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Published byAaron Bentley Modified over 2 years ago

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Mean-Field Theory and Its Applications In Computer Vision3 1

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Gaussian Pairwise Potential 2 Spatial Expensive message passing can be performed by cross-bilateral filtering Range

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Cross bilateral filter 3 outputinput reproduced from [Durand 02] outputinput

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Efficient Cross-Bilateral Filtering Based on permutohedral lattice (PLBF) 2 Embed the points on the permutohedral lattice Apply Gaussian Blurring 4

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Efficient Cross-Bilateral Filtering Based on permutohedral lattice (PLBF) 2 Embed the points on the permutohedral lattice Apply Gaussian Blurring 5 Based on the domain-transform (DTBF) 3 Project the point to lower dimension Perform filtering in the transformed domain

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Efficient Cross-Bilateral Filtering Based on permutohedral lattice (PLBF) 2 Embed the points on the permutohedral lattice Apply Gaussian Blurring 6 Based on the domain-transform (DTBF) 3 Project the point to lower dimension Perform filtering in the transformed domain Filtering in frequency domain Apply fast fourier transform convolution in (s) domain=multiplication in (f) domain

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Barycentric Interpolation 7

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Efficient Cross-Bilateral Filtering 8

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Permutohedral Lattice based filtering For each pixel (x, y) 9 Downsample all the points (dependent on standard deviations)

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Embed to the permutohedral lattice Embed each downsampled points to the lattice 10

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Embed to the permutohedral lattice Embed each downsampled points to the lattice 11

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Embed to the permutohedral lattice Embed each downsampled points to the lattice 12

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Embed to the permutohedral lattice Embed each downsampled points to the lattice 13

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Gaussian blurring Apply Gaussian blurring along axes 14

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Gaussian blurring Apply Gaussian blurring along axes 15

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Gaussian blurring Apply Gaussian blurring along axes 16

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Splatting Upsample the points 17

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Splatting Upsample the points 18

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PLBF Final upsampled points 19

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Domain Transform Filtering 20 Project points in low-dimension preserving the distance in the high dimension Projecting to the original space Filtering performed in low-dimension space

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Distance in high-dimension space 21

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Filtering in high-dimension space 22 Spatial Range Inefficient

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Projection in low-dimension space 23 Project to low-dimension Maintain geodesic distance high-dimension space

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Projection in low-dimension space 24 Project to low-dimension Maintain geodesic distance high-dimension space

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Projection in low-dimension space 25 Project to low-dimension Maintain geodesic distance high-dimension space

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Gaussian blurring in low-dimension 26 Apply Gaussian blurring in low-dimension space

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Project 27 Project the blurred values in the original space

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Project 28 Project the blurred values in the original space

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PLBF Vs DTBF 29 Filter parameter: PLBF runtime is inversely proportional to the kernel size defined over space and range Use PLBF with the relatively large (~10) range Use DTBF with relatively smaller (~1-2) range Processing Time: Both linear in the number of pixels

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Filtering in frequency domain 30

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Convergence 31 Iteration vs. KL-divergence value In theory: (since parallel update) convergence is not guaranteed In practice: converges observe a convergence

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MSRC-21 dataset colour images, 320x213 size, 21 object classes

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MSRC-21 dataset colour images, 320x213 size, 21 object classes RuntimeStandard ground truthAccurate ground truth GlobalAverageGlobalAverage Unary Classifiers ± ±2.3 Grid CRF1 sec ± ±1.8 Robust Pn30 sec ± ±1.5 Dense CRF0.2 sec ± ±0.7

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PascalVOC-10 dataset colour images, 320x213 size, 21 object classes

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PascalVOC-10 dataset colour images, 320x213 size, 21 object classes RuntimeOverallAv. RecallAv. I/U Dense CRF0.67 sec

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Long-range connections 36 Accuracy o n increasing the spatial and range standard deviations On MSRC-21 spatial – 61 pixels, range – 11

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Long-range connections 37 On increasing the spatial and range standard deviations On MSRC-21 spatial – 61 pixels, range – 11

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Long-range connections 38 Sometimes propagates misleading information

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Mean-field Vs. Graph-cuts 39 Measure I/U score on PascalVOC-10 segmentation Increase standard deviation for mean-field Increase window size for graph-cuts method Both achieve almost similar accuracy

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Mean-field Vs. Graph-cuts 40 Measure I/U score on PascalVOC-10 segmentation Increase standard deviation for mean-field Increase window size for graph-cuts method Time complexity very high, making infeasible to work with large neighbourhood system

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