B. Wavelet-RX Anomaly Detector

Reed and Xi [11] developed an algorithm commonlyreferred to as the RX anomaly detector, which canbe used to detect targets of unknown spectral distri-bution against a background with unknown spectralcovariance. This algorithm is widely used to solve theanomaly detection in multispectral and hyperspec-tral imaging. The RX algorithm is a CFAR adaptiveanomaly detector that is derived from theGLRT. Thisalgorithm computes the difference between the spec-tral signature of an input pixel at a given location andits surrounding neighbors. In this algorithm, the cov-ariance of the background clutter is considered eitherunknown or is computed from the data.

In the conventional RX algorithm, a nonstationarylocal mean μ is subtracted from each spectral pixel.The localmean μ is obtained by sliding a dual window,as shown in Fig. 4, over every spectral pixel in the im-age, and calculating the mean of the spectral pixelsfalling within the outer window. The size of the innerwindow is assumed to be the size of a typical target ofinterest at a given range in the image. A guardbandsurrounding the IWR is also sometimes used to pre-vent any spillage of target pixels during the calcula-tion of the background OWR statistics. The residualsignal after mean subtraction is assumed to approx-imate a zero-mean pixel-to-pixel independent Gaus-sian random process. In the discussion to follow inthis section, we focus on a single-band FLIR imagery,such as LW, and define our proposedwavelet-RX algo-rithm. The same definition can be adopted to derivean expression for the MW FLIR imagery. Let eachinput pixel for B uniform wavelet subbands beexpressed by

xLWði; jÞ ¼ ðx1ði; jÞ; x2ði; jÞ;…; xBði; jÞÞT ; ð2Þwhere the wavelet coefficient at location ði; jÞ for asubband b can be represented as xbði; jÞ, andb ¼ 1; 2; 3;…;B. This is shown in Fig. 5 and repre-sents a wavelet subband-image cube. This sub-

band-image cube is constructed by concatenatingLWwavelet subbands or by concatenating MWwave-let subbands at pixel level. The cube obtained by con-catenating LW wavelet subbands is called the LWwavelet subband cube, and the cube achieved by con-catenating MW wavelet subbands is called the MWwavelet subband cube. Now, let us define X to be aB ×N matrix of N-centered (mean-removed) refer-ence background clutter pixels (or pixels in the outerwindow). Each observation subband pixel is repre-sented as a column in the sample matrix X and canbe written as

X ¼ ½xð1Þ; xð2Þ;…; xðNÞ�: ð3Þ

Consider a test pixel rij at pixel location ij. The RXalgorithm output at each pixel of the LW waveletsubband cube is given by

δrxðrijÞ ¼ ðrij − μÞTC−1LWðrij − μÞ; ð4Þ

Fig. 4. (Color online) Sliding dual window: inner window region(IWR) and an outer window region (OWR).

Fig. 5. (Color online) Wavelet subband-image cube: B uniformsubbands concatenated.


where rij represents the pixel under considerationlocated at the center of the IWR, μ represents the es-timated mean of the pixels within the OWR, and CLWis the estimated covariance matrix of the pixels with-in the OWR and is given by

CLW ¼ 1N

ðXXTÞ: ð5Þ

When the dual window is placed within a spatiallyhomogeneous region, such as natural backgrounds,the statistical characteristics of the IWR and OWRwill be similar to each other, and the RX output[Eq._(4)] will have a small value. On the other hand,the IWR and OWRwill contain significantly differentstatistical features if the dual window is centered ona region in which the target is surrounded by the lo-cal background. Use of an appropriate thresholdingon the RX output [Eq. (4)] allows most targets to bedetected as anomalies at a given false alarm rate.

C. Wavelet-RX for Dual-Band FLIR

To develop an RX-like joint dual-band anomalydetection algorithm, let the concatenated wave-let-transformed LW and MW pixel xLW−MWði; jÞ berepresented by the partition vector

xLW−MWði; jÞ ¼�xLWði; jÞxMWði; jÞ

�; ð6Þ

where xLWði; jÞ and xMWði; jÞ are the pixel vectorsfrom the LW and MW subband-image cubes, respec-tively. The RX algorithm on the concatenated dataxLW−MWði; jÞ is given by

