A Generative Perspective on MRFs in Low-Level Vision Supplem(4)

pairwise(generalizedLaplacian[9])pairwise(Laplacian)pairwise(Student-t[3])pairwise(ours)715×15FoEfrom[12]3×3FoE(ours)conj.gradientα-expansionσ=10σ=20σ=10σ=2027.3522.9726.9722.7029.3624.2729.3724.2528.1924.0427.8323.7230.2726.4828.1424.1222.5120.45––30.3325.15––conj.gradientα-expansionσ=10σ=20σ=10σ=200.7450.5590.7270.5400.8320.6240.8320.6240.7840.6020.7710.5840.8550.7200.7840.6040.5150.445––0.8380.638––

conj.gradientα-expansionσ=10σ=20σ=10σ=2031.5427.5931.4627.4831.9128.1131.9028.1131.2226.7031.2626.8330.4126.5530.0525.9832.2728.47––32.1927.98––conj.gradientα-expansionσ=10σ=20σ=10σ=200.8860.7770.8850.7730.8970.8010.8970.8000.8870.7460.8890.7610.8540.7250.8530.7180.9030.820––0.9090.798––

σ=10

28.6430.3429.3832.0923.2232.85

σ=2023.9225.4724.6828.3221.4728.91

3σ=100.8040.8690.8250.9040.5640.923

σ=200.6090.7030.6310.8080.4890.839

pairwise(generalizedLaplacian[9])pairwise(Laplacian)pairwise(Student-t[3])pairwise(ours)715×15FoEfrom[12]3×3FoE(ours)

103Model

75×5FoEfrom[8]pairwise(ours)3×3FoE(ours)Non-localmeans[2]BLS-GSM[6]Learning

discriminativeCD(generative)CD(generative)––InferenceMAPMMSEMMSE(MMSE)MMSE

averagestd.dev.27.862.0927.542.0527.952.3027.502.1228.022.2410averagestd.dev.0.7760.0510.7580.0450.7880.0590.7340.0460.7890.059

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IEEETIP,13(4):600–612,2004.

[11]Y.Weiss.Personalcommunication,2005.

[12]Y.WeissandW.T.Freeman.Whatmakesagoodmodelofnaturalimages?CVPR2007.

[13]M.Welling,G.E.Hinton,andS.Osindero.LearningsparsetopographicrepresentationswithproductsofStudent-tdistributions.

NIPS*2002.