A Generative Perspective on MRFs in Low-Level Vision Supplem(13)

Figure10.256×256pixelsamplefromourlearnedmodelsafterreachingtheequilibriumdistribution.Theboundarypixelsareremovedforbetter

visualization.

Figure11.Monitoringtheconvergenceofsampling.(a)Samplinga50×50imagefromthelearnedpairwiseMRFpriorconditionedona1-pixelboundary.Threechainsandover-dispersedstartingpoints(red,dashed–interioroftheboundaryimage;blue,solid–median- <1.1).(b)Samplingthe lteredversion;black,dash-dotted–noisyversion).Approximateconvergenceisreachedafter25iterations(R

posterior(σ=20,imagesize160×240)withfourchainsandover-dispersedstartingpoints(red,dashed–noisyimage;blue,dash-dotted–Gauss lteredversion;green,solid–median lteredversion;black,dotted–Wiener lteredversion).Approximateconvergenceisreachedafter24iterations.

Figure12.Ef ciencyofsampling-basedMMSEdenoisingwithdifferentnumberofsamplers.LearnedpairwiseMRF,σ=20,imagesize160×240.(a)Incaseofparallelcomputing(onesamplerpercomputingcore),fasterconvergenceofthedenoisedimagecanbeachieved.(b)Evenwhenusingsequentialcomputing,multiplesamplerscanimproveperformance,asthesamplesarelesscorrelated.