δLW−MWrx ði; jÞ ¼

��xLWði; jÞxMWði; jÞ

�−

�μLWμMW

��T

×�CLWLW CLWMWCMWLW CMWMW

�−1

×��

xLWði; jÞxMWði; jÞ

�−

�μLWμMW

��; ð7Þ

where μLW and μMW are the estimated means of allthe pixels (xLW and xMW) in the corresponding outerwindows of LWand MW images, respectively. CLWLWand CMWMW are the estimated covariance matrices ofthe LWand MW data, respectively. CLWMW ¼ CMWLWrepresents the cross-covariance matrix between LWand MW data. In Eq. (7), the linear correlation be-tween the LWand the MW data is exploited throughthe inverse covariance matrix of the concatenateddata. If the LW data are not correlated to the MWdata, then CLWMW ¼ CMWLW ¼ 0. In this case, thisis the same as performing RX on each sensor dataindividually, then adding their results.

The inverse covariance matrix can also be repre-sented by the precision matrix as

C−1 ¼�CLWLW CLWMWCMWLW CMWMW

�−1

¼�ΛLWLW ΛLWMW

ΛMWLW ΛMWMW

�:

Now, the RX output can be expanded into fourindependent terms:

δLW−MWrx ði; jÞ ¼

��xLWði; jÞxMWði; jÞ

�−

�μLW

μMW

��T

×� ΛLWLW ΛLWMW

ΛMWLW ΛMWMW

�

×��

xLWði; jÞxMWði; jÞ

�−

�μLW

μMW

��

¼ ðrLWði; jÞ − μLWÞT ΛLWLW

× ðrLWði; jÞ − μLWÞþ ðrLWði; jÞ − μLWÞT ΛLWMW

× ðrMWði; jÞ − μMWÞþ ðrMWði; jÞ − μMWÞT ΛMWLW

× ðrLWði; jÞ − μLWÞþ ðrMWði; jÞ − μMWÞT ΛMWMW

× ðrMWði; jÞ − μMWÞ: ð8Þ

The first and the fourth terms in Eq. (8) are the RXoutput contributions from each sensor data with thejoint precision matrix, and the second and thirdterms are the contributions from the cross precisionmatrices and the two FLIR (LW and MW) data.

ApplyingEq. (8) to thewavelet subband-image cubeconstructed from the dual-band FLIR images, we ob-tain subfigures [Figs. 6(a)–6(d)] for each term in Eq.(8). In Fig. 6, the off-diagonal subfigures [Figs. 6(b)and6(c)] represent the contributions fromthe twosen-sors because there is significant cross-correlation be-tween the LWand theMWdata. Figures 6(a) and 6(d)represent the contributions from the LW and MWsensors with their corresponding precision matrices,respectively.

It is also possible to implement Eq. (8) on the LWand MW concatenated raw data (without wavelet de-composition). In this case, at each location ði; jÞ, theconcatenated pixel vector is

xLW−MWði; jÞ ¼�xLWði; jÞxMWði; jÞ

�; ð9Þ

where xLWði; jÞ and xMWði; jÞ correspond to the LWand MW pixel values at location ði; jÞ, respectively.Each subfigure [Figs. 7(a)–7(d)] represents the con-tribution from each term in Eq. (8). The off-diagonalFigs. 7(b) and 7(c) represent the major contributionsfrom the two sensors, and Figs. 7(a) and 7(d) repre-sent the contribution from each sensor data withtheir corresponding precision matrices.


4. Results and Analysis

A number of experiments were used to evaluatethe performance of the proposed algorithm. We used12 bit gray-scale FLIR input images that were ob-tained using a pair of LW and MW experimentallaboratory infrared sensors. The LW sensor used aquantum well infrared photodetector focal plane ar-ray, while theMW sensor used an indium antimonide(InSb) focal plane array. Both the LW and the MWsystems were designed so that they had the same re-solution, and their fields of view were both set to2:20° and 1:65° horizontally and vertically, respec-tively. Each input image is of size 304 × 504, and ex-amples of the LWand MW images are shown in Figs.8(a) and 8(b), respectively. In our database, therewere 461 pairs of LWand MWmatching images with572 legitimate targets posed at ranges between 1 and

4km. The LWandMW sensor operating wavelengthsare 8–12 and 3–5 μm, respectively.

A. CFAR Results on a Single Band and a Dual-BandFLIR Sensor

The CFAR algorithm is first applied to LW and thento MW images. The CFAR output of the LWand MWimages is shown in Figs. 9(a) and 9(b), respectively.The CFAR algorithm is also applied to the dual band,which is obtained by concatenating LWand MW rawimages, and the CFAR result is shown in Fig. 9(c).

