1. Mean-Field Theory and Its Applications In Computer Vision3 1

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

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

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

5. 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

6. 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

7. Barycentric Interpolation 7

8. Efficient Cross-Bilateral Filtering 8

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

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

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

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

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

14. Gaussian blurring Apply Gaussian blurring along axes 14

15. Gaussian blurring Apply Gaussian blurring along axes 15

16. Gaussian blurring Apply Gaussian blurring along axes 16

17. Splatting Upsample the points 17

18. Splatting Upsample the points 18

19. PLBF Final upsampled points 19

20. 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

21. Distance in high-dimension space 21

22. Filtering in high-dimension space 22 Spatial Range Inefficient

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

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

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

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

27. Project 27 Project the blurred values in the original space

28. Project 28 Project the blurred values in the original space

29. 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

30. Filtering in frequency domain 30

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

32. MSRC-21 dataset 32 591 colour images, 320x213 size, 21 object classes

33. MSRC-21 dataset 33 591 colour images, 320x213 size, 21 object classes RuntimeStandard ground truthAccurate ground truth GlobalAverageGlobalAverage Unary Classifiers 84.076.683.2±1.580.6±2.3 Grid CRF1 sec84.677.284.8±1.582.4±1.8 Robust Pn30 sec84.977.586.5±1.083.1±1.5 Dense CRF0.2 sec86.078.388.2±0.784.7±0.7

34. PascalVOC-10 dataset 34 591 colour images, 320x213 size, 21 object classes

35. PascalVOC-10 dataset 35 591 colour images, 320x213 size, 21 object classes RuntimeOverallAv. RecallAv. I/U Dense CRF0.67 sec71.6334.5328.4

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

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

38. Long-range connections 38 Sometimes propagates misleading information

39. 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

40. 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