{"title": "Bayesian Robustification for Audio Visual Fusion", "book": "Advances in Neural Information Processing Systems", "page_first": 742, "page_last": 748, "abstract": "", "full_text": "Bayesian Robustification for  Audio Visual \n\nFusion \n\nJavier  Movellan * \n\nmovellanOcogsci.ucsd.edu \n\nDepartment of Cognitive Science \nUniversity of California, San Diego \n\nLa Jolla, CA 92092-0515 \n\nPaul Mineiro \n\npmineiroOcogsci.ucsd.edu \n\nDepartment of Cognitive Science \nUniversity of California,  San Diego \n\nLa Jolla,  CA  92092-0515 \n\nAbstract \n\nWe discuss the problem of catastrophic fusion in multimodal recog(cid:173)\nnition  systems.  This  problem  arises  in systems  that  need  to  fuse \ndifferent  channels in  non-stationary environments.  Practice shows \nthat when  recognition modules  within each modality are tested in \ncontexts inconsistent with their assumptions, their influence on the \nfused  product tends to increase,  with catastrophic results.  We  ex(cid:173)\nplore  a  principled  solution  to  this  problem  based  upon  Bayesian \nideas  of  competitive  models  and  inference  robustification:  each \nsensory channel is  provided  with  simple  white-noise context mod(cid:173)\nels,  and  the  perceptual  hypothesis  and  context  are  jointly  esti(cid:173)\nmated.  Consequently, context deviations are interpreted as changes \nin white noise contamination strength, automatically adjusting the \ninfluence of the module.  The approach is  tested on  a fixed  lexicon \nautomatic audiovisual speech  recognition problem  with very good \nresults. \n\nIntroduction \n\n1 \nIn this paper we address the problem of catastrophic fusion in automatic multimodal \nrecognition systems.  We explore a principled solution based on the Bayesian ideas of \ncompetitive models and inference robustification  (Clark & Yuille,  1990;  Box,  1980; \nO'Hagan, 1994).  For concreteness, consider an audiovisual car telephony task which \nwe  will  simulate in  later sections.  The task is  to recognize spoken  phone numbers \nbased on input from a camera and a microphone.  We want the recognition system to \nwork on environments with non-stationary statistical properties:  at times the video \nsignal (V)  may be relatively clean and the audio signal (A)  may be contaminated by \nsources like the radio, the engine,  and friction  with the road.  At other times the A \nsignal may be more reliable than the V signal, e.g., the radio is off,  but the talker's \nmouth  is  partially occluded.  Ideally  we  want  the audio-visual  system  to  combine \nthe A and V sources optimally given the conditions at hand, e.g., give more weight \nto whichever channel is  more reliable at that time.  At  a  minimum  we  expect that \nfor  a wide variety of contexts, the performance after fusion should not be worse than \nthe independent  unimodal systems  (Bernstein  & Benoit,  1996).  When component \nmodules  can  Significantly  outperform  the overall system  after  fusion,  catastrophic \nfusion  is  said to have occurred. \n\n\u2022 To whom correspondence should be addressed. \n\n\fBayesian Robustification for Audio Visual Fusion \n\n743 \n\nFixed  vocabulary  audiovisual  speech  recognition  (AVSR)  systems  typically  con(cid:173)\nsist  of two  independent  modules,  one  dedicated  to A  signals  and one  to  V signals \n(Bregler,  Hild,  Manke  &  Waibel,  1993;  Wolff,  Prasad,  Stork  &  Hennecke,  1994; \nAdjondani &  Benoit,  1996;  Movellan &  Chadderdon,  1996).  From a  Bayesian per(cid:173)\nspective  this  modularity  reflects  an  assumption  of conditional  independence  of  A \nand V signals  (i.e.,  the likelihood function  factorizes) \n\nP(XaXvIWi.Aa.Av)  <X  P(XaIWi.Aa)P(xvlwi.Av), \n\n(1) \nwhere  Xa  and  Xv  are  the  audio  and  video  data,  Wi  is  a  perceptual  interpretation \nof the  data  (e.g.,  the  word  \"one\")  and  {.Aa,.Av}  are  the  audio  and  video  models \naccording to which these probabilities are calculated, e.g., a  hidden Markov model, \na neural network, or an exemplar model.  