{"title": "Image Representations for Facial Expression Coding", "book": "Advances in Neural Information Processing Systems", "page_first": 886, "page_last": 892, "abstract": null, "full_text": "Image representations for  facial  expression \n\ncoding \n\nMarian Stewart Bartlett* \n\nV.C.  San Diego \nmarni<Osalk.edu \n\nGianluca Donato \n\nDi~ital Persona, Redwood  City,  CA \nglanlucad<Odigitalpersona.com \n\nJavier R.  Movellan \n\nV.C.  San Diego \n\nmovellan<ocogsci.ucsd.edu \n\nPaul Ekman \n\nV.C.  San Francisco \n\nekman<ocompuserve.com \n\nJoseph C.  Hager \n\nNetwork Information Res.,  SLC,  Utah \n\njchager<Oibm.com \n\nTerrence J. Sejnowski \n\nHoward  Hughes Medical Institute \nThe Salk Institute; V.C.  San Diego \n\nterry<osalk.edu \n\nAbstract \n\nThe  Facial  Action  Coding  System  (FACS)  (9)  is  an  objective \nmethod  for  quantifying  facial  movement  in  terms  of  component \nactions.  This  system  is  widely  used  in  behavioral  investigations \nof emotion,  cognitive  processes,  and  social  interaction.  The  cod(cid:173)\ning is  presently  performed by  highly trained human experts.  This \npaper  explores  and  compares  techniques  for  automatically  recog(cid:173)\nnizing facial actions in sequences of images.  These methods include \nunsupervised  learning techniques  for  finding  basis  images  such  as \nprincipal component analysis, independent component analysis and \nlocal  feature  analysis,  and supervised learning  techniques  such  as \nFisher's  linear  discriminants.  These  data-driven  bases  are  com(cid:173)\npared to Gabor wavelets, in which the basis images are predefined. \nBest  performances  were  obtained  using  the  Gabor  wavelet  repre(cid:173)\nsentation and the  independent  component  representation,  both of \nwhich achieved 96%  accuracy for  classifying 12 facial  actions.  The \nICA  representation employs  2 orders of magnitude fewer  basis im(cid:173)\nages than the  Gabor representation and takes 90%  less  CPU  time \nto compute for new images.  The results provide converging support \nfor using local basis images, high spatial frequencies, and statistical \nindependence for  classifying facial  actions. \n\n1 \n\nIntroduction \n\nFacial expressions provide information not only about affective state, but also about \ncognitive activity, temperament and personality, truthfulness, and psychopathology. \nThe  Facial  Action  Coding  System  (FACS)  (9)  is  the  leading  method  for  measur(cid:173)\ning facial  movement in  behavioral science.  FACS  is  performed  manually by highly \ntrained  human  experts.  A  FACS  coder  decomposes  a  facial  expression  into  com(cid:173)\nponent  muscle  movements  (Figure  1).  Ekman  and  Friesen  described  46  distinct \nfacial  movements,  and  over  7000  distinct  combinations  of  such  movements  have \n\n*  To  whom  correspondence  should be addressed.  (UCSD  0523,  La Jolla,  CA  92093.) \n\nThis research was supported by NIH  Grant No.  IF32  MH12417-01. \n\n\fImage Representations for Facial Expression Coding \n\n887 \n\nbeen  observed  in  spontaneous behavior.  An  automated system would  make facial \nexpression measurement more widely accessible as a research tool for behavioral sci(cid:173)\nence and medicine.  Such a  system would also have application in human-computer \ninteraction tools and low bandwidth facial  animation coding. \nA number of systems have appeared in the computer vision literature for  classifying \nfacial  expressions  into  a  few  basic  categories  of emotion,  such  as  happy,  sad,  or \nsurprised.  While such approaches are important, an objective and detailed measure \nof facial activity such as FACS is needed for basic research into facial behavior.  In a \nsystem being developed  concurrently for  automatic facial  action coding,  Cohn  and \ncolleagues  (7)  employ feature  point  tracking of a  select set of image points.  Tech(cid:173)\nniques  employing 2-D  image filters  have  proven  to be  more  effective  than feature(cid:173)\nbased  representations  for  face  image  analysis  [e.g.  (6)].  Here  we  examine  image \nanalysis techniques that densely analyze graylevel information in  the face  image. \nThis  work  surveys  and  compares  techniques  for  face  image  analysis  as  applied  to \nautomated FACS encoding. l  The analysis focuses on methods for face  image repre(cid:173)\nsentation in  which image graylevels are described as a  linear superposition of basis \nimages.  