Bilateral Mesh Denoising

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Bilateral Mesh Denoising

• Shachar FleishmanIddo DroriDaniel Cohen-Or
• Tel Aviv University

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Denoising

• Input (scanned) model
• Additive noise

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Denoising

• Input (scanned) model
• Additive noise
• Noise free model
• Preserve features

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Image denoising

• Wavelet denoising Donoho 95
• Anisotropic diffusion Perona Malik 90
• 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

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Original and noisy ( ?2900) images
Images courtesy of Michael Elad
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TV filtering 50 iterations 10
iterations (MSE146.3339)
(MSE131.5013)
Images courtesy of Michael Elad
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Wavelet Denoising (soft) Using DB5 Using
DB3 (MSE144.7436)
(MSE150.7006)
Images courtesy of Michael Elad
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Images courtesy of Michael Elad
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Mesh denoising, smoothing and fairing

• Adapt image denoising algorithms to meshes
• Wiener filter Peng et al. 01
• Isotropic diffusion Desbrun et al. 99
• Anisotropic diffusion of height fields Desbrun
  et al. 00
• Anisotropic diffusion on meshes Clarenz et al.
  00, Xu Bajaj 03
• Bilateral filter Choudhury Tumblin 03 Jones
  et al. 03

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Bilateral mesh denoising

• Fast
• Simple
• Intuitive parameter selection

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Bilateral filtering

• Gaussian filter

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Bilateral filtering
Denoise
Feature preserving

• Bilateral filter

Normalization
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Bilateral filtering of meshes
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Bilateral filtering of meshes
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Bilateral filtering of meshes

• Height above surface is equivalent to the gray
  level values in images

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Bilateral filtering of meshes

• Height above surface is equivalent to the gray
  level values in images
• Apply the bilateral filter to heights

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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

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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

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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

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Solution

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

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Solution

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

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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

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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
v
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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
iterate over neighborhood
v
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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
closeness
v
q
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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
height similarity
v
q
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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
v
weights
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DenoisePoint(Vertex v, Normal n) qi
neighborhood(v) Kqi sum0 normalizer0 fo
r i 1 to K t v-qi h
ltn,v-qigt Wcexp(-t2/(2sc2)) Wsexp(-h2/(2ss2))
Sum (wcws)h Normalizer
wcws End Return vn(sum/normalizer)
v
Move the vertex in the normal direction
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Parameters

• The two parameters to the weight function sc, ss
• Interactively select a point p and the
  neighborhood radius ?
• sc 1/2 ?
• ss stdv(Nbhd(p, ?))
• Number of Iterations

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Robustness

• Sharp features are treated as outliers

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Robustness

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

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Results
Bilateral mesh denoising
Anisotropic denoising of height fields - Desburn
00
Source
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Results
Anisotropic Geometric Diffusion in Surface
Processing - Clarenz 00
Bilateral mesh denoising
Source
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Results
Two iterations
Five iterations
Source
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(No Transcript)
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Future Work

• Adapt the algorithm to point sets
• Robust estimator of normals

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Acknowledgements

• Models and images courtesy of Jean-Yves Bouguet,
  Mathieu Desbrun, Alexander Belyaev, Christian
  Rossl from Max Planck Insitut fur Informatik, Udo
  Diewald and Michael Elad
• Israel Science Foundation funded by the Israel
  Academy of Sciences and Humanities
• Israeli Ministry of Science
• A grant from the German Israel Foundation (GIF).

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Input
Bilateral mesh denoising
Non-iterative, Feature Preserving Mesh smoothing
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Bilateral mesh denoising
Non-iterative, Feature Preserving Mesh smoothing
Source
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Bilateral mesh denoising
Non-iterative, Feature Preserving Mesh smoothing
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Comparison - predictors
Bilateral mesh denoising
Non-iterative, Feature Preserving Mesh smoothing
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New results
Bilateral mesh denoising
Extended Bilateral mesh denoising