Training is also typically modularized:  the \nA module is trained to maximize the likelihood of a sample of A signals while the V \nmodule is  trained on the corresponding sample of V signals.  At test  time new data \nare presented to the system and each module  typically  outputs the log probability \nof its input given each perceptual alternative.  Assuming conditional independence, \nBayes' rule calls  for  an affine  combination of modules \n\n'Ii; \n\nargmax {logp(wilxaxv.Aa.Av)} \n\nWi \n\nWi \n\nwhere 'Ii;  is the interpretation chosen by the system, and p( Wi)  is the prior probability \nof each  alternative.  This  fusion  rule  is  optimal in  the sense  that  it  minimizes  the \nexpected  error:  no  other  fusion  rule  produces  smaller  error  rates,  provided  the \nmodels  {.Aa,.Av} and the assumption of conditional independence are correct. \nUnfortunately  a  naive  application  of Bayes'  rule  to  AVSR  produces  catastrophic \nfusion.  The  A  and  V  modules  make  assumptions  about  the  signals  they  receive, \neither  explicitly,  e.g.,  a  well  defined  statistical  model,  or  implicitly,  e.g.,  a  black(cid:173)\nbox  trained with a  particular data sample.  In  our notation these  assumptions  are \nreflected  by  the  fact  that  the  log-likelihoods  are  conditional on  models:  {.A a ,  .Av}. \nThe fact  that  modules  make  assumptions  implies  that  they  will  operate  correctly \nonly  within  a  restricted  context,  i.e,  the  collection  of situations  that  meet  the  as(cid:173)\nsumptions.  In practice one typically finds  that  Bayes'  rule  assigns  more  weight  to \nmodules operating outside their valid  context, the opposite of what is  desired. \n2  Competitive Models and  Bayesian Robustification \nClark and Yuille  (1990)  and Yuille  and  Bulthoff (1996)  analyzed  information inte(cid:173)\ngration in  sensory systems from  a  Bayesian perspective.  Modularity  is  justified  in \ntheir view by the need to make assumptions that disambiguate the data available to \nthe perceptual system (Clark &  Yuille,  1990, p.  5).  However, this produces modules \nwhich  are valid only  within  certain contexts.  The solution  proposed by  Clark and \nYuille  (1990)  is  the creation of an ensemble of models  each of which  specializes  on \na  restricted context  and automatically checks  whether the  context is  correct.  The \nhope is that by working with such an ensemble of models, robustness under a variety \nof contexts can be achieved  (Clark &  Yuille,  1990, p.  13). \nBox (1980)  investigated the problem of robust statistical inference from  a  Bayesian \nperspective.  He  proposed  extending inference  models  with  additional  \"nuisance\" \nparameters a,  a  process  he  called  Bayesian  robustification.  The idea is  to  replace \nan implicit  assumption about  the specific  value  of a  with a  prior distribution over \na,  representing uncertainty about that parameter. \nThe  approach  here  combines  the  ideas  of competitive  models  and  robustification. \nEach of the  channels in the  multimodal  recognition system  is  provided  with  extra \n\n\f744 \n\n1.  Movellan and P.  Mineiro \n\nparameters  that  represent  non-stationary  properties  of the  environment,  what  we \ncall  a  context  model.  By  doing so  we  effectively  work  with  an infinite ensemble of \nmodels each of which compete on-line to explain the data.  As  we will see later even \nunsophisticated context models provide superior performance when the environment \nis  non-stationary. \n\nWe  redefine  the estimation problem  as  simultaneously choosing the most  probable \nA and V context parameters and the most probable perceptual interpretation \n\nw = argmax  {max P(WwaO'vIXaXvAaAv)} \n\nWi \n\nUo,U v \n\n(3) \n\nwhere  0' a  and  0' v  are  the  context  parameters  for  the  audio  and  visual  channels \nand Wi  are the different  perceptual interpretations.  