A Bayesian Approach to inferring vascular tree structure from 2D imagery

We describe a method for inferring tree-like vascular structures from 2D imagery. A Markov Chain Monte Carlo (MCMC) algorithm is employed to produce approximate samples from the posterior distribution given local feature estimates, derived from likelihood

ABAYESIANAPPROACHTOINFERRINGVASCULARTREESTRUCTUREFROM

2DIMAGERY

ElkeTh¨onnes,AbhirBhalerao,WilfridKendall,andRolandWilson

DepartmentsofComputerScienceandStatistics

UniversityofWarwick,UK

elke|wsk@stats.warwick.ac.uk

abhir|rgw@dcs.warwick.ac.uk

ABSTRACT

Wedescribeamethodforinferringtree-likevascularstruc-turesfrom2Dimagery.AMarkovChainMonteCarlo(MCMC)algorithmisemployedtoproduceapproximatesamplesfromtheposteriordistributiongivenlocalfeatureestimates,derivedfromlikelihoodmaximisationforaGaus-sianintensitypro le.Amultiresolutionscheme,inwhichcoarsescaleestimatesareusedtoinitialisethealgorithmfor nerscales,hasbeenimplementedandusedtomodelreti-nalimages.Resultsarepresentedtoshowtheeffectivenessofthemethod.

1.INTRODUCTION

Theproblemofinferringvascularstructurefromimagedataisanimportantone,especiallyintheareaofsurgicalplan-ning,whichrequiresbothef cientcomputationandeffec-tiveuseofpriorknowledge.Previousworkintheareahastendedtofocusonthemodellingofspeci cvascularfea-tures[1]ortouseapproachessuchasadaptivethresholding[4].

Theaimoftheworkdescribedhereistoformulateageneralmethodfortheinference,whichcanbeappliedintwoorthreedimensionsandmakeseffectiveuseofpriorknowledge,yetwhichissuf cientlygeneraltobeappliedtoawiderangeofproblems.Thecommonstatisticalmeth-odsforsuchmedicalimageanalysishavetypicallyusedlikelihoodtechniques,suchasExpectation-Maximisation(EM)[6,5].AlthoughEMmethodscanbeef cientcom-putationally,theyhaveonlylimitedscopeforincorporatingpriorknowledge.AmorepowerfulwayofincludingpriorinformationistouseaBayesianmethod,suchasmaximumaposteriori(MAP)estimation.Theprincipaldif cultywithBayesiantechniquesisacomputationalone:theynormallyrequiretheuseofMarkovchainMonteCarlo(MCMC)al-gorithms,whichmayrunforhundredsofthousandsofiter-ationstoyieldreliableresults[3].Thishasrestrictedtheir

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