Mesh Denoising via L 0 Minimization Lei He Scott Schaefer Texas - - PowerPoint PPT Presentation

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Mesh Denoising via L 0 Minimization Lei He Scott Schaefer Texas - - PowerPoint PPT Presentation

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Mesh Denoising via L 0 Minimization Lei He Scott Schaefer Texas A&M University Surface Denoising Related Work [Vollmer et al. 1999] [Desbrun et al. 1999] [Kim et al. 2005] [Nealen et al. 2006] [Clarenz et al. 2000] [Bajaj and Xu

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Mesh Denoising via L0 Minimization

Lei He Scott Schaefer Texas A&M University

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SLIDE 2

Surface Denoising

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SLIDE 3

Related Work

[Desbrun et al. 1999] [Vollmer et al. 1999] [Nealen et al. 2006] [Kim et al. 2005] [Clarenz et al. 2000] [Bajaj and Xu 2003] [Hildebrandt et al. 2004] [Tasdizen et al. 2002] [Yagou et al. 2002] [Fleishman et al. 2003] [Jones et al. 2003] [Zheng et al. 2012]

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SLIDE 4

Related Work

[Desbrun et al. 1999] [Vollmer et al. 1999] [Nealen et al. 2006] [Kim et al. 2005] [Clarenz et al. 2000] [Bajaj and Xu 2003] [Hildebrandt et al. 2004] [Tasdizen et al. 2002] [Yagou et al. 2002] [Fleishman et al. 2003] [Jones et al. 2003] [Zheng et al. 2012]

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SLIDE 5

Related Work

[Desbrun et al. 1999] [Vollmer et al. 1999] [Nealen et al. 2006] [Kim et al. 2005] [Clarenz et al. 2000] [Bajaj and Xu 2003] [Hildebrandt et al. 2004] [Tasdizen et al. 2002] [Yagou et al. 2002] [Fleishman et al. 2003] [Jones et al. 2003] [Zheng et al. 2012]

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SLIDE 6

Motivation

[Xu et al. 2011]

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SLIDE 7

L0 Norm

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L0 Minimization for Images

[Xu et al. 2011]

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SLIDE 9

L0 Minimization for Images

auxiliary variables

[Xu et al. 2011]

> 1, for L=0,1,2,…

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SLIDE 10

L0 Minimization for Images

  • Fix , update locally
  • Fix , update globally
  • Increment

[Xu et al. 2011]

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SLIDE 11

L0 Minimization for Images

[Xu et al. 2011]

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SLIDE 12

L0 Minimization for Images

piecewise constant images!

[Xu et al. 2011]

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SLIDE 13

L0 Minimization for Images

[Xu et al. 2011]

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SLIDE 14

L0 Minimization for Surfaces

?

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SLIDE 15

L0 Minimization for Surfaces

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SLIDE 16

L0 Minimization for Surfaces

  • Properties of
  • a discrete linear operator
  • measure planarity
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SLIDE 17

Discrete Differential Operator

  • When are planar,
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Discrete Differential Operator

A

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Discrete Differential Operator

  • When are planar,
  • Vertex-based cotangent operator
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Discrete Differential Operator

  • When are planar,
  • Vertex-based cotangent operator
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SLIDE 21

Discrete Differential Operator

  • When are planar,
  • Vertex-based cotangent operator

[Pinkall and Polthier 1993]

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Discrete Differential Operator

input surface vertex-based cotangent operator cotangent edge operator area-based edge operator

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Discrete Differential Operator

  • When are planar,
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Discrete Differential Operator

  • When are planar,
  • Edge-based cotangent operator
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SLIDE 25

Discrete Differential Operator

  • When are planar,
  • Edge-based cotangent operator

[Bergou et al. 2006]

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SLIDE 26

Discrete Differential Operator

input surface vertex-based cotangent operator cotangent edge operator area-based edge operator

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SLIDE 27

Discrete Differential Operator

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SLIDE 28

Discrete Differential Operator

  • When are planar,
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SLIDE 29

Discrete Differential Operator

  • When are planar,
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Discrete Differential Operator

  • When are planar,
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SLIDE 31

Discrete Differential Operator

  • When are planar,
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SLIDE 32

Discrete Differential Operator

  • When are planar,
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SLIDE 33

Discrete Differential Operator

input surface vertex-based cotangent operator cotangent edge operator area-based edge operator

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Regularization

ground truth noisy input without regularization With regularization

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Regularization

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Regularization

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Regularization

ground truth noisy input without regularization with regularization

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Optimization

> 1, for L=0,1,2,…

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Optimization

> 1, for L=0,1,2,…

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Parameters

input mesh increase

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Parameters

ground truth noisy input decrease

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Results

[Desbrun et al. 1999] [Vollmer et al. 1999] [Nealen et al. 2006] [Kim et al. 2005] [Clarenz et al. 2000] [Bajaj and Xu 2003] [Hildebrandt et al. 2004] [Tasdizen et al. 2002] [Yagou et al. 2002] [Fleishman et al. 2003] [Jones et al. 