One way  to think  of this joint \ndecision  approach  is  that  we  let  all  context  models  compete  and  we  let  only  the \nmost probable context models have an influence on the fused  percept.  Hereafter we \nrefer to this  approach as  competitive  fusion. \n\nAssuming conditional independence of the audio and video data and uninformative \npriors for  (0' a, 0' v),  we  have \n\nw = ar~ax {logp(Wi) + \n\n[~~IOgP(XalwwaAa)] + [~::XIOgP(xvIWiO'vAv)]}. \n\n(4) \n\nThus  conditional  independence  allows  a  modular  implementation  of  competitive \nfusion,  Le.,  the A  and V  channels do  not  need  to talk to each other  until  the  time \nto make a joint decision,  as  follows. \n\n1.  For each Wi  obtain conditional estimates of the context  parameters for  the \n\naudio and video signals: \n\nand \n\no-~IWi  ~ argmax { 10gp(xalwWaAa)  } , \n\n(To. \n\no-~IWi  ~ argmax{ 10gp(xvlwWvAv)  }. \n\n(Tv \n\n2.  Find the best Wi  using the conditional context estimates. \n\nw = argmax {IOgp(Wi)  + logp(xalwio-alwi Aa) + logp(xv IWio-vlwi Av)} \n\nWi \n\n(5) \n\n(6) \n\n(7) \n\n3  Application to A VSR \nCompetitive  fusion  can  be  easily  applied  to  Hidden  Markov  Models  (HMM),  an \narchitecture  closely  related  to  stochastic  neural  networks  and  arguably  the  most \nsuccessful for  AVSR.  Typical hidden Markov models  used in  AVSR are defined  by \n\u2022  Markovian state dynamics:  p(qt+ll2.t )  = p(qt+llqt),  where qt  is  the state at \n\ntime t  and 2.t  = (ql,\"  . qt), \n\n\u2022  Conditionally  independent  sensor  models  linking  observations  to  states \n\n! (Xt Iqt),  typically a  mixture of multivariate Gaussian densities \n\n!(xtlqt) = L p(mi Iqt)(27l') -N/2  1~I-l/2  exp(d(xt, qt, Pi, ~)), \n\n(8) \n\n\fBayesian Robustification for Audio VIsual Fusion \n\n745 \n\nwhere N  is the dimensionality of the data, mi is  the mixture label, p(milqt) \nis  the  mixture  distribution  for  state qt,  Pi  is  the centroid for  mixture  mi, \nE  is  a  covariance matrix, and d is  the Mahalanobis norm \n\n(9) \n\nThe approach explored here consists  on modeling contextual changes  as  variations \non  the variance parameters.  This  corresponds  to  modeling non-stationary proper(cid:173)\nties  of  the  environments  as  variations  in  white  noise  power  within  each  channel. \nCompetitive fusion calls for  on-line maximization of the variance parameters at the \nsame time we  optimize with  respect to the response alternative. \n\n11;  =  arg:ax{ logp(wi)  + \n\n[ ~~logp(xalwiEaAa)]  + [ ~~logp(xvlwiEv'\\v)] }. \n\n(10) \n\nThe maximization with respect to the variances can be easily integrated into stan(cid:173)\ndard  HMM  packages  by  simply  applying  the  EM  learning  algorithm  (Dampster, \nLaird & Rubin,  1977)  on the  variance parameters at test time.  Thus  the  only  dif(cid:173)\nference  between  the  standard  approach  and  competitive  fusion  is  that  we  retrain \nthe variance parameters of each  HMM  at test time.  In practice this training takes \nonly one or two iterations of the EM algorithm and can be done on-line.  We  tested \nthis approach on the following  AVSR problem. \n\nTraining database  We  used  Tulips1  (Movellan,  1995)  a  database consisting of \n934  images  of  9  male  and  3  female  undergraduate  students  from  the  Cognitive \nScience  Department at the University  of California,  San Diego.  For each of these, \ntwo samples were taken for  each of the digits  \"one\"  through  \"four\".  Thus, the total \ndatabase consists of 96 digit utterances.  The specifics of this database are explained \nin  (Movellan,  1995).  