A Two-level Pose Estimation Framework Using Majority Voting of Gabor Wavelets and Bunch Graph Analysis

Transcription

1 Technical Repot pepaed fo the Pointing'04: Visual Obsevation of Diectic Gestues, ICPR Woshop, May, 004. A Two-level Pose Estimation Famewo Using Maoity Voting of Gabo Wavelets and Bunch Gaph Analysis Junwen Wu, Jens M. Pedesen, Duangmanee (Pew) Putthividhya, Daniel ogaad and Mohan M. Tivedi Compute Vision and Robotics Reseach Lab Univesity of Califonia, San Diego La Jolla, CA 9037, USA {uwu, medahl, putthi, nogaad, mtivedi}@ucsd.edu Abstact In this pape a two-level appoach fo estimating face pose fom a single static image is pesented. Gabo wavelets ae used as the basic featues. The obective of the fist level is to deive a good estimate of the pose within some uncetainty. The obective of the second level pocessing is to minimize this uncetainty by analyzing fine stuctual details captued by the bunch gaphs. The fist level analysis enables the use of igid bunch gaph. The famewo is evaluated with extensive seies of expeiments. Using only a single level, 90% accuacy (within ±5 degee) and ove 98% (within ±30 degee) was achieved on the complete dataset of,395 images. Second level classification was evaluated fo thee sets of poses with accuacies anging between 67-73%, without any uncetainty. Intoduction In this pape, we pesent a two-level classification famewo fo the accuate pose detemination, so as to detemine the face pointing diection. The two-level appoach is based upon the ationale that visual cues chaacteizing facial pose has unique multi-esolution spatial fequency and stuctual signatues. The fist level of the appoach has the obective of deiving pose estimates with some uncetainty. Fist level output confines the poses in a small ange so that igid bunch gaph can be used theeafte. The obective of the second level pocessing is to minimize this uncetainty by systematically analyzing the fine stuctual details captued by the bunch gaphs. Gabo wavelets ae used as the featues. In the coase level, evey Gabo wavelet esponse is classified using the subspace poection. Two diffeent subspaces ae used to get the best desciptos, which ae PCA and Kenel Disciminant Analysis (KDA) []. The classification esults fom diffeent Gabo wavelet ae combined by maoity voting. The fist level localizes the poses up to an x (=3) sub-window aound the tue poses. In the fine level, the pose estimation efined by using igid bunch gaph matching [][3], which utilizes the geometical details of the salient facial component. Related eseach Human-compute inteaction is an active eseach topic in compute vision and intelligent systems. The essential aim is to detemine human s identity and activity in diffeent envionment settings [4-6]. Development of pactical systems fo intelligent envionments can utilize gestues; pointes o the diection in which a peson's face is pointed Figue. Illustation of face pointing poblem and possible applications. Top left image shows the application of face pointing in intelligent oom, whee the face diection shows the use s focus of attention. The bottom two images ae fom out system of intelligent vehicles: dive's vigilance based on head pose analysis. to identify an aea of inteest [7]. The top ight image in Fig. illustates the face-pointing poblem. Face pose is detemined uniquely by both the pan angel β and the tilt angle α. The top left and bottom two images give some typical application scenaios fo face pointing. Existing pose estimation algoithms can be categoized into one of the following two classes: 3D pose estimation and D pose estimation. Fo 3D pose estimation, the poblem setup is based on multiple inputs. The input could be