The techniques were compared on a common image testbed using common \nsimilarity measures and classifiers. \nWe  compared  four  representations  in  which  the  basis  images  were  learned  from \nthe  statistics  of  the  face  image  ensemble.  These  include  unsupervised  learning \ntechniques  such  as  principal  component  analysis  (PCA),  and  local  feature  analy(cid:173)\nsis  (LFA),  which are learned from  the second-order dependences among the image \npixels, and independent component analysis (ICA)  which is learned from  the high(cid:173)\norder  dependencies  as  well.  We  also  examined  a  representation  obtained  through \nsupervised  learning  on  the  second-order  image  statistics,  Fisher's  linear  discrimi(cid:173)\nnants (FLD).  Classification performances with these data-driven basis images were \ncompared to Gabor  wavelets,  in  which  the  basis  images  were  pre-defined.  We  ex(cid:173)\namined  properties  of optimal  basis images,  where  optimal was  defined  in terms of \nclassification. \nGeneralization  to  novel  faces  was  evaluated  using  leave-one-out  cross-validation. \nTwo basic classifiers were employed:  nearest neighbor and template matching, where \nthe templates were the mean feature vectors for each class.  Two similarity measures \nwere employed for each classifier:  Euclidean distance and cosine of the angle between \nfeature  vectors. \n\n2 \n\n1 \n\n4 \n4 \n\nh. \n\na. \n\nAU 1  Inner brow raiser \n\nAU 2  Outer brow raiser \n\nAU 4  Brow lowerer \n\nFigure 1:  a.  The facial  muscles underlying six  of the 46 facial  actions.  b.  Cropped \nface  images and 8-images for  three facial  actions  (AU's). \n\n1 A  detailed description of this work  appears in  (8). \n\n\f888 \n\nM  S.  Bartlett,  G.  Donato, J.  R.  Movellan, J.  C.  Hager,  P.  Ekman and T.  J.  Sejnowski \n\n2 \n\nImage Database \n\nWe  collected a  database of image sequences of subjects performing specified  facial \nactions.  The database consisted of image sequences of subjects performing specified \nfacial actions.  Each sequence began with a neutral expression and ended with a high \nmagnitude muscle contraction.  For this investigation,  we  used  111  sequences from \n20  subjects and attempted to classify  12 actions:  6 upper face  actions and 6 lower \nface  actions.  Upper  and  lower-face  actions  were  analyzed  separately  since  facial \nmotions in  the lower face  do not effect  the upper face,  and vice versa (9). \nThe  face  was  located  in  the first  frame  in  each  sequence  using  the  centers  of the \neyes and mouth.  These coordinates were obtained manually by a  mouse click.  The \ncoordinates  from  Frame  1  were  used  to  register  the  subsequent  frames  in  the  se(cid:173)\nquence.  The  aspect  ratios  of the  faces  were  warped  so  that  the  eye  and  mouth \ncenters coincided across all images.  The three coordinates were then used to rotate \nthe eyes  to horizontal, scale,  and finally  crop a  window  of 60 x 90 pixels containing \nthe  upper  or  lower  face.  To  control  for  variations  in  lighting,  logistic  threshold(cid:173)\ning  and  luminance scaling was  performed  (13).  Difference  images  (b-images)  were \nobtained by subtracting the neutral expression in  the first  image of each sequence \nfrom  the subsequent images in  the sequence. \n\n3  Unsupervised learning \n3.1  Eigenfaces  (peA) \n\nA  number  of  approaches  to  face  image  analysis  employ  data-driven  basis  vectors \nlearned from  the statistics of the face  image ensemble.  Techniques  such as  eigen(cid:173)\nfaces  (17)  employ principal component analysis,  which  is  an unsupervised learning \nmethod  based  on  the  second-order  dependencies  among  the  pixels  (the  pixelwise \ncovariances).  PCA has been applied successfully to recognizing facial identity  (17), \nand full  facial  expressions  (14). \nHere we  performed PCA on the dataset of b-images,  where each b-image comprised \na  point  in  Rn  given  by  the  brightness  of the  n  pixels.  The  PCA  basis  images \nwere  the  eigenvectors  of  the  covariance  matrix  (see  Figure  2a),  and  the  first  p \ncomponents  comprised  the  representation.  Multiple  ranges  of  components  were \ntested,  from  p  = 10  to P = 200,  and  performance  was  also  tested  excluding  the \nfirst  1-3  components.  