B. Wavelet-RX Results on a Single Band anda Dual-Band FLIR Sensor

In this subsection, the RX detection algorithm is ap-plied to the wavelet decomposed FLIR images. First,we took each LW FLIR image and decomposed it intoB uniform subbands. The resulting subbands fromeach imageare then sorted on the basis of their energycontents and concatenated to form a subband-imagecube. The energy in each subband is calculated as thesum of the squared wavelet coefficients.

Fig. 6. Wavelet-RX dual-band output of the four terms in Eq. (8)using LWandMW concatenated wavelet decomposed data: (a) firstterm, (b) second term, (c) third term, and (d) fourth term.

Fig. 7. CFAR dual-band outputs of the four terms in Eq. (8) usingLWandMW concatenated raw data: (a) first term, (b) second term,(c) third term, and (d) fourth term.

Fig. 8. Original (a) LW and (b) MW images.


We evaluated the performance of the RX algorithmwith a dual-window approach for all the subband-image cubes from our database. Each image cubeconsists of a number of energy-sorted and concate-nated wavelet subbands. The dual window used inour experiment consists of an inner window of size5 × 5 (roughly equal to the size of the largest targetin the database), and an outer window of size 13 × 13was used to calculate the background statistics sur-rounding the test pixel. A guardband window of size

8 × 8 was employed to circumvent any spillage of tar-get pixels in the background statistics calculation.

Figure 10 shows the results for the wavelet-RX applied to LW, MW, and LWþMW image cubes.Figures 10(a) and 10(b) show the outputs of thewavelet-RX algorithm using the top five highest-energy subbands of the LW and MW sensors, respec-tively. In the case of the dual band, the detectionoutput is shown in Fig. 10(c) using 10 subbands, con-structed by concatenating the top five highest-energysubbands from the LWand MW image cubes, respec-tively. The CFAR outputs and wavelet-RX outputscan be compared in terms of clutter suppression. Ifwe look at Figs. 9 and 10, it is clear that our proposedwavelet-based RX algorithm suppresses more clutterthan the CFAR algorithm does. In fact, the receiveroperating characteristic (ROC) plots in Fig. 14 verifyour observation.

C. ROC Results for FLIR Processed Images

The ROC curves representing detection probabilityðPdÞ versus false alarm rate ðPfaÞ were generatedin order to provide a quantitative performance com-parison. The ROC curves are based on the groundtruth information about the target locations in theFLIR images. The ground truth information givesthe x and y coordinates of all the targets in our da-tabase. The ground truth of each target was recordedwhen the FLIR images were captured and were pro-vided to us by the Night Vision Laboratory, and theywere checked manually and found to be correct. Toconstruct the ROC, first, all the pixel locations inthe processed image having score values above a pre-defined low threshold value are selected. These loca-tions, as well as their score values, are recorded andsorted with respect to the highest score value. Eachof these locations corresponds to a possible targetcandidate, which is compared to the ground truthtarget location. Starting with the target candidatehaving the highest score value, an acceptance win-dow (roughly equal to the size of the largest target)is centered on each possible target candidate, andif the ground truth information is within the accep-tance window, then this candidate is selected as atarget and all the remaining scores within this accep-tance window are set equal to zero. This is done toensure that a target is picked only once within theacceptance window.

Let the total number of targets from the groundtruth information be represented byNt, and the totalnumber of hits be obtained by adding all the hits andbe represented by Nhit. The expression for Pd canthen be written as

Pd ¼ Nhit

Nt: ð10Þ

Similarly, the expression for the false alarm rate canbe written as

Pfa ¼ Nmiss

Ntot; ð11Þ

Fig. 9. CFAR output results from (a) LW, (b) MW, and (c)LWþMW.


where Nmiss denotes the total number of missed tar-gets, andNtot represents the total number of pixels inthe image under consideration. We plotted ROCcurves for both CFAR and wavelet-RX applied toLW, MW, and dual-band cases.

