A Bayesian Approach to inferring vascular tree structure from 2D imagery(3)

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

Fig.2.MovesusedinMCMCsimulationontrees.iterative,EM-typealgorithmtomaximiselikelihood

(4)

(5)

(6)

wherethedataarewindowedwithacosinewindow,whosesizeistwicetheblockwidthatagivenscale,togivethedatausedintheestimator.Theindexdenotesiterationnumber;typically4-5iterationsaresuf- cienttogiveaccurateestimates.Figures3(b)-(c)showreconstructionsusingthe2DGaussiansineachblock(atcorrespondingblocksizes)basedontheMLfeatureesti-matesatblocksizesofandrespectively.Clearly,atlowerspatialresolutions,themodelcannoteas-ilydescribethepresenceofmultiplevesselswithinthewin-dow,suchasoccuratbifurcations,andtheresultinglow-amplitude,isotropicGaussiansarelocallythe‘best’de-scriptionoftheseregions.However,theseblockscanbemodelledaccuratelyathigherspatialresolutions.Thesec-ondsetofimagesshowshowthelocalestimatesfromdif-ferentwindowscalesisusedinacoarse- nestochasticsim-ulation,inordertogetaBayesianestimateoftheforest

structure.Afterthe rst200iterations,thescaleishalvedandtheappropriatelocalfeatureestimatesareusedtoguidethesampler;after3000,thescaleishalvedagain,asitisafter6000iterations,atwhichpoint,thehighestspatialres-olutionisreached.Thisapproachhasbeenfoundtospeedconvergencetotheequilibriumdistribution,whileavoidingbecomingtrappedinlocalmodes,inasimilarmannertomanycoarse- nealgorithms.Notethatoneiterationcon-sistsofthegenerationandacceptanceofasingleproposal(for‘editing’thetree).Inotherwords,100000iterationsiscomparable,intermsofcomputation,toasinglescanthroughtheimage.Ithasbeennotedfromexperimentsthatequilibriumisreachedinapproximately50000iterations,acomparativelylowburdencomputationally.

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新人文社科A Bayesian Approach to inferring vascular tree structure from 2D imagery(3)全文阅读和word下载服务。