Best  performance  of  79.3%  correct  was  obtained  with  the \nfirst  30  principal components, using the Euclidean distance similarity measure and \ntemplate matching classifier. \nPadgett  and  Cottrell  (14)  found  that  a  local  PCA  representation  outperformed \nglobal  PCA for  classifying full  facial  expressions  of emotion.  Following  the  meth(cid:173)\nods  in  (14),  a  set of local  basis images  was  derived from  the principal  components \nof  15x 15  image  patches  from  randomly  sampled  locations  in  the  b-images  (see \nFigure  2d.)  The first  p  principal  components  comprised  a  basis  set  for  all  image \nlocations,  and  the representation was  downsampled  by  a  factor  of 4.  Best  perfor(cid:173)\nmance of 73.4%  was obtained with components 2-30, using Euclidean distance and \ntemplate matching.  Unlike the findings in (14), local basis images obtained through \nPCA were  not  more  effective  than  global  PCA for  facial  action  coding.  A  second \nlocal  implementation  of PCA,  in  which  the  principal  components  were  calculated \nfor  fixed  15x 15 image patches also failed  to improve over global PCA. \n\n3.2  Local Feature Analysis  (LFA) \n\nPenev and Atick  (15)  recently developed  a  local,  topographic representation based \non second-order image statistics called local feature analysis (LF A).  The kernels are \nderived  from  the  principal  component  axes,  and  consist  of  a  \"whitening\"  step  to \nequalize the variance of the PCA coefficients, followed  by a  rotation to pixel space. \n\n\fImage Representations for Facial Expression Coding \n\n889 \n\na. \n\nh. \n\nc. \n\nd. \n\nFigure 2:  a.  First 4 PCA basis images.  b.  Four ICA basis images.  The ICA basis \nimages  are  local,  spatially  opponent,  and  adaptive.  c.  Gabor  kernels  are  local, \nspatially opponent, and predefined.  d.  First 4 local PCA basis images. \n\nWe  begin  with  the  matrix  P  containing  the  principal  component  eigenvectors  in \nits  columns,  and  Ai  are  the  corresponding eigenvalues.  Each row  of the  matrix  K \nserves as an element of the LFA  image dictionary2 \n\nK  = pVpT  where  V  = D-! = diag(  ~)  i  = 1, ... ,p \n\nV  Ai \n\n(1) \n\nwhere Ai  are the eigenvalues.  The rows of K  were found to have spatially local prop(cid:173)\nerties, and are  \"topographic\"  in the sense that they are indexed by spatial location \n(15).  The dimensionality of the LFA  representation  was  reduced by employing  an \niterative  sparsification  algorithm  based  on  multiple  linear  regression  described  in \n(15). \nThe  LFA  representation  attained  81.1 % correct  classification  performance.  Best \nperformance was obtained using the first  155 kernels, the cosine similarity measure, \nand nearest  neighbor  classifier.  Classification performance using LFA  was not sig(cid:173)\nnificantly  different  from  the  performance using  peA. Although  a  face  recognition \nalgorithm  based  on  the  principles  of LFA  outperformed  Eigenfaces  in  the  March \n1995 FERET competition, the exact algorithm has not been disclosed.  Our results \nsuggest that an aspect of the algorithm other than the LFA representation accounts \nfor  the difference in performance. \n\n3.3 \n\nIndependent  Component Analysis  (ICA) \n\nRepresentations such  as  Eigenfaces,  LFA,  and  FLD  are based on the second-order \ndependencies among the pixels,  but are insensitive to the high-order dependencies. \nHigh-order dependencies are relationships that cannot be described by a linear pre(cid:173)\ndictor.  Independent component analysis  (ICA)  learns the high-order dependencies \nin addition to the second-order dependencies among the pixels. \n\n2 An image  dictionary  is  a  set  of images  that decomposes  other images,  e.g.  through \n\ninner product.  Here it finds  the coefficients for  the basis set K- 1 \n\n\f890 \n\nM.  S.  Bartlett,  G.  Donato, J.  R.  Movellan,  J.  C.  Hager,  P.  Ekman and T.  J.  Sejnowski \n\nThe  ICA  representation  was  obtained  by  performing  Bell  &  Sejnowski's  infomax \nalgorithm  (4)  (5)  on  the  ensemble  of ~-images in  the  rows  of the  matrix  X.  The \nimages in X  were assumed to be a linear mixture of an unknown set of independent \nsource  images  which  were  recovered  through  ICA.  In  contrast  to  PCA,  the  ICA \nsource images  were  local  in  nature  (see  Figure  2b).  