2 Registeed Face Region Gabo Wavelet Tansfomation Level Classifie Classifie Classifie K Classifie PCA/KDA in the tansfomed domain eaest Pototype featue space Maoity Voting using K classifies Pose Estimation localized within a 3x3 sub-window aound tue position Level Elastic Bunch Gaph and Template Matching Elastic Bunch Gaph and Template Matching Elastic Bunch Gaph and Template Matching Estimated pose at the fine esolution Estimated pose at the fine esolution Estimated pose at the fine esolution Figue. The Two-level Pose Estimation Famewo. Estimates povided by Level- pocessing ae efined by consideing fine stuctual details at Level-. subsequent fames fom a time sequence [8-0], fom which the motion of the face, including scaling, tanslation and otation, can be obtained by head tacing. This can be used fo a vaiety of compute vision systems. In ou own

3 eseach we have consideed this in the context of an intelligent meeting oom [4][6], intelligent vehicles [], and wide aea suveillance []. The input could be steeo pai of the face images [3]. Coespondences between the steeo pai ae established fom salient facial featues, using which the depth map can be econstucted. The 3-D coodinates of the salient facial featues ae estimated hence afte to detemine the face pose. The D pose estimation poblem poses a diffeent challenge. In geneal, the input is limited to single images. Many appoaches have been poposed to investigate the poblem [4-6]. Howeve, most effots ae not sufficient fo face pointing due to insufficient esolution of the estimation. Also, many eseaches estict themselves to the case that poses ae diffeent only in the pan angle (angle β as shown in Fig. ). Howeve, fo face pointing applications, both the pan angle and the tilt angle need to be estimated accuately. 3. Face pose estimation appoach Aligned faces ae tansfomed into the multi-scale spatial fequency domain by Gabo wavelets [7]. In ou implementation, face egion is egisteed manually to avoid eo fom alignment. Automatic face copping can be ealized by face detection algoithms [8][9] followed by alignment, o image egistation. In Fig. some examples of the copped face images at diffeent poses ae given. PCA and KDA [] ae used to find the most disciminant subspace in the tansfom domain. A multi-level tee stuctue is pesented to classify the face egions into diffeent poses in a coase-to-fine fashion. Consideing the limited numbe of samples available, in the fist level we use the neaest pototype as the basic classifie. The basic classifie output fom wavelets in diffeent scales and oientations is combined by maoity voting. It gives estimation with some uncetainty, in the sense that it is accuate up to ±5 degee in both pan and tilt. In the second level, the output is efined by igid bunch gaph [][3] to give the accuate position. The flowchat of the whole coase-to-fine scheme is shown as follows in Fig.. In section 3., the featue extaction algoithm is shown. In section 3., the details of the classification stategy ae descibed. 3. Multi-esolution featue extaction Gabo wavelets ae oint spatial fequency domain epesentation. Fequency domain analysis techniques have a nice popety in extacting the stuctual featues as well as suppessing the undesied vaiants, such as changes of illumination, changes with peson identity, etc. Due to its multi-esolution analysis methodology, wavelet is one of the most poweful fequency domain analysis techniques. Howeve, fequency domain epesentation alone has its essential disadvantage: the localization infomation is lost. atually, people will see a oint spatial fequency epesentation. Gabo wavelet is one solution. Gabo wavelets ae ecognized to be good featue detectos since the optimal wavelets can ideally extact the position and oientation of a local featue. Thee is consideable evidence [7] that images in pimay visual cotex ae epesented in tems of Gabo wavelet, that is, hieachically aanged, Gaussian-modulated sinusoids. 