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- 1. IMAGE AND VIDEO ABSTRACTIONBY MULTI-SCALE ANISOTROPICKUWAHARA FILTERINGNPAR 2011JAN ERIC KYPRIANIDISHASSO-PLATTNER-INSTITUT, GERMANY
- 2. ABSTRACTMulti-scale Anisotropic Kuwahara Filter - a coarse-to-fine edgepreserving smoothing filter1. Strong image abstraction2. Avoid artifacts in large low-contrast region original image anisotropic Kuwahara filter proposed method
- 3. OUTLINE1. Introduction Image abstraction & Edge preserving smoothing filters2. Related work3. Method 1. Pyramid structure : coarse fine 2. Anisotropic Kuwahara filter 3. Merging function : (upper level, this level)4. Results5. Conclusions
- 4. INTRODUCTION Temporal coherence in video Segmentation NPR (mean-shift) Edge preserving smoothing filter • Bilateral • Kuwahara Image abstractionImage abstraction is useful for NPR or temporal coherence in video
- 5. PROBLEM OFSEGMENTATIONRegions segmented by mean-shift [DeCarlo & Santella 02; Wen et 1l. 06]have rough boundaries and require elaborate post-processing original image Mean-shift results in rough-boundary
- 6. PROBLEM OFEDGE PRESERVINGSMOOTHIHG FILTERBilateral filter or Kuwahara filter cause overblurring • Remove detail in low-contrast region original image Bilateral filter results in overblurring in low-contrast regions.
- 7. PROBLEM OFANISOTROPICKUWAHARA FILTERPreserve features, directions, and is robust against high-contrastnoise original image Bilateral Anisotropic Kuwahara (direction) • However .. • level of abstraction depending on filter radius • Artifacts in large low-contrast regions
- 8. ADVANCE OFMULTI-SCALE ANISOTROPICKUWAHARA FILTERING 1.down sample to create 2. from coarse-to- image pyramid first fine, apply anisotropic Kawahara filter and Down Up merge the previous sample sample• Avoid artifacts and smooth results • By adding thresholding to the weighting term• Strong abstraction and avoidance of artifacts in large low-contrast regions • Coarse-to-fine from multi-scale image pyramids• Real-time processing on GPU
- 9. RELATED WORK1. Image pyramids2. Bilateral filter3. Kuwahara filters edge preserving4. Anisotropic Kuwahara filter smoothing filter5. Mean curvature flow + shocking filtering6. Diffusion and shock filtering7. Image abstraction on gradient domain
- 10. IMAGEPYRAMIDS Gaussian filter + down-sample Gaussian filter + down-sample Gaussian filter + down-sample
- 11. down-sampling without smoothing aliasing
- 12. BILATERAL FILTER [Smith 97, Tomasi 98] Input Result edge preserving + smoothing filter Weights • Gaussian on space distance • Gaussian on range distance • sum to 1 smoothing preserve edges space rangeSylvain Paris and Frédo Durand. A Fast Approximation of the Bilateral Filter using a Signal Processing Approach. ECCV’ 06.
- 13. KUWAHARAFILTER[Kuwahara et al. 76] [76]Select the ave. value ofsub-region whose var. ismin. [07]where q in the sub-regionRi of p with min. variance Anisotropic Kuwahara [09]
- 14. A tiled & aliased image filtered byKuwahara filter Due to 1. Rectangular sub-regions 2. Unstable if noise exits 3. Subregions have the same variance. origin Kuwahara filter
- 15. GENERALIZEDKUWAHARAFILTER[Papari et al. 07] [76]New val. is sum of mean ofeach sub-region weightedby the inverse stdv. [07] si : variance of sub-region i mi : mean of sub-region i Anisotropic Kuwahara [09]
- 16. Fail to capture directional features &clustering artifacts non directional Generalized Kuwahara Anisotropic Kuwahara
- 17. GENERALIZEDKUWAHARAFILTER[Kyprianidis et al. PG09] [76]New val. is sum of mean ofeach sub-region weightedby the inverse stdv. [07] si : variance of sub-region i mi : mean of sub-region i Anisotropic Kuwahara [09]
- 18. ANISOTROPICKUWAHARAFILTER[Kyprianidis et al. PG09]• Smooth image tangents 2nd eigen vector v2 of smoothed by local gradients Gaussian filter• Set the ellipse kernel
- 19. ANISOTROPICKUWAHARAFILTER[Kyprianidis et al. PG09]• Smooth image tangents 2nd eigen vector v2 of smoothed by local gradients Gaussian filter• Set the ellipse kernel 1. Image tangent = 2nd eigen vector of Jij structure tensor (fx, fy) = mean(local gradients (gx,gy)) Jij 2nd eigen vector Image tangent = 2nd eigen PCA of image gradients vector of local gradients