These source images  provided \na  basis  set  for  the expression  images.  The coefficients  of each  image  with  respect \nto  the new  basis  set  were  obtained from  the estimated  mixing  matrix  A  ~ W- 1 , \nwhere W  is  the ICA  weight matrix [see  (1),  (2)]. \nUnlike  PCA,  there  is  no  inherent  ordering to the independent  components  of the \ndataset.  We therefore selected as an ordering parameter the class discriminability of \neach component, defined as the ratio of between-class to within-class variance.  Best \nperformance of 95.5% was  obtained with the first  75  components selected  by class \ndiscriminability, using the cosine similarity measure, and nearest neighbor classifier. \nIndependent component analysis gave the best performance among all of the data(cid:173)\ndriven image  kernels.  Class discriminability  analysis of a  PCA representation was \npreviously found  to have little effect  on classification performance with PCA  (2). \n\n4  Supervised learning:  Fisher's Linear Discriminants (FLD) \n\nA  class  specific  linear  projection  of  a  PCA  representation  of  faces  was  recently \nshown  to  improve  identity  recognition  performance  (3).  The  method  employs  a \nclassic pattern recognition technique, Fisher's linear discriminant  (FLD), to project \nthe images into a  c - 1 dimensional subspace in  which  the c classes  are maximally \nseparated.  Best performance was obtained by choosingp =  30 principal components \nto first  reduce  the dimensionality  of the data.  The data was  then projected down \nto 5 dimensions  via the FLD  projection matrix,  W,ld.  The FLD  image  dictionary \nwas  thus  Wpca  * W,ld.  Best  performance  of 75.7%  correct  was  obtained  with  the \nEuclidean distance similarity measure and template matching classifier. \nFLD provided a much more compact representation than PCA. However, unlike the \nresults  obtained  by  (3)  for  identity  recognition,  Fisher's  Linear  Discriminants  did \nnot improve over basic PCA (Eigenfaces) for facial  action classification.  The differ(cid:173)\nence in performance may be due to the low dimensionality of the final representation \nhere.  Class  discriminations that are approximately linear in  high  dimensions  may \nnot be linear when projected down to as  few  as 5 dimensions. \n\n5  Predefined image kernels:  Gabor wavelets \n\nAn  alternative  to  the  adaptive  bases  described  above  are  wavelet  decompositions \nbased  on  predefined  families  of Gabor kernels.  Gabor  kernels  are  2-D  sine  waves \nmodulated by a Gaussian (Figure 2c).  Representations employing families of Gabor \nfilters  at  multiple  spatial  scales,  orientations,  and  spatial  locations  have  proven \nsuccessful  for  recognizing  facial  identity  in  images  (11).  Here,  the  ~-images were \nconvolved with a family  of Gabor kernels 'l/Ji,  defined  as \n\n'l/Ji  X  =  --2-e \n\n( .... ) \nki  =  (  it c~s'Pl-'  ) \n\nJ v  sm 'PI-' \n\nwhere \n\nIIkill2  _\"kjlI2IzI2  [}'k .i \nu \n\n20'2 \n\ne'  - e \n\n_0'2] \n\n2 \n\nIv  =  2-~7r, \n\n'PI-'  =  J.t'!!g. \n\n' \n\n(2) \n\nFollowing (11), the representation consisted of the amplitudes at 5 frequencies  (v = \n0-4) and  8  orientations  (J.t  =  1 - 8).  Each filter  output  was  downsampled  by  a \nfactor  q  and  normalized  to unit  length.  We  tested  the performance  of the system \nusing  q  =  1,4,16 and found  that q =  16 yielded  the best generalization rate.  Best \nperformance was  obtained with the cosine  similarity measure and nearest neighbor \n\n\fImage Representations for Facial Expression Coding \n\n891 \n\nclassifier.  Classification  performance  with  the  Gabor  representation  was  95.5%. \nThis performance was  significantly higher than all of the data-driven approaches in \nthe comparison except independent  component analysis,  with which it tied. \n\n6  Results and  Conclusions \n\nPCA \n79.3  \u00b13.9  73.4  \u00b14.2 \n\nLocal PCA  LFA \n\nICA \n\n81.1  \u00b13.7  95.5  \u00b12.0  75.7 \u00b14.1  95.5  \u00b12.0 \n\nFLD \n\nGabor \n\nTable 1:  Summary of classification performance for  12 facial  actions. \n\nWe  have  compared  a  number  of  different  image  analysis  methods  on  a  difficult \nclassification  problem,  the classification  of facial  actions.  Best  performances were \nobtained with the Gabor and ICA  representations, which both achieved 95.5% cor(cid:173)\nrect  classification  (see  Table  1).  