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arget detection with a liquid-crystal-basedassive Stokes polarimeter

rancois Goudail, Patrick Terrier, Yoshitate Takakura, Laurent Bigue, Frederic Galland,nd Vincent DeVlaminck

We present an imaging system that measures the polarimetric state of the light coming from each pointof a scene. This system, which determines the four components of the Stokes vector at each spatiallocation, is based on a liquid-crystal polarization modulator, which makes it possible to acquire four-dimensional Stokes parameter images at a standard video rate. We show that using such polarimetricimages instead of simple intensity images can improve target detection and segmentation performance.© 2004 Optical Society of America

OCIS codes: 120.5410, 260.5430, 100.0100, 100.5010, 230.3720.

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. Introduction

he polarization state of light contains important in-ormation about a scene that is complementary tonformation provided by the light’s intensity andolor. Forming an image of the polarization proper-ies of the light reflected or emitted by a scene is thusseful in such applications as scene analysis, robot-

cs, and automatic target recognition.1–3 Such anmage can reveal contrasts between two zones of thecene that have the same intensity reflectivity �sohat no contrast appears in the intensity image� butifferent polarimetric properties, which can improvehe detectability of small, low-contrast objects inmages.4–6

Polarimetric imaging systems can be classified intowo categories: passive and active. An active sys-em uses an artificial light source to illuminate thecene. In a passive system the image is formed fromreflection of the ambient light7,8 or from the radia-

F. Goudail �[email protected]� and F. Galland are withhe Fresnel Institute, Unite Mixte de Recherche au Centre Na-ional de la Recherche Scientifique �UMR CNRS 6133�, Marseille,rance; P. Terrier and V. DeVlaminck are with the Laboratoirenteraction, Image et Ingenierie de la Decision �FRE CNRS 2497�,ille, France; Y. Takakura is with the Laboratoire des Sciences de

’Image, de l’Information et de la Teledetection �UMR CNRS 7005�,trasbourg, France; L. Bigue is with the Laboratoire de modelisa-ion, Intelligence, Processus, et Systems �MIPS 2332�, Mulhouse,rance.Received 14 April 2003; revised manuscript received 11 Septem-

er 2003; accepted 8 October 2003.0003-6935�04�020274-09$15.00�0© 2004 Optical Society of America

74 APPLIED OPTICS � Vol. 43, No. 2 � 10 January 2004

ion emitted in an IR system.6,9,10 A polarimetricamera measures the polarization state of the lightncident upon the camera, and its usual output is aet of Stokes parameter images. By analyzing theirection of polarization and the degree of partialolarization of the reflected light, one can obtain im-ortant information about the presence and the ori-ntation of occluding edges3,7 or about the surfacerientation of the observed objects.3,11–13 Anothermportant application of polarimetric imagery is inhe determination from their polarimetric propertiesf the nature of the materials that are present in acene.14 Polarimetric imagery has been found use-ul in detecting rust during inspection of ships’ hulls13

nd in discriminating between dielectric and metallicreas on circuit boards,3,12 which can be difficult withntensity or even color images.

We describe in this paper a passive imaging systemhat measures the Stokes vector at each spatial loca-ion in a scene. It uses a variable retardancecheme,15 and the polarimetric modulation is per-ormed by two liquid-crystal variable retardersLCVRs�. Because of the rapid action of these de-ices, Stokes parameter images can be acquired andormed at a standard video rate. The LCVRs areey components of the system, and we characterizeheir performance in terms of precision of modulationnd image quality with a high-precision Mueller im-ger. Finally, we address the important problem offficiently extracting information from these vecto-ial images. For that purpose we consider statistics-ased detectors and a state-of-the-art segmentationlgorithm based on statistically active contours andhe principle of minimum description length

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MDL�.16 We demonstrate the efficiency of these al-orithms for the detection of small objects in Stokesmages and for the characterization of their polari-

etric properties.In Section 2 we describe the Stokes imaging system

nd characterize the polarimetric response of theCVRs used in the system to assess the precision of

heir measurements. In Section 3 we address thessue of designing efficient processing techniques forectorial polarimetric images. After characterizinghe statistical properties of the noise that affects themages and describing the operation of the image-rocessing algorithms that we shall consider, we il-ustrate the performance of the algorithms witheveral images acquired by the Stokes imaging sys-em.

