Evaluating error functions for robust active appearance models

Active appearance models (AAMs) are generative parametric models commonly used to track faces in video sequences. A limitation of AAMs is they are not robust to occlusion. A recent extension reformulated the search as an iteratively re-weighted least-squar

EvaluatingErrorFunctionsforRobustActiveAppearanceModels

Barry-JohnTheobald

SchoolofComputingSciences,UniversityofEastAnglia,Norwich,UK,NR47TJ

bjt@cmp.uea.ac.ukIainMatthewsandSimonBaker

TheRoboticsInstitute,CarnegieMellonUniversity,Pittsburgh,USA,PA15213

{iainm,simonb}@cs.cmu.edu

Abstract

Activeappearancemodels(AAMs)aregenerativeparametricmodelscommonlyusedtotrackfacesinvideosequences.AlimitationofAAMsistheyarenotrobusttoocclusion.Arecentextensionreformulatedthesearchasaniterativelyre-weightedleast-squaresprob-lem.Inthispaperwefocusonthechoiceoferrorfunc-tionforuseinarobustAAMsearch.Weevaluateeighterrorfunctionsusingtwoperformancemetrics:accu-racyofocclusiondetectionand ttingrobustness.Weshowforanyreasonableerrorfunctiontheperformanceintermsofocclusiondetectionisthesame.However,thisdoesnotmeanthat ttingperformancewillbethesame.Wedescribeexperimentsformeasuring ttingro-bustnessforimagescontainingrealocclusion.ThebestapproachassumestheresidualsateachpixelareGaus-sianalydistributed,thenestimatestheparametersofthedistributionfromimagesthatdonotcontainocclusion.Ineachiterationofthesearch,theerrorimageisusedtosamplethesedistributionstoobtainthepixelweights.

arebymeasuringtheaccuracyofocclusiondetection,ormeasuringtherobustnessofthesearch.Inthispaperwetesteighterrorfunctionsusingbothofthesemetrics.Weshowthatforanyreasonableerrorfunction(mono-tonicandsymmetric),theocclusiondetectionperfor-manceisthesame.However,thisdoesnotmeanthat ttingperformancewillbethesameasthetypeofer-rorisimportant.Asearchthatincludesasmallnumberofborderlineoutlierpixels(TypeIerror)mayconvergeasthesepixelsaredown-weightedtoreducedtheirin- uence.Likewise,asearchthatignoresanumberofinlierpixels(TypeIIerror)mayalsoconverge.Inthiscasenotalloftheavailableinformationisusedinthesearch.Allevaluationinthispaperisconductedonavideosequenceofadeaf-signerandweshowthebestresultsareobtainedwhenthedistributionoftheresid-ualateachpixelisassumedtobeGaussian.Clean,un-occludedimagesareusedtoestimatetheparametersofthesedistributions,whicharesampledineachiterationofthesearchusingtheerrorimage.

2.ActiveAppearanceModels:AAMs

1.Introduction

ActiveAppearanceModels(AAMs)aregenerativeparametricmodelscommonlyusedtotrackfacesinvideo[4,9].AmajorlimitationofAAMsistheyarenotrobusttoocclusionandonlyasmallamountofoc-clusioncancausetheAAMsearchtodiverge.ArobustextensiontoAAMsthatisanef cientformulationofearlier ttingalgorithms[3,6]wasdescribedin[5].InthispaperweconsiderthechoiceoferrorfunctionforuseinthisrobustAAMsearch.Thisisnotaproblemthatbeansweredusingsyntheticallyoccludeddata,aswasdonein[5].Choosinganerrorfunctioniseffec-tivelythesameasaskingwhatistherealdistributionofoutliersinimages?Twowaysthiscouldbeanswered

Theshape,s,ofanAAMisde nedbythe2Dcoor-dinatesoftheNverticesthatformatriangulatedmesh:

s=(x1,y1,x2,y2,...,xN,yN)T.

(1)

AAMsallowlinearshapevariation,meaningashapecanbeexpressedasabaseshape,s0,plusalinearcom-binationofntemplateshapes,si:

s=s0+∑pisi,

i=1n

(2)

wherethecoef cientspiaretheshapeparameters.

AAMsarenormallycomputedbyhand-aligningtheverticesofthemeshwiththecorrespondingfeatures

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