The database is  available at http://cogsci.ucsd.edu. \n\nVisual processing  We  have tried a  wide variety of visual processing approaches \non this database, including decomposition with local Gaussian templates (Movellan, \n1995), PCA-based templates (Gray, Movellan & Sejnowski, 1997), and Gabor energy \ntemplates  (Movellan  & Prayaga,  1996).  To  date,  best  performance  was  achieved \nwith the local Gaussian approach.  Each frame of the video track is  soft-thresholded \nand symmetrized along the vertical axis, and a temporal difference frame is obtained \nby subtracting the previous symmetrized frame from the current symmetrized frame. \nWe calculate the inner-products between the symmetrized images and a set of basis \nimages.  Our  basis  images  were  lOx15  shifted  Gaussian  kernels  with  a  standard \ndeviation  of 3  pixels.  The loadings  of the  symmetrized  image  and the  differential \nimage are combined  to form  the final  observation frame.  Each of these composite \nframes  has  300  dimensions  (2xlOx15).  The process  is  explained  in  more  detail  in \nMovellan  (1995). \n\nAuditory processing  LPC /cepstral analysis is  used  for  the auditory front-end. \nFirst,  the auditory  signal  is  passed  through  a  first-order  emphasizer  to  spectrally \nflatten  it.  Then  the  signal  is  separated into  non-overlapping frames  at  30  frames \nper second.  This  is  done  so  that there are an equal number  of visual and auditory \nfeature vectors for each utterance, which are then synchronized with each other.  On \neach frame we perform the standard LPC / cepstral analysis.  Each 30 msec auditory \nframe  is  characterized  by  26  features:  12  cepstral  coefficients,  12  delta-cepstrals, \n1 log-power,  and 1  delta-log-power.  Each of the  26  features  is  encoded  with  8-bit \naccuracy. \n\n\f746 \n\nJ  Movellan and P.  Mineiro \n\nFigure  1:  Examples  of the  different  occlusion  levels,  from  left  to  right:  0%,  10%, \n20%,  40%,  60%,  80%.  Percentages are in terms  of area. \n\nIn  previous  work  (Chadderdon & Movellan,  1995)  a  wide \nRecognition  Engine \nvariety of HMM architectures were  tested on  this  database including architectures \nthat  did  not  assume  conditional  independence.  Optimal  performance  was  found \nwith  independent  A and V modules  using  variance matrices of the form  uI, where \nu  is  a  scalar  and  I  the  identity  matrix.  The  best  A  models  had  5  states  and  7 \nmixtures  per  state and  the  best  V  models  had  3  states  and  3 mixtures  per state. \nWe  also determined the optimal weight of A and V modules.  Optimal performance \nis  obtained by weighting the output of V times  0.18. \n\nIn  this  experiment  we  used  the  pre(cid:173)\n\nFactorial  Contamination  Experiment \nviously  optimized  architecture  and  compared  its  performance  under  64  different \nconditions  using  the  standard and  the  competitive  fusion  approaches.  We  used  a \n2 x 8 x 8 factorial design,  the first  factor  being the fusion  rule,  and the second and \nthird factors the context in the audio and  video channels.  To our knowledge  this  is \nthe first  time  an  AVSR  system is  tested with  a  factorial experimental  design  with \nboth A and V contaminated at various levels.  The independent variables  were: \n\n1.  Fusion rule:  Classical,  and competitive fusion. \n2.  Audio  Context:  Inexistent, clean,  or  contaminated at one  of the following \nsignal to noise ratios:  12 Db, 6 Db, 0 Db,  -6  Db, -12 Db and -100 Db.  The \ncontamination was  done  with  audio digitally  sampled from  the interior of \na  car while  running on  a  busy highway  with  the  doors open and the radio \non a  talk-show station. \n\n3.  Video  Context:  Inexistent,  clean  or  occluded  by  a  grey  level  patch.  