The  performance of these  two  methods  equaled \nthe agreement level of expert human subjects on these images  (94%).  Image repre(cid:173)\nsentations derived from  the second-order statistics of the dataset  (PCA  and LFA) \nperformed in the 80% accuracy range.  An image representation derived from super(cid:173)\nvised  learning on  the second-order statistics  (FLD)  also did  not significantly differ \nfrom  PCA.  We  also  obtained evidence that high  spatial frequencies  are important \nfor  classifying facial  actions.  Classification with the three highest frequencies of the \nGabor representation (1/  =  0,1,2, cycles/face =  15,18,21 cycles/face) was 93%  com(cid:173)\npared to 84%  with the three lowest frequencies  (1/  = 2,3,4, cycles/face = 9,12,15). \nThe two representations that significantly outperformed the others, Gabor and Inde(cid:173)\npendent Components,  employed local basis images,  which  supports recent  findings \nthat  local  basis  images  are  important for  face  image  analysis  (14)  (10)  (12).  The \nlocal  property alone,  however,  does not  account for  the good performance of these \ntwo  representations,  as  LFA  performed  no  better than  PCA  on  this  classification \ntask, nor did local implementations of PCA. \nIn addition  to spatial  locality,  the ICA  representation  and  the  Gabor filter  repre(cid:173)\nsentation  share  the  property  of  redundancy  reduction,  and  have  relationships  to \nrepresentations in the visual cortex.  The response properties of primary visual cor(cid:173)\ntical cells are closely modeled by a bank of Gabor kernels.  Relationships have been \ndemonstrated between Gabor kernels and independent component analysis.  Bell & \nSejnowski  (5)  found using ICA that the kernels that produced independent outputs \nfrom  natural scenes were spatially local,  oriented edge kernels, similar to a  bank of \nGabor kernels.  It has also been shown that Gabor filter  outputs of natural images \nare at least pairwise independent  (16). \nThe Gabor wavelets and ICA each provide a way to represent face images as a linear \nsuperposition of basis functions.  Gabor wavelets employ  a  set of pre-defined  basis \nimages,  whereas  ICA  learns  basis  images  that  are  adapted  to  the  data ensemble. \nThe Gabor wavelets are not specialized to the particular data ensemble,  but would \nbe advantageous when the amount of data is small.  The ICA representation has the \nadvantage of employing two  orders  of magnitude fewer  basis images.  This  can  be \nan advantage for  classifiers that involve parameter estimation.  In addition, the ICA \nrepresentation takes 90% less CPU time than the Gabor representation to compute \nonce the ICA  weights are learned,  which need only  be done once. \nIn  summary,  this  comparison  provided  converging  support  for  using  local  basis \nimages,  high  spatial frequencies,  and statistical independence for  classifying facial \nactions.  Best  performances  were  obtained  with Gabor wavelet  decomposition  and \nindependent component analysis.  These two representations employ gray level basis \nfunctions  that share properties of spatial locality, independence, and have relation(cid:173)\nships to the response properties of visual cortical neurons. \nAn  outstanding  issue  is  whether  our  findings  depend  on  the  simple  recognition \nengines  we  employed.  Would  a  smarter recognition  engine  alter the relative  per-\n\n\f892 \n\nM. S.  Bartlett.  G.  Donato. J.  R.  Movellan. J.  C.  Hager,  P.  Ekman and T.  J.  Sejnowski \n\nformances?  Our  preliminary  investigations  suggest  that  is  not  the  case.  Hidden \nMarkov  models  (HMM's)  were  trained  on  the  PCA,  ICA  and  Gabor  representa(cid:173)\ntions.  The  Gabor representation  was  reduced  to 75  dimensions  using  PCA  before \ntraining  the  HMM.  The  HMM  improved  classification  performance  with  ICA  to \n96.3%,  and  it  did  not  change  the  overall  findings,  as  it  gave  similar  percent  im(cid:173)\nprovements to the PCA and PCA-reduced Gabor representations over their nearest \nneighbor performances.  The dimensionality reduction of the Gabor representation, \nhowever,  caused  its  nearest  neighbor  performance  to  drop,  and  the  performance \nwith the HMM  was 92.7%.  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