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Texture synthesis by non-parametric sampling

A non-parametric method for texture synthesis is proposed. The texture synthesis process grows a new image outward from an initial seed, one pixel at a time. A Markov random field model is assumed, and the conditional distribution of a pixel given all its

IEEEInternationalConferenceonComputerVision,Corfu,Greece,September1999

TextureSynthesisbyNon-parametricSampling

AlexeiA.EfrosandThomasK.Leung

ComputerScienceDivisionUniversityofCalifornia,BerkeleyBerkeley,CA94720-1776,U.S.A.efros,leungt@cs.berkeley.edu

Abstract

Anon-parametricmethodfortexturesynthesisispro-posed.Thetexturesynthesisprocessgrowsanewimageoutwardfromaninitialseed,onepixelatatime.AMarkovrandom eldmodelisassumed,andtheconditionaldistri-butionofapixelgivenallitsneighborssynthesizedsofarisestimatedbyqueryingthesampleimageand ndingallsim-ilarneighborhoods.Thedegreeofrandomnessiscontrolledbyasingleperceptuallyintuitiveparameter.Themethodaimsatpreservingasmuchlocalstructureaspossibleandproducesgoodresultsforawidevarietyofsyntheticandreal-worldtextures.

ofspatiallocality.Theresultisaverysimpletexturesyn-thesisalgorithmthatworkswellonawiderangeoftexturesandisespeciallywell-suitedforconstrainedsynthesisprob-lems(hole- lling).

1.1.Previouswork

Mostrecentapproacheshaveposedtexturesynthesisinastatisticalsettingasaproblemofsamplingfromaprobabil-itydistribution.Zhuet.al.[12]modeltextureasaMarkovRandomFieldanduseGibbssamplingforsynthesis.Un-fortunately,Gibbssamplingisnotoriouslyslowandinfactitisnotpossibletoassesswhenithasconverged.HeegerandBergen[6]trytocoercearandomnoiseimageintoatexturesamplebymatchingthe lterresponsehistogramsatdifferentspatialscales.Whilethistechniqueworkswellonhighlystochastictextures,thehistogramsarenotpow-erfulenoughtorepresentmorestructuredtexturepatternssuchasbricks.

DeBonet[1]alsousesamulti-resolution lter-basedap-proachinwhichatexturepatchata nerscaleiscondi-tionedonits“parents”atthecoarserscales.Thealgorithmworksbytakingtheinputtexturesampleandrandomizingitinsuchawayastopreservetheseinter-scaledependen-cies.Thismethodcansuccessfullysynthesizeawiderangeoftexturesalthoughtherandomnessparameterseemstoex-hibitperceptuallycorrectbehavioronlyonlargelystochas-tictextures.Anotherdrawbackofthismethodisthewaytextureimageslargerthantheinputaregenerated.Thein-puttexturesampleissimplyreplicatedto llthedesireddi-mensionsbeforethesynthesisprocess,implicitlyassumingthatalltexturesaretilablewhichisclearlynotcorrect.ThelatestworkintexturesynthesisbySimoncelliandPortilla[9,11]isbasedon rstandsecondorderpropertiesofjointwaveletcoef cientsandprovidesimpressiveresults.Itcancapturebothstochasticandrepeatedtexturesquitewell,butstillfailstoreproducehighfrequencyinformationonsomehighlystructuredpatterns.

1.Introduction

Texturesynthesishasbeenanactiveresearchtopicincomputervisionbothasawaytoverifytextureanalysismethods,aswellasinitsownright.Potentialapplicationsofasuccessfultexturesynthesisalgorithmarebroad,in-cludingocclusion ll-in,lossyimageandvideocompres-sion,foregroundremoval,etc.

Theproblemoftexturesynthesiscanbeformulatedasfollows:letusde netextureassomevisualpatternonanin nite2-Dplanewhich,atsomescale,hasastationarydistribution.Givena nitesamplefromsometexture(animage),thegoalistosynthesizeothersamplesfromthesametexture.Withoutadditionalassumptionsthisproblemisclearlyill-posedsinceagiventexturesamplecouldhavebeendrawnfromanin nitenumberofdifferenttextures.Theusualassumptionisthatthesampleislargeenoughthatitsomehowcapturesthestationarityofthetextureandthatthe(approximate)scaleofthetextureelements(texels)isknown.

Textureshavebeentraditionallyclassi edaseitherreg-ular(consistingofrepeatedtexels)orstochastic(withoutexplicittexels).However,almostallreal-worldtexturesliesomewhereinbetweenthesetwoextremesandshouldbecapturedwithasinglemodel.Inthispaperwehavechosenastatisticalnon-parametricmodelbasedontheassumption

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