3.. Gabo wavelets tansfomation A Gabo wavelets tansfom is defined as a convolution of the image with a family of Gabo enels. All Gabo enels ae geneated by a mothe wavelet by dilation and otation. Fo Gabo Wavelets, the mothe wavelet is a plane wave geneated fom complex exponential and esticted by a Gaussian envelop. In equation () - (3), a DCfee mothe wavelet is given [][3]: σ ψ () ( x) : = B(, x) ( ) exp i x exp B ( ) =, x exp x σ σ ( x ) ~ () ψ (3) The set of Gabo enel can be given as: ψ x = ψ R ϕ x, (4) whee = (,ϕ ) is the spatial fequency in pola coodinates and ( ) ( ( ) ) 0 R cosϕ sinϕ sinϕ ( ϕ ) = cosϕ DC-fee vesions of Gabo enels ae of geat inteests to the eseaches in compute vision aea due to its invaiance popety to the unifom bacgound illumination change [][3]. To eliminate the divesity fom vaying contast, all filte esponses ae nomalized. An example of the Gabo enel is shown in Fig. 3 (eal pat as well as imaginay pat). In ou implementation, a family of Gabo enels with 48 spatial fequencies is used, 6 scales and 8 in oientations. Only the magnitude of the wavelet tansfomation is used in the featue epesentation because the phase esponse is highly sensitive to the non-pefect alignment of the data. Example of the tansfomed data is shown in Fig Featue selection in the tansfomed domain The wavelets tansfom epesentation suffes fom high dimensionality. Subspace poection is used to educe the dimension. Two diffeent subspaces ae used individually, and thei pefomance is compaed. One is the PCA subspace poection, and anothe one is the KDA. PCA is a widely used method in subspace featue extaction. It selects the most epesentative subspace by finding the othogonal poection diections that have lage vaiances. Howeve, PCA is calculated based on the second-ode statistics of examples fom all the classes, it is not clea if (5)

4 the subspace fom PCA contains most disciminant infomation fo classification. KDA is a nonlinea vaiant of Linea Disciminant Analysis (LDA). Fo LDA, it finds the poection that maximizes the between-class vaiance as well as minimizing the within-class vaiance. Howeve, it is still a linea poection, which will be poblematic fo sevee nonlinea poblem. By intoducing the enel tic, KDA is able to get good pefomance fo the nonlinea poblem as well. In the fist level, both the PCA and the KDA with Gaussian enel ae implemented and the pefomance is compaed. It is not supising that KDA gets a C C T A = KcKc c= c c= c ( K ) ( x, x ) c i i K c c K T c (9) :=, (0) x i x ( x, x ) e σ i =, () whee K c is an c matix and c is the size of class c. Fo nomalized filte esponses, we let σ =. The subspace can be found by eigen-decomposition: AV = Λ, () A V A whee = ( λ λ L ) Λ A diag A, A λad is a diagonal matix with elements λa λa L λad, which ae A s ei- V = v, v,, v is the matix whose genvalues. [ ] A A A L columns ae the coesponding eigenvectos. The KDA subspace is: AD [ v, v,, v ]; M D U A = A A L AM A < (3) The KDA poection is obtained by: A whee ( ( x, x ), L( x, )) =. x x y = U A x, (4) The poected vectos y in the subspace ae the featues we use. T Figue. 3 Example of the Gabo enel. Top one is the eal pat and the bottom one is the imaginay pat. bette pefomance than PCA. The following equations (6)-(8) give the PCA tansfomation: Φ = ( ( x i )( x i µ ) ) µ, (6) T i= µ =, (7) i= x i whee = ( λ λ L ) ΦV = VΛ, (8) Λ diag, λ D is a diagonal matix whose elements λ λ L λd ae Φ s eigenvalues. V = [ v, v, L, v D ] is the matix whose columns ae the coesponding eigenvectos. The PCA subspace is fomed by the fist M < D eigenvectos. The KDA tansfomation we use in the implementation is given as follows []: Figue.4 Example of the wavelet tansfoms. The leftmost column shows the oiginal face egions. The middle column shows the 7 th Gabo enel esponses, fo which =(.5,0). The ightmost column shows the 33 d Gabo enel esponses, fo which =( -.5,0).