The \npercentages of visual area occupied by the patch were 10%,20%,40%,60%, \n80%  and  100%  (see  Figure  1). \n\nThe dependent variable was performance on the digit  recognition task evaluated in \nterms of generalization to new  speakers.  In all  cases  training was  done  with  clean \nsignals  and testing  was  done  with  one  of the  64  contexts  under  study.  Since  the \ntraining sample is small, generalization performance was estimated using a jackknife \nprocedure  (Efron,  1982).  Models  were  trained with  11  subjects,  leaving a  different \nsubject out for generalization testing.  The entire procedure was repeated 12  times, \neach  time  leaving  a  different  subject  out  for  testing.  Statistics  of generalization \nperformance  are  thus  based  on  96  generalization trials  (4  digits  x  12  subjects  x \n2  observations  per  subject).  Standard  statistical  tests  were  used  to  compare  the \nclassical and competitive context rules. \n\nThe results  of this  experiment are displayed in  Table  1.  Note how  the experiment \nreplicates the phenomenon of catastrophic fusion.  With the classic approach, when \none of the channels  is  contaminated, performance  after fusion  can  be significantly \n\n\fBayesian Robustificationfor Audio Visual Fusion \n\n747 \n\nVideo \nNone \n\nClean \n\n10% \n\n20% \n\n40% \n\n60% \n\n80% \n\n100% \n\nVideo \nNone \nClean \n\n10% \n\n20% \n\n40% \n\n60% \n\n80% \n\n100% \n\none \n\n84.37 \n\n73.95 \n\n62.50 \n\n37.50 \n\n34.37 \n\n27.00 \n\n25.00 \n\none \n\n86.45 \n\n73.95 \n\n54.16 \n\n29.16 \n\n32.29 \n\n29. 16 \n\n25.00 \n\n95.83 \n\n97.92 \n\n93.75 \n\n96.87 \n\n93.75 \n\n93.75 \n\n95.83 \n\n93.75 \n\nean \n95 .83 \n\n98.95 \n\n93.75 \n\n89.58 \n\n81.25 \n\n77.08 \n\n70.83 \n\n61.46 \n\n95.83 \n\n97.92 \n\n93.75 \n\n96.87 \n\n89.58 \n\n91.66 \n\n90.62 \n\n92.71 \n\n90.62 \n\n94.80 \n\n94 .79 \n\n94.79 \n\n87.50 \n\n84.37 \n\n80.20 \n\n90.62 \n\n87.50 \n\n89.58 \n\n83.30 \n\n82.29 \n\n79.16 \n\n78.12 \n\n-6 \n67.70 \n\n89.58 \n\n80.20 \n\n80.20 \n\n70.83 \n\n65.62 \n\n64.58 \n\n63.54 \n\n-1 \n42.70 \n\n81.25 \n\n71.87 \n\n16 2 .501 \n\n43.75 \n\n42.70 \n\n146.871 \n\n44.79 \n\n19 .80 \n\n82\n20 \n64.58 \n\n.\n\nI \n\n1\n\n41.66 \n\n30.20 \n\n26.04 \n\n25 .00 \n\n26.04 \n\nPerformance  wIth  C/a .. 1e  Fu\" on \n\nAudio \n\n94.79 \n\n96.87 \n\n93 .75 \n\n61.45 \n\n89.58 \n\n95.83 \n\n93.75 \n\n84.37 \n\n78.12 \n\n72.91 \n\n68.75 \n\n58.33 \n\n79. 16 \n\n93.75 \n\n89.58 \n\n84.37 \n\n67.20 \n\n62.50 \n\n54.16 \n\n51.04 \n\n65 .62 \n\n87.50 \n\n79.16 \n\n40.62 \n\n79. 16 \n\n70.83 \n\n20 .83 \n\n83\n70\n52 .58 \n\n.\n\n1\n\n/ \n\n75.00  ~ 43 .00 \n\n52 .08 \n\n38.54 \n\n34.37 \n\n47.91 \n\n44 .79 \n\n42.70 \n\n37.50 \n\n133 .831 \n\n38.54 \n\n29. 16 \n\n28.12 \n\n29 . 16 \n\nTable 1:  Average generalization performance with standard and competitive fusion. \nBoxed  cells  indicate a  statistically significant  difference  a  =  0.05  between  the  two \nfusion  approaches. \n\nworse than performance with the clean channel alone.  For example, when the audio \nis clean, the performance of the audio-only system is  95.83%.  When combined with \nbad video  (100% occlusion), this performance drops down to 61.46%, a statistically \nsignificant  difference,  F(l,ll)  =  132.0,  p  <  10-6 .  Using  competitive  fusion,  the \nperformance of the joint system is 93.75%, which is  not significantly  different from \nthe  performance  of the  A  system  only,  F(l,ll)  =  2.4,  p= 0.15.  The  table  shows \nin  boxes  the regions  for  which  the classic  and competitive fusion  approaches  were \nsignificantly different  (a =  0.05).  Contrary to the classic approach, the competitive \napproach behaves robustly in  all tested conditions. \n4  Discussion \nCatastrophic fusion may occur when the environment is non-stationary forcing mod(cid:173)\nules to operate outside their assumed context.  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