- 20. ANISOTROPICKUWAHARAFILTER[Kyprianidis et al. PG09]• Smooth image tangents 2nd eigen vector v2 of smoothed by local gradients Gaussian filter• Set the ellipse kernel 1. Image tangent = 2nd eigen vector of Jij structure tensor (fx, fy) = mean(local gradients (gx,gy) Jij 2. Smooth the image tangents by Gaussian filter
- 21. ANISOTROPIC KUWAHARA FILTER [Kyprianidis et al. PG09] • Smooth the tangent of image • Set the ellipse kernel K0rotate K0 to generate kernel of each subregion scale & rotate as ellipse kernel
- 22. ANISOTROPICKUWAHARAFILTER[Kyprianidis et al. PG09]• Smooth the tangent of image• Set the ellipse kernel K0
- 23. ANISOTROPIC KUWAHARA FILTER [Kyprianidis et al. PG09] • Smooth the tangent of image • Set the ellipse kernel Kirotate K0 to generate kernel of each region
- 24. ANISOTROPICKUWAHARAFILTER[Kyprianidis et al. PG09]• Smooth the tangent of image scale & rotate as ellipse kernel• Set the ellipse kernel1. Scale 2. Rotation α=1 Jij
- 25. MEAN CURVATURE FLOW (MCF)+ SHOCKING FILTERING[Kang and Lee. PG08]• Mean curvature flow simplifies shape of boundaries • Users must protect important features• Shock filter sharpens the discontinuities and flattens each homogenous regions
- 26. IMAGE ABSTRACTION ONGRADIENT DOMAIN[Orzan et al. NPAR’07] origin reconstruction thickness = importance
- 27. IMAGE ABSTRACTION ONGRADIENT DOMAIN1. Importance Canny edge (small scale large scale) lifetimesource ∝ |gradient| ∝ thickness2. Gradient reconstruction ∝ importance • Solve Poisson eq. with constrain of gradients
- 28. METHOD – OVERVIEW1. Down sample to 2. From coarse-to-fine, apply anisotropic create image Kawahara filter and merge the previous pyramid firstfK+1 New image fk = Merge (fk, upsample (Filter(fk+1, Jk+1))) Down UpfK sample sample tensor Jk := covariance matrix of gradients of fk New tensor Jk = Merge (gk, upsample (smooth(Jk+1)))
- 29. GRADIENTReplace (Gaussian derivatives and Sobel filter) with Jähne Filter Jähne Filter
- 30. STRUCTURE TENSOR 2nd eigen vector as image tangent
- 31. SMOOTH THESTRUCTURE OF TENSOR
- 32. Cal. v to min. err(local gradients, v) v x = =
- 33. = v(x) is the 1st eigen vector of local gradients vx The image tangent vector of x is vertical to v(x) The 2nd eigen vector is the image tangent vector
- 34. Taylor series If a = v2 min. c(x,y)Konstantinos G. Derpanis. “The Harris Corner Detector”. 2004
- 35. ANISOTROPYMEASURE anisotropic ellipse kernel A = 1 …. λ1>> λ2 isotropic circle kernel A = 0 …. λ1= λ2
- 36. ANISOTROPICKUWAHARA FILTERKernel of each sub-regionNew val. is sum ofmean of each sub-region weighted bythe inverse stdv. Add threshold to avoid artifacts and smooth results …. Why ?
- 37. Lower bound of stdv. to avoid1. Zero stdv. in flat region divided by zero2. Small differences in the stdv. in large low contrast region artifacts
- 38. MERGE BETWEEN SCALES1. Down sample to 2. From coarse-to-fine, apply anisotropic create image Kawahara filter and merge the previous pyramid firstfK+1 New image fk = Merge (fk, upsample (Filter(fk+1, Jk+1))) Down UpfK sample sample tensor Jk := covariance matrix of gradients of fk New tensor Jk = Merge (gk, upsample (smooth(Jk+1)))
- 39. MULTI-SCALE ESTIMATION –MERGE TENSOR f f K+1 K =Always prefer the more anisotropic tensor !ex2. Ak+1 = 0, Ak = 1 αk = 1 ~Jk = Jkex1. Ak+1 = 1, Ak = 0 αk = 0 ~Jk = Jk+1
- 40. MULTI-SCALE ESTIMATION –MERGE TENSOR f f K+1 KAlways prefer the more anisotropic tensor !
- 41. fK+1MULTI-SCALE fKFILTERING
- 42. fK+1fK
- 43. RESULT By C++, GLSL NVDIA GTX580 512x512 … 42 ms HD 720p (1280x720) .. 150 ms
- 44. (b) the fur above the nose is less abstracted than at the neck.very consistent strong abstraction wherelevel of abstraction slightly less abstraction above the nose
- 45. stronger contrast,
- 46. LIMITATIONFail to produce good-looking results parts above the plant are blended with the ground
- 47. LIMITATIONImages with high frequency texture is hard to abstract
- 48. CONCLUSION• Avoid artifacts and smooth results • By adding thresholding to the weighting term• Strong abstraction and avoidance of artifacts in large low-contrast regions • Coarse-to-fine from multi-scale image pyramids• Real-time processing on GPU
- 49. ANY QUESTION ?If the area of a sub-region in a Kuwahara filter is very verysmall, is it similar to a bilateral filter ? Kernel of 2D Kuwahara filter Sub-regionc can not too small Kernel of 1D bilateral filter
- 50. END

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