5 3. Classification Two-level classification scheme is poposed. In the fist level, the pose is estimated with localization ability up to ± 5 degee in both pan and tilt. It coesponds to the 3 3 neighbohood aound the tue pose position. Then the poblem tuns to a 9-class classification poblem instead of a 93-class one. This maes it possible to use igid bunch gaphs in the second level to efine the estimation. 3.. Level- classification by maoity voting We use the neaest pototype as the basic classifie fo the fist level classification. Fo evey Gabo wavelet esponse, class mean in the tansfomed featue subspace is calculated and used as the pototype. Fo evey Gabo enel, we can get a basic classifie. Theefoe, thee ae 48 basic classifies altogethe. Assuming that the 48 Gabo wavelets ae equally impotant fo the pose estimation, we use the maoity voting to detemine the pose. The pototype of each class is given by the mean of taining samples in the tansfom domain subspace poection: whee f =, L,48 and c =, L, 93. c µ y, c, f = yi, f, (5) c i= ( y, c, f ) y f µ y, c f d, =, (6) ( y, f ) = ag mind( y, c, f ) The classification esult is given by: l. (7) ( y) = ag max{ # ( l( y, f ) = c) } c c C (8) Both the featue set fom PCA and KDA ae used fo the fist level classification. 3.. Level- classification by bunch gaph template matching The coase pose estimation is efined in the second level. The use of filte esponses computed fom the entie face image poses cetain dawbacs to the poblem of accuate pose estimation. Due to a small diffeence between neighboing poses, PCA and KDA might not be able to select the featues that best disciminate poses that ae stiingly simila. In this section, we pesent a landma based appoach which attempt to exploit accuate localization of salient featues on a human face, e.g. pupils, nose tip, cones of mouth, and etc. togethe with thei geometic configuation to aid in pose classification. The motivation behind the use of geometic elationships between salient points on a face lies in a simple obsevation that with diffeent degees of otation in depth (both in the pan and tilt diections), the distances between salient points coespondingly change. In this step, we poposed the use of face bunch gaph algoithm [][3] to fist accuately locate a pedefined set of salient featues on a face. Template matching is used in the second level efinement Face epesentation & Model Gaph Geneation The basic obect epesentation that we use is labeled gaph. In ou implementation, we adopt the same epesentation of face bunch gaph as used in [][3] fo the tas of face ecognition. A face is epesented as a gaph with nodes coesponding to the wavelet esponses of Gabo enels in diffeent scales and oientations. The nodes ae connected and labeled with distance infomation. Ou implementation uses the esponses fom 5 scales and 8 oientations of Gabo enels. Fo each pose, a model gaph fo is geneated. Fist, the issue of which salient points on a face to be used as nodes is addessed. In the fontal paallel view case as shown in the leftmost image of Fig. 5, 9 nodes ae selected. In a moe oblique view in the middle and ight of Fig. 5, only nodes ae used. To geneate a model gaph fo each pose, all the 5 taining images ae used. A face bunch gaph is constucted by bundling the model gaph fom each taining image togethe as shown in Fig. 5 [][3] Similaity Measuement The cascade of the wavelets esponses fo each node is called ets. Matching between diffeent gaphs is ealized by evaluating the similaity between the odeed Gabo ets [][3]. The similaity function is used as poposed in, whee x ( f ) coesponds to the th sample s magnitude esponse of the f th filte. x i f xi ( f ) x ( f ) ( f ) x ( f ) Figue 5. Examples of the elastic bunch gaph f x i S ( J, J ) = (9) A gaph similaity between an image gaph, G I, and the m- th face bunch gaph, B m, is computed by seaching though the staced model gaph fo each node to find the best fitting et in the bundle that maximizes the et similaity function. The level- classification enables us to confine the gaph to be igid. Only the magnitude similaity is exploited. The aveage esponse ove all the nodes is used as the oveall gaph similaity. I I Bm S B ( G, B) = max( S x ( J n, J n )) (0) m Template Matching n In second-level pose classification, we attempt to classify 9 neighboing poses that ae stiingly simila. The idea behind this step is simple. Fo each of the 9 poses, a model bunch gaph is constucted fom the 5 taining images of f

6 the same pose. The similaity between a test image and all the 9 model templates ae computed and the model that gives the highest similaity esponse is declaed a match. 4 Expeimental valuations and analysis Expeimental esults fom both levels ae discussed individually. if the pose estimation falls out of the sub-window aound its tue value, it is detemined as falsely classified. In ou implement =3 is used. Bigge gives bette accuacy, howeve, the localization ability is weae, which will cause moe difficulty fo the second level efinement. In Fig. 6, the eos fom PCA and KDA ae shown espectively. In these plots, each bloc epesents the subwindow aound the tue pose. The colo shows the numbe 85.6% 97.7% (a) 90.3% 98.7% (b) Figue 6. Results evaluated fo the fist level classification in PCA and KDA subspaces. The top column image gives the legend. The middle coumn (a) gives the eos in the PCA subspaces of 48 wavelets. The left figue evaluates the localization ability up to the 3x3 sub-window aound the tue pose, which coesponds to ±5 degee; the ight figue evaluates eo on the localization ability up to 5x5 sub-window aound the tue pose, which coesponds to ±30 degee. The bottom column (b) gives the simila eo evaluation fo KDA subspace (Gaussian enel). 4. Level- classification The pupose of the fist level is to localize the poses at the accuacy up to the sub-window aound the tue pose. The accuacy is evaluated accoding to this pupose: of the false classified samples. The left diagams show the eo ate evaluated on the 3x3 sub-windows, which means ±5 degee uncetainty. PCA subspace poection can give us a total accuacy of 85.6%. As expected, KDA can impove the accuacy to 90.6%.

