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Mean-Field Theory and Its Applications In Computer Vision3

Mean-Field Theory and Its Applications In Computer Vision3. Gaussian Pairwise Potential. Expensive message passing can be performed by cross-bilateral filtering. Spatial. Range. Cross bilateral filter. output. input. output. input. reproduced from [Durand 02].

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Mean-Field Theory and Its Applications In Computer Vision3

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

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

  3. Cross bilateral filter output input output input reproducedfrom [Durand 02]

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

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

  8. Efficient Cross-Bilateral Filtering

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

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

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

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

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

  14. Gaussian blurring • Apply Gaussian blurring along axes

  15. Gaussian blurring • Apply Gaussian blurring along axes

  16. Gaussian blurring • Apply Gaussian blurring along axes

  17. Splatting • Upsample the points

  18. Splatting • Upsample the points

  19. PLBF • Final upsampled points

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

  21. Distance in high-dimension space

  22. Filtering in high-dimension space Inefficient Spatial Range

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

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

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

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

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

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

  29. PLBF Vs DTBF • Processing Time: • Both linear in the number of pixels • 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

  30. Filtering in frequency domain

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

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

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

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

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

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

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

  38. Long-range connections • Sometimes propagates misleading information

  39. Mean-field Vs. Graph-cuts • 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 • 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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