1. ROC Results for CFAR

First, we performed CFAR on 461 LW images, one byone. The processed output of these images in conjunc-

tion with the ground truth information was thenused to plot the ROC curve. We repeated the sameprocess for the MW images and also plotted the ROCcurve. For the dual band, we concatenated LW andMWand repeated the same process. The ROC resultsfor LW, MW, and concatenated LWþMW are shownin Fig. 11. It is evident from Fig. 11 that the overallperformance of LW is superior to the concatenatedLWþMW and MW, particularly at a low false alarmrate. From the ROC plot, it can be seen that the MWperformance is the worst at low false alarm rate, butit improves a bit at high false alarm rate and almostmeets the LW curve at a 90% detection rate. One pos-sible reason behind MW’s poor performance is thatthe contrast quality of the MW images for targetdetection is poorer than that of the LW images.Therefore, when concatenating the low-contrastMW images with the LW images, the resulting over-all performance degrades compared to the LW perfor-mance in the ROC plot.

2. ROC Results for the Wavelet-RX Algorithm

This sectiondiscusses theROCcurves for thewavelet-RXprocessed images.We investigate theperformanceof the wavelet-RX algorithm on the LW, MW, andLWþMW subband-image cubes for a range of conca-tenated wavelet subbands. Figures 12(a)–12(c) showthe ROC plots for LW, MW, and LWþMW subband-image cubes, respectively, with 1, 5, 10, 20, 40, and64 concatenated subbands. Note that in Fig. 12(c),in the case of LWþMW, the subband-image cube con-sists of an equal number of wavelet subbands fromeach sensor. It is evident from theROC curves in Figs.12(a) and 12(b) that the best performance for a singlesensor is obtained by using only the top five subbandsfrom the LW and MW subband-image cubes.

However, as shown in Fig. 12, the worst perfor-mance is obtained by using only one subband, whichhas the highest energy in the image cube. The reasonfor this is that the subband with the highest energy is

Fig. 11. ROC plots for CFAR applied to LW, MW, and LWþMW.

Fig. 10. Wavelet-RX output results from (a) LW, (b) MW, and (c)LWþMW.


the wavelet baseband that is the low-passed versionof the original image, and the RX algorithm collapsesto a CFAR because all the high-frequency subbandsare completely discarded. Figure 12(c) shows theROC results for the LWþMW, and the best perfor-mance is obtained by using 10 subband-image cubesobtained by concatenating the top five energy sub-bands from LW and the top five energy subbandsfrom MW.

In order to perform a closer comparison betweenthe use of a single sensor (LW or MW) or a dual-bandsensor, we have reproduced the plots representingthe best results from Fig. 12 in Fig. 13. As seen fromthe ROC plots in Fig. 13, the LWþMW results out-perform the LW and MW ROC plots. The concate-nated wavelet subbands LWþMW perform thebest at a low false alarm rate, as well as at a highfalse alarm rate. This is because, when we concate-nate only the informative LWand MW subbands anddiscard the noninformative subbands, we have moreuseful information about the targets and the overallperformance improves, as shown in Fig. 13.

In Fig. 14, a comparison is also shown betweenCFAR and wavelet-RX by plotting the LW and MWROC curves from Fig. 11 against the ROC curvesfrom Fig. 12 for the five subbands of LW and MW.It is clear from the plots shown in Fig. 14 that theproposed wavelet-RX performs much better thanthe CFAR algorithm applied to the sensor data. Thisis due to the fact that the proposed wavelet-RX algo-rithm exploits both the spatial and the frequency in-formation from the data. Furthermore, by discardingsome of the high-frequency subbands, we are also

Fig. 12. ROC plots for wavelet-RX applied to (a) LW, (b) MW, and(c) LWþMW.

Fig. 13. ROC plots for LWþMW, LW, and MW separately.

Fig. 14. ROC plots for CFAR and wavelet-RX using LWand MW.


removing the noninformative and noisy portion ofthe data.

Finally, in Fig. 15, we have compared our proposeddual-band wavelet-RX algorithm with the averaging,or taking the maximum output values of the LWandMWwavelet-RX results. As seen from theROC curvesin Fig. 15, the dual-band wavelet-RX results outper-form the averaging and maximum fusion approachresults. In fact, the proposed dual-band wavelet-RXapproach simultaneously exploits the joint informa-tion between the dual-band FLIR data, as well aswithin each individual FLIR data.