7 To get a bette undestanding of how these eos distibuted, we also evaluated the eo on the 5x5 sub-windows, coesponding to ±30 degee uncetainty. The esults ae shown as the ight diagams in Fig. 6. The PCA gives a total accuacy of 97.7%, while KDA gives 98.7%. It shows that only few samples has lage estimation deviation fom its tue value. 4. Level- efinement Due to the labo-intensive step in geneating templates fo each pose, the landma based pose efinement has been evaluated in the neighbohood of only a few epesentative poses, which ae shown in Fig. 5. The efinement step wos on the 3x3 sub-window located in the fist level. Fig. 7 gives some example fo the bunch gaphs in a 3x3 sub-window. Using the templates consisting of 9 nodes as shown in the leftmost image of Fig. 5, we ae able to obtain 0 coect classifications fo 5 testing images. Fo the pose shown in the middle image, we use templates consisting of nodes as shown in the middle image of Fig. 5, we obtained coect classifications fo 5 testing images. The thid set of poses we analyzed is shown in the ightmost image of Fig. 5. Eleven nodes ae used in the template. In this case, we obtained 0 coect classifications fo 5 test images. The final classification esults ae summaized in Table. The esults show that face bunch gaph template matching is a pomising candidate fo the level- Table. Second-level efinement on some epesentative poses umbe of odes in % Accuacy Template Pose 46 (Pan 0 degee; tilt 0 degee) Pose 6 (Pan 60 degee; 73.3 tilt 30 degee) Pose 68 (Pan 60 degee; tilt +30 degee) 66.7 efinement. In analyzing the eos made by the template matching classifie, we encounte a few misclassification eos that aise fom the use of templates with inadequate stuctual details to distinguish between simila poses. In an example shown below in Fig. 8, the geen nodes coesponds to the coect template being matched to the coect pose, while the ed nodes coesponds to the wong template being matched. Howeve, the indicated by the ed maes yielded a highe similaity esponse and thus is declaed a coect match. The inadequacy of disciminant stuctual details could be fixed by adding moe nodes and edges to constain the templates. In the cuent pose shown below, a few exta nodes aound the ight eye and eyebow of the subect will help constain the stuctue of the template and allow fo matching to be moe accuate. Howeve, futhe investigation of this idea must be caied out. Seveal misclassification eos esult fom the inheent ambiguity pevalent in both the taining and the testing Figue 7. Examples of face bunch gaphs fo the 3x3 sub-windows to be examined in the second level. Top 3 ows: sub-window aound pose 68; middle 3 ows: sub-window aound pose 46; bottom 3 ows: sub-window aound pose 6. images. As seen in the Fig. 9 below, in the leftmost image pai, pose 6 (uppe image) is misclassified as pose 8 shown in the lowe image. Howeve, these poses ae supposed to be diffeent by 5 degees in the pan and tilt diection, which obviously is not the case. In the ight im-