. Stokes Imaging System

he measurement device is based on the use of twoeadowlark Optics LRC-300 LCVRs. Each one of

hese optical components makes it possible to modifyhe polarization state of the incident light wave with-ut requiring mechanical actions on the device �rota-ions�. The Stokes parameters of the incident light,

� �S0, S1, S2, S3�T �T denotes transposition�, canhus be estimated precisely and rapidly. In theresent case the variable parameter of the device isot an angular position but a pair of retardances ��1,2�. These retardances are adjusted by the ampli-ude of a rectangular alternative voltage that is ap-lied to the LCVR through an intermediately locatedommand interface board. First we describe the op-ration of the proposed Stokes polarimeter, and thene characterize the polarimetric response of theCVR.

. Operation of the Stokes Imaging Polarimeter

schematic of the device is illustrated in Fig. 1. Aight wave passes successively through a monochro-

atic filter centered on wavelength �0 � 520 nmmiddle of the visible spectrum�, two variable retard-rs, and a linear polarizer. The resultant light in-ensity is then measured by a CCD camera. Thenfluence of each of these optical components on the

Fig. 1. Schematic of the prop

tate of polarization of the light wave is modeled by atokes–Mueller formalism. Stokes vector Sout of the

ight wave at the polarizer output �denoted S� in Fig.� is thus related to input Stokes vector Sin �denotedin Fig. 1� by the following matrix multiplication:

Sout � MPOLMR��1� MR��2�Sin � MglobalSin, (1)

here MR�� is the Mueller matrix of a pure retarderith retardance � and MPOL is the Mueller matrix oflinear polarizer.15 For a given pair of retardances

�1, �2�, light intensity Ii measured by the CCD cam-ra corresponds to Stokes parameter S0

out. It is thuslinear function of the input Stokes parameters Sin of

he observed light:

I � S0out

� A��1, �2�S0in � B��1, �2�S1

in � C��1, �2�S2in

� D��1, �2�S3in, (2)

here the parameters �A, B, C, D� correspond to therst line of Mglobal. As a consequence, for each pixelf the image of the observed scene, one can estimatehe four parameters of Stokes vector S by carryingut N acquisitions I � Ii, i � �1, N� for N combina-ions of delays ��1, �2�:

I � MLIGHTS 7 �I1

I2···IN

� � �A1 B1 C1 D1

A2 B2 C2 D2······

······

AN BN CN DN

��S1

S2

S3

S4

� ,

(3)

here matrix MLIGHT is a function of the N couples ofelays �one couple per line� and of the positioning ofhe optical components. For expression �3� to be in-ertible, N must be equal at least to 4. However, inractice, better results are obtained with larger num-ers of measurements. When N � 4, one can obtain

Stokes imaging polarimeter.
osed
10 January 2004 � Vol. 43, No. 2 � APPLIED OPTICS 275

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he Stokes parameters by minimizing function F,iven by

F � �i�1

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he positioning of each optical component � 1, 2, andin Fig. 1� is chosen to produce parameters Ai, Bi, Ci,nd Di that correspond to sufficient conditioning ofatrix MLIGHT that expression �3� can be safely in-

erted.17

The maximum acquisition speed of 25 images�sstandard video rate� implies that Stokes vector S, forll the pixels of the imaged scene, is obtained in ainimum time of 160 ms. However, in practice, ob-

aining a more robust estimate of the Stokes param-ters often requires a sequence of at least N � 8cquisitions. A 320-ms period is thus necessary toroduce an overdetermination of the system of equa-ions.