5. Conclusion

We have proposed a wavelet-based RX anomaly de-tector for locating military targets in a single broad-band FLIR imagery and a dual-band FLIR imagery.The results from the ROC curves prove that by per-forming RX on a set of concatenated uniform waveletsubbands, a significant improvement can be achievedwhen compared with the results of the classicalCFAR algorithm. Additionally, it is shown that theproposed wavelet-RX algorithm can be easily ex-tended to a dual-band FLIR system. Experimentalresults also show that the wavelet-RX algorithm ap-plied to dual-band FLIR data outperforms that of asingle FLIR system. One major advantage of the pro-posed wavelet-RX algorithm is that some of thehigh-frequency subbands are discarded because theymainly represent the system noise. Furthermore,spatial/frequency information, as well as intercorre-lation between multisensor data, is exploited by theproposed anomaly detector. The only disadvantagethat can be attributed to this algorithm is that forvery small-sized targets, the proposed algorithmwould not work because we are performing decima-tion during wavelet decomposition. However, withslight modification by not performing decimation,the proposed algorithm can be used for small-sizedtargets at the expense of high computational cost.

References

1. H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomalydetection using subspace separation for hyperspectral imag-ery,” Opt. Eng. 42, 3342–3351 (2003).

2. D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P.Schaum, and A. D. Stocker, “Anomaly detection from hyper-spectral imagery,” IEEESignal Process.Mag. 19, 58–69 (2002).

3. S. Kuttikkad and R. Chellappa, “Non-Gaussian CFAR techni-ques for target detection in high resolution SAR images,” inProceedings of the International Conference on Image Proces-sing (IEEE, 1994), pp. 910–914.

4. B.Bhanu,“Automatictargetrecognition:stateoftheartsurvey,”IEEE Trans. Aerosp. Electron. Syst. AES-22, 364–379 (1986).

5. A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive opticaltarget detection using correlated images,” IEEE Trans.Aerosp. Electron. Syst. AES-21, 394–405 (1985).

6. S. Z. Der and R. Chellappa, “Probe-based automatic targetrecognition in infrared imagery,” IEEE Trans. Image Process.6, 92–102 (1997).

7. B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correla-tion Pattern Recognition (Cambridge U. Press, 2005).

8. A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistageinfrared target detection,” Opt. Eng. 42, 2746–2754 (2003).

9. M. Burton and C. Benning, “Comparison of imaging infrareddetection algorithms,” Proc. SPIE 302, 26–32 (1981).

10. A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIRfusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).

11. I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detectionof an optical pattern with unknown spectral distribution,”IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).

12. S. G. Mallat, Wavelet Tour of Signal Processing, 2nd ed.(Academic, 2008).

13. E. Abdelkawy and D. McGaughy, “Wavelet-based image targetdetection methods,” Proc. SPIE 5094, 337–347 (2003).

14. S. Wen, J. Yang, and J. Liu, “Small IR target detectionapproach based on multiscale relative distance image,” Proc.SPIE 4077, 194–197 (2000).

15. F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distortedimages,” Opt. Eng. 34, 3187–3192 (1995).

16. K. Riley and A. J. Devaney,”Wavelet processing of images fortarget detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).

17. S. Arivazhagan and L. Ganesan, “Automatic target detectionusing wavelet transform,” EURASIP J. Appl. Signal Process.2004, 2663–2674 (2004).

18. X.-P. Zhang and M. D. Desai, “Segmentation of bright targetsusing wavelets and adaptive thresholding,” IEEE Trans.Image Process. 10, 1020–1030 (2001).

19. F. A. Sadjadi, “Infrared target detection with probabilitydensity functions of wavelet transform subbands,” Appl.Opt. 43, 315–323 (2004).

20. R. N. Strickland and H. L. Hahn, “Wavelet transformmethodsfor object detection and recovery,” IEEE Trans. Image Process.6, 724–735 (1997).

21. G. Kronquist and H. Storm, “Target detection with localdiscriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).

22. X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robustadaptive multi-spectral object detection by using wavelettransform,” IEEE Trans. Acoust. Speech Signal Process. 5,141–144 (1992).

23. J. D. Barnes, “Multiscale anomaly detection and imageregistration algorithms for airborne landmine detection.”M.S. thesis (University of Missouri-Rolla, 2006).

Fig. 15. ROC plots for five subbands concatenated versus averageand maximum.


24. J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluationfor image compression,” IEEE Trans Image Process. 4,1053–1060 (1995).

25. K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets,subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).

26. M. J. Shensa, “The discrete wavelet transform: wedding the átrous and Mallat algorithms,”IEEE Trans. Signal Process. 40,2464–2482 (1992).

27. S. G. Mallat, “A theory for multiresolution signal decomposi-tion: the wavelet representation,” IEEE Trans. Pattern Anal.Mach. Intell. 11, 674–693 (1989).


wavelet-rx anomaly detection for dual-band forward-looking infrared imagery

Documents