8 age pai, pose 46 (uppe image) is misclassified as pose 45 as shown in the lowe image. Again, the 5-degee angle diffeence is not appaent. Figue.8 Example of eo fom inadequate nodes Figue. 9 Example of the ambiguity in data. Also the copping pocedue is impotant. In the expeiment, we noticed that the images with lage estimation deviation fom the fist level classification ae mostly fom subect th with high tilt angles (looing up). Afte caefully compaison of the image set, we found that the th subect seems to be copped too closely. It is suspected that missed chin is the eason of the high eo ate fo this subect. Figue 0 gives the example of the th subect compaed with othe subects. Figue 0. Subect th with high tilt angle compaed with some othe subects 5 Conclusion and discussions In this pape we discussed a two-level appoach fo estimating face pose fom a single static image. The ationale fo this appoach is the obsevation that visual cues chaacteizing facial pose has unique multi-esolution spatial fequency and stuctual signatues. Fo effective extaction of such signatues, we use Gabo wavelets as basic featues. Fo systematic analysis of the fine stuctual details associated with facial featues, we employ igid bunch gaphs. The fist level of the appoach has the obective of confining the estimation into a smalle ange; theefoe igid bunch gaph is sufficient in the second level efinement. Bunch gaph exploits the stuctual details in the facial featues, which maes it capable fo pose location efinement Extensive seies of expeiments wee conducted to evaluate the pose estimation appoach. Using only a single level, 90% accuacy (within ±5 degee) was achieved on the complete dataset of,395 images. Second level classification was evaluated fo thee sets of poses with accuacies anging between 67-73%, without any uncetainty. Having veified the basic efficacy of the poposed appoach, futhe eseach fo impoving the computational pefomance and fo evaluation using data sets with moe pecise gound tuth infomation is desied. Acnowledgements Ou eseach was suppoted in pat by gants fom the UC Discovey Pogam and the Technical Suppot Woing Goup of the US Depatment of Defense. We ae thanful fo the guidance of and inteactions with ou colleagues D. Doug Fidaleo, Joel McCall and Kohsia Huang and, Shino Cheng fom the CVRR Laboatoy. We also than Pofesso Thomas Moselund of the Aalbog Univesity fo his encouagement and suppot. Finally, we than the oganizes of the Pointing'04 Woshop and the PRIMA goup of IRIA fo poviding the dataset used in ou evaluation. Refeences []. Y Li, S Gong and H Liddell. Recognising Taectoies of Facial Identities Using Kenel Disciminant Analysis, In Poceedings of The Bitish Machine Vision Confeence, 00 []. M. Potzsch,. Kuge and C. von de Malsbug. Detemination of face position and pose with a leaned epesentation based on labeled gaphs. Institut fo euoinfomati. Intenal Repot, RuhUnivesitat, Bochum, 996. [3]. L. Wisott, J. Fellous,. Küge and C von de Malsbug. Face Recognition by Elastic Bunch Gaph Matching. In Poceedings of the 7th Intenational Confeence on Compute Analysis of Images and Pattens, CAIP'97, Kie [4]. K. Huang and M. Tivedi, Video aays fo eal-time tacing of peson, head, and face in an intelligent oom. Machine Vision and Applications, vol. 4, no., pp. 03-, June 003. [5]. K. Huang and M. Tivedi, Robust Real-Time Detection, Tacing, and Pose Estimation of Faces in Video Steams, In Poceedings of Intenational Confeence on Patten Recognition 004, (to appea). [6]. M. Tivedi, K. Huang, and I. Miic, Dynamic Context Captue and Distibuted Video Aays fo Intelligent Spaces, IEEE Tansactions on Systems, Man, and Cybenetics, special issue on Ambient Intelligence. (To appea in July 004) [7]. Cowley, J., Coutaz, J., Bead, F., Things That See. Communications of the ACM, Mach 000, p

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