It is important to note that, in the experimentaletup considered here, the light illuminating thecene may be supposed to be diffuse or nonpolarized.he observed polarimetric effect comes from the ca-acity of the various materials in the scene to polarizeight. One of the physical phenomena that can leado this effect is Fresnel reflection at a dielectric inter-ace. Indeed, during this process the componentsarallel and orthogonal to the plane of incidence un-ergo different coefficients of reflection, which canreate a partial polarization of the light.18

. Characterization of the Polarimetric Response of theCVRs

he LCVRs are key components of the proposedtokes imaging system, and they determine the ac-uracy of its measurements. It is thus important toharacterize their properties. The LRC-300 LCVRssed in the measurement system are constructed byse of optically flat fused-silica windows and nematic

iquid-crystal materials. These true zero-order re-arders are designed for maximum transmission from00 to 700 nm. With no voltage applied, the liquid-rystal molecules lie parallel to the glass substrates,nd maximum retardation is achieved. When volt-ge is applied, liquid-crystal molecules begin to tip indirection perpendicular to the fused-silica windows.s voltage increases, the molecules tip further, caus-

ng a reduction in the effective birefringence and,ence, retardance. The response time for the LCVRo switch from one-half to zero wave �low to higholtage� is �5 ms; it is 20 ms for switching from zeroo one-half wave �high to low voltage�.

We are interested in a full characterization of po-arization controllers, as suggested by Drewes andhipman,19 and in studying the spatial response of

he LCVR by taking an imaging approach. For thisurpose we used the imaging Mueller polarimeterituated at the Laboratoire des Sciences de l’Image,e l’Information et de la Teledetection, Strasbourg.20


his system can accurately measure the Mueller ma-rix at each point of a scene. The advantage of suchevice compared with a standard nonimaging polar-meter is that it makes possible the estimation of thepatial homogeneity of the polarimetric response.n fact, for liquid-crystal modulators the lack of spa-ial homogeneity is often the main problem. How-ver, we tested regions at the center and on the edgesf the device, and the device’s response proved quiteomogeneous. Figure 2 gives examples of Mueller

mages obtained for a 2-V input voltage, correspond-ng to an approximate half-wave operation, when ainary pattern is placed in the input beam. It can beeen that the Mueller response corresponds to that ofpure retarder.15 Up to the accuracy of the imaging

etup, the diffusion or depolarization effects thatharacterize some liquid-crystal modulators have noteen observed. Moreover, the contrast of the binaryattern is preserved, which indicates good spatialesolution of the device.

. Target Detection and Characterization inolarimetric Images

n this section we show some examples of applica-ions in which the Stokes parameter image, com-ared to simple intensity imaging, can improvenformation extraction from a scene. One of the ad-antages of precise Stokes imaging is that it revealslight variations in the polarimetric properties of thebjects that are present in a scene. Because the con-rasts are weak, it is necessary to take into accounthe nature of the noise that is present in the image toe able to perform efficient information extraction.lgorithms based on statistical decision and estima-

ion theory are good candidates for addressing thisroblem.

ig. 2. Mueller image of the LCVR. Each subimage representshe image of a coefficient of the Mueller matrix. The gray scale isuch that negative values appear in dark colors, zero in mediumray, and positive in lighter gray. All images are normalized withespect to the positive part of image M00, which thus appearsompletely white here.

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In Subsection 3.A we determine the nature of theoise that is present in the images of interest to beble to design detection and segmentation algo-ithms. The characteristics of such algorithms areescribed in Subsection 3.B, and they are applied inubsections 3.C and 3.D to images acquired with theroposed Stokes imager.

. Characterization of Noise

tatistics-based detection and segmentation algo-ithms rely on a probabilistic model of the images.et us characterize the noise that affects the imageso we can determine an adequate image model fromhich processing algorithms will be derived. Figurepresents the four components of the Stokes param-

ter image acquired with the system described inection 2. Ten different pairs of retardances ��1, �2�ave been used, corresponding to every combinationf �1 � 80°, 240° and �2 � 0°, 80°, 160°, 240°, 320°.or each of these ten pairs of retardances the CCDamera measures, for each pixel of the observedcene, light intensity Ii used for minimization of func-ion F �Eq. �4��. The positioning of the optical com-onents is 1 � 20°, 2 � 45°, and � � 90° �Fig. 1�.hese values lead to parameters Ai, Bi, Ci, and Di,hich allow for sufficient conditioning of matrixLIGHT �expression �3��.The scene represents three small objects on a uni-

orm background. The background is made of card-oard, and the objects are small pieces of transparentellophane tape. It is interesting to note that com-onent S0, which represents the intensity image,ooks quite different from the three other channels.

2 3 3 3

he objects, which are transparent, do not appearlearly in this image, whereas some spots that areue to dust are quite apparent. In the three otherhannels, however, the objects of interest appear inlear contrast �positive or negative� to a rather uni-orm background. Indeed, these last three channelsf the Stokes vector represent the polarimetric prop-rties of the light. It can be seen that the light re-ected from the cardboard background hasomogeneous polarimetric properties, which are dif-erent from those of the light reflected from the ob-ects of interest.

It can also be noted that the noise in channels S1,2, and S3 is quite important. This is so because theolarimetric contrast is weak and thus the dynamicange of the image is low. Let us now determine thetatistical properties of this noise so we can designhe processing algorithms. We consider the regionutlined by a white rectangle in Fig. 3, channel S1.e have represented in Fig. 4 histograms of this

egion for the three polarimetric channels S1, S2, and3. We have superimposed upon the histogramsaussian curves with the same means and variancess the samples.It can be seen that the noise is close to Gaussian.e thus consider an image model in which the noise

s Gaussian. More precisely, to process the polari-etric data we consider a vectorial, three-channel

mage S� � �S1, S2, S3� composed of the last threetokes parameters. This vector will be the input tohe detection and segmentation algorithms. Each ofts channels will be assumed to be statistically inde-endent and distributed with a Gaussian probability-ensity function.

Fig. 3. Stokes parameter image of three small pieces of transparent cellophane tape on a cardboard background.

ig. 4. Histograms of a homogeneous region in the three channels, S1, S2, and S3. The region considered here is the area outlined inhite in Fig. 3, channel S1. A Gaussian with same mean and variance as the corresponding histogram is drawn �dotted curve� over eachistogram. Mean m and standard deviation � in the three channels are m1 � �2.24 and �1 � 1.12 in S1; m2 � �0.20 and �2 � 1.46 in; m � �0.40 and � � 1.28 in S .


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. Statistical Image Processing

e describe in this subsection algorithms based ontatistical decision and estimation theory that canolve problems of target detection and shape segmen-ation in the vectorial Stokes parameter images.

e assume that the image—or the subimage—of in-erest is composed of two regions: region a, whichorresponds to the object of interest, and region b,hich corresponds to the background. The shape of

he object, which corresponds to the borders betweenhe two regions, is defined by a set of parameters w.s explained above, the gray levels in each of theseegions are assumed to be random vectors distributedith Gaussian probability-density functions. Weescribe, in what follows, detection and segmentationlgorithms based on this image model.

. Target Detection Based on the Generalizedikelihood Ratio Testhe problem that we address is detection of a targetith shape w �which defines region a� in an image.or small targets, w can be defined as a square with

he size of the expected targets. We define anotherhape, F, which contains w, and we denote the com-lement of w in F: w� � F � w. The number ofixels in shape F �w, w� � is NF �Na, Nb�, with NF �

a � Nb.The image is scanned with mask F and, for each

osition � � �x, y� in the image, detection is made byse of a generalized likelihood ratio test �GLRT�.21

nasmuch as the Stokes channels are modeled withaussian probability-density functions with un-nown means and variances, the GLRT consists inomputing, for each position �, the following expres-ion22:

��, w� � �k�1

3

�Na log��a2�k� � Nb log��b

2�k�

� NF log��F2�k�, (5)

here ��u2�k is the variance empirically estimated in

egions a, b, and F in channel Sk. We then compare��, w� with a threshold to determine whether a

arget is present at position �.In practice, the sizes of the searched-for objectsay not be known. The size can then be considered

s a nuisance parameter that can be estimated in theaximum-likelihood sense. More precisely, let us

enote by wk, k � �1, K� the K possible shapes. Theetection criterion that will be used has the followingxpression23:

�� maxk

�R��, wk��. (6)

t consists of choosing the mask wk that leads to theighest value of the GLRT.

. Target Segmentationet us now consider segmentation of a single object inn image. To solve this problem, we use a methodased on polygonal active contours and on the MDLrinciple.16 This method consists in determining


he polygon with the minimal number of nodes thatest approximates the shape of the object, in theense of the MDL criterion.16,24,25 We deform theolygon and determine its number of nodes by opti-izing a mathematical criterion that depends on theumber and the position of the nodes of the polygon.

denotes the shape of the object, that is, the coor-inates of the nodes of polygonal shape, k is the num-er of nodes of the polygon, and N is the total numberf pixels in the image. In the case where the noise inach channel is Gaussian, the expression of the math-matical criteria is

J�w, k� � �k�1

3

(Na�w�log��a2�k�w�

� Nb�w�log��b2�k�w�) � k log N, (7)

here Na�w� and Nb�w� are the number of pixels onhe target and on the background, respectively, whichepend on the shape of the object w. This criterionorresponds to an approximation of the average codeength necessary for encoding the image data.16

In practice, this criterion is optimized in twoteps.16 In the first step we segment the object byptimizing J�w, k� with respect to w for an increasingumber of nodes k to obtain a precise estimation ofhe object’s shape. The second step consists in re-oving the less-useful nodes �i.e., decreasing k� one

y one until the criterion J�w, k� is minimized. It isorth noting that this segmentation algorithm pos-

esses no free parameter to be adjusted by the user.xamples of application of this method are shown inubsection 3.C.

. Determination of the Shapes of Large Objects

et us consider first the segmentation of complexhapes in Stokes images. Figure 5 presents imagesf two shapes made from transparent cellophane tapen a cardboard background. The physical configu-ation that we used to obtain these images is theame as that used for Fig. 3. The shapes are barelyisible on intensity images S0, which are also per-urbed by dust. In channels S1–S3, however, thehapes appear in clear contrast �positive of a nega-ive� to the background. As we said above, we thusork on the vectorial three-channel image composedf Stokes components S1–S3, to which we apply theultichannel snake defined in Eq. �7�. We present

n Fig. 6 the result of the segmentation of these ob-ects. The two leftmost figures represent the initialhape, which is a rectangle. The two central figuresepresent the polygonal contour estimated after therst step of the segmentation algorithm, which con-ists in progressively adding nodes to the contour tobtain a precise segmentation. It can be seen thathe global shapes are correctly segmented but thathere are many spurious nodes. Finally, the right-ost two figures represent the result of the second

tep, in which the less useful nodes are pruned. Onean see that the objects are accurately segmentedith a limited number of nodes. These accurate and

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arsimonious shape estimates could be used in shapeecognition systems, for example.

. Detection and Characterization of Regions of Interest

et us now consider the detection of the three smallbjects in the Stokes parameter image of Fig. 3. Ase said above, we are working on a vectorial three-

hannel image composed of the Stokes components1, S2, and S3. We apply the multiscale GLRTefined in Eq. �6�, where mask F is a rectangle of

Fig. 5. Stokes param

ig. 6. Segmentation of the two objects in Fig. 5, in the reduced S1�; center, results of the first step of the segmentation process �seegmentation process �node pruning�.

9 � 13 pixels and four masks wk, k � �1, 4� areonsidered: They are rectangles of sizes 5 � 3,1 � 5, 21 � 7, and 31 � 9. The GLRTs adapted tohese masks are applied to the image, and the re-ults are fused according to Eq. �6�. The likelihoodatio plane �� is represented in Fig. 7, togetherith vertical and horizontal cross sections. Theositions of the three objects of interest appearlearly in this image.Once the regions of interest have been detected by

images of two objects.

s parameter images S� � S1, S2, S3. Left, initial shape �channelntation with node adding�; right, results of the second step of the

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he GLRT, it can be useful to determine their shapesnd to estimate their average polarization propertieso characterize the nature of the objects. We seehat the MDL-based snake algorithm can performhis operation efficiently.

Let us consider 50 � 50 pixel subimages centeredn the detected regions of interest. The snake isnitialized as a rectangular shape on the corner of themages, as shown in Fig. 8, upper row. The contourhen evolves to segment the object, as can be seenrom the bottom row of Fig. 8.

Once the shape of the object has been determined,t can be used to estimate some parameters, such ashe average polarimetric properties. For example,e have estimated the average Stokes parametersithin each object, and we have converted them intonother representation of the polarimetric parame-

ig. 7. Plane �� obtained with the multitarget GLRT on themage of Fig. 3; maximum of each column and of each line of thislane.

ig. 8. Result of the segmentation of the three objects detecteegmentation.


ers: intensity I, degree of polarization �, and polarngles � and � of the Poincare representation of therincipal polarization state of the light. It is wellnown that the relation between this representationnd the Stokes parameter is the following26:

I � S0,

� � �S12 � S2

2 � S32�1�2�S0,

� �12 tan�1�S2�S1�,

� �12 sin�1�S3�I��. (8)

ased on the segmentation results obtained in Fig. 8,he estimated parameters of the objects and of theirurroundings are listed in Table 1. It can be seenhat the average intensities of the objects and of theurrounding backgrounds are almost identical:here is no intensity contrast between the objectsnd the background. Furthermore, the principal po-arization states in the objects and in the backgroundre similar. Indeed, the observed surfaces lie in ap-roximately the same plane, and it can be conjecturedhat the direction and ellipticity of the polarized partf the light is due to the Fresnel reflection, whoseolarimetric characteristics are linked to the angle ofncidence of the light on the surface and to the dielec-ric constant. In fact, it can be seen from Table 1hat the main contrast is due to the degree of polar-zation. The objects, which are pieces of transparentape, depolarize the light less than does the coarserardboard.

The proposed method is thus able to detect andegment objects based on their polarimetric proper-ies. By construction, it takes as an input the lasthree components of the Stokes vector and performs

the scene of Fig. 3. Top, initial snake; bottom, result of the
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etection based on this information. One does noteed to know a priori in which Stokes parameter–or

n which combination of Stokes parameters–a con-rast exists. In the example given here, it was de-uced a posteriori �that is, after segmentation� thathe relevant information was the degree of polariza-ion, but this information was not required for per-orming the segmentation: The same algorithmsre also efficient if the contrast is in terms of polar-zation direction or ellipticity.

. Conclusions

e have presented a Stokes imaging system based onvariable retardance scheme and liquid-crystal po-

arization modulators that acquires Stokes parame-er images at a standard video rate. Because of theuality of the modulators, this system can detectaint variations of the polarimetric properties of thebserved materials and thus reveal contrasts that doot appear in standard intensity images. To extract

nformation efficiently from the vectorial Stokes pa-ameter images we used statistics-based detectorsnd segmentation algorithms based on statistical ac-ive contours and the MDL principle. These algo-ithms were adapted to the processing of such noisymages, and we have shown some examples of theirerformance with real-world data.The global system composed of the Stokes imaging

ystem and of the processing algorithm can be usedor such applications as default detection in indus-rial process control. Of course, it can be improvedn many ways. In particular, calibration is a keyoint in such devices,8 and work to automate thisperation is under way.

This research was performed in the framework ofulti-Laboratory Project Team 8, “Polarization im-

gery, from the components to the processing,” of theepartment of Sciences et Technologies de’Information et la Communication of the Centre Na-ional de la Recherche Scientifique, whose support isratefully acknowledged. The authors thank Pierrembs, Julien Charreyron, Philippe Refregier, and Ji-ad Zallat for fruitful discussions.

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Table 1. Average Polarimetric Param

PolarimetricParameter

Object 1

Object Background O

I 183 181 18� 0.037 0.014� �°� 73 82 7� �°� 2.5 �2.9

aThe parameters are averaged over the regions determined by tity�, � �degree of polarization�, and � and � �polar angles� are de

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of the Objects Segmented in Fig. 8a

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