Bilateral Filtering for Images & Meshes

1. Bilateral Filtering for Images & Meshes speaker: Di jiantao Sep 20,2007

2. Related Papers • “Bilateral Filtering for Gray and Color Images” C.Tomasi , R.Manduchi (ICCV 1998) • “Bilateral Mesh Denoising”Shachar Fleishman, Iddo Drori, Daniel Cohen-Or (SIGGRAPH 2003)

3. Bilateral Filtering for Gray and Color Images C.Tomasi, R.Manduchi ICCV 1998

4. About the author----C.Tomasi • Professor of Computer Science , Duke University • Main research activities are in computer vision.

5. Image denoising • Anisotropic diffusion [Perona & Malik ’90] • Wavelet denoising [Donoho ’95] • Bilateral filter [Smith & Brady ’97], [Tomasi & Manduchi ’98] • [Black et al. ’98] • Anisotropic diffusion • Robust statistics • [Elad ’01], [Durand & Dorsey ’02] relate • Anisotropic diffusion • Robust statistics • Bilateral filter

6. Denoising • Input (scanned) mode • Additive noise + =

7. filter + = Denoising • Input (scanned) mode • Additive noise • Noise free model • Preserve features

8. Filter Functions • Noise removal • Image smoothing • Preserve features

9. How to Compute Every Pixel Output Image Origin Image Weight ∑f(i)*w(i) ×

10. * = Filter methods: Gaussian Filter

11. Filter methods: Bilateral Filter • For image I(u), at coordinate u=(x,y): -----geometric closeness between p and u -----photometric similarity between I(p) and I(u)

12. * = Filter methods: Bilateral Filter Feature preserving Denoise Normalization

13. Parameters

14. Results Origin image Bilateral (3)

15. Results Bilateral (3) Origin image

16. Results Origin Image One iteration five iterations

17. Conclusion • Advantages • Fast • Simple • Intuitiveparameter selection • Edges preserving • Limitations • Over smooth • Can’t iterate many times

18. Bilateral Mesh Denoising Shachar Fleishman, Iddo Drori, Daniel Cohen-Or SIGGRAPH 2003

19. About the Author---Shachar Fleishman • Scientific Computing and Imaging Institute, university of Utah. • Main research interests in point-based graphics, surface modeling and representation and surface reconstruction from noisy data.

20. About the Author---Daniel Cohen-Or • Professor of Computer Science, Tel Aviv University • Main interests: Motion and Transformations, Visibility techniques, Shapes and Surfaces, and Point-based modeling.

21. About the author----Iddo Drori • received PhD from the Department of Computer Science at Tel-Aviv University (2004) • He was a post-doc at the Department of Statistics at Stanford University (2004-2006) • Research interests: Optimization, Computation biology, Computer graphics and version, Image and signal processing, Applied Computational geometry.

22. Mesh denoising, smoothing and fairing • Adapt image denoising algorithms to meshes • Isotropic diffusion [Desbrun et al. ’99] • Anisotropic diffusion of height fields [Desbrun et al. ’00] • Wiener filter [Peng et al. ’01] • Anisotropic diffusion on meshes [Clarenz et al. ’00, Xu & Bajaj ’03]

23. Traits • Fast • Simple • Intuitive parameter selection • Edge preserving

24. Bilateral filtering of meshes

25. Bilateral filtering of meshes

26. Bilateral filtering of meshes • Height above surface is equivalent to the gray level values in images

27. Bilateral filtering of meshes • Height above surface is equivalent to the gray level values in images • Apply the bilateral filter to heights

28. Bilateral filtering of meshes • Height above surface is equivalent to the gray level values in images • Apply the bilateral filter to heights • Move the vertex to its new height

29. Bilateral filtering of meshes • Height above surface is equivalent to the gray level values in images • Apply the bilateral filter to heights • Move the vertex to its new height • In practice: • Sharp features

30. Bilateral filtering of meshes • Height above surface is equivalent to the gray level values in images • Apply the bilateral filter to heights • Move the vertex to its new height • In practice: • Sharp features • The noise-freesurface is unknown

31. n P L Solution • A plane that passes through the point is the estimator to the smooth surface • Plane L=(p,n)

32. n P L Similarity closeness Solution • A plane that passes through the point is the estimator to the smooth surface • Plane L=(p,n)

33. Computing the plane • The approximating plane should be: • A good approximation to the surface • Preserve features • Average of the normal to faces in the 1-ring neighborhood

34. Algorithm DenoisePoint(Vertex v, Normal n) { } = neighborhood(v) K=|{ }| sum=0 normalizer=0 for i := 1 to K t = ||v- || h = <n,v-> Wc=exp(- /(2 )) Ws=exp(- /(2 )) Sum +=(Wc*Ws)h Normalizer += Wc*Ws End Return v+n*(sum/normalizer)

35. Algorithm DenoisePoint(Vertex v, Normal n) { } = neighborhood(v) K=|{ }| sum=0 normalizer=0 for i := 1 to K t = ||v- || h = <n,v-> Wc=exp(- /(2 )) Ws=exp(- /(2 )) Sum +=(Wc*Ws)h Normalizer += Wc*Ws End Return v+n*(sum/normalizer) iterate over neighborhood

36. Algorithm DenoisePoint(Vertex v, Normal n) { } = neighborhood(v) K=|{ }| sum=0 normalizer=0 for i := 1 to K t = ||v- || h = <n,v-> Wc=exp(- /(2 )) Ws=exp(- /(2 )) Sum +=(Wc*Ws)h Normalizer += Wc*Ws End Return v+n*(sum/normalizer) closeness q

37. Algorithm DenoisePoint(Vertex v, Normal n) { } = neighborhood(v) K=|{ }| sum=0 normalizer=0 for i := 1 to K t = ||v- || h = <n,v-> Wc=exp(- /(2 )) Ws=exp(- /(2 )) Sum +=(Wc*Ws)h Normalizer += Wc*Ws End Return v+n*(sum/normalizer) height – similarity v q

38. Robustness • Sharp features are treated as outliers

39. Robustness • Sharp features are treated as outliers • The bilateral filter does not recover smoothed signal

40. Results Bilateral mesh denoising Anisotropic denoising of height fields - Desburn ’00 Source

41. Results Anisotropic Geometric Diffusion in Surface Processing - Clarenz ‘00 Bilateral mesh denoising Source

42. Results Two iterations Five iterations Source

43. Conclusion • Advantages • Fast • Simple • Intuitiveparameter selection • Edges preserving • Limitations • Over smooth • Can’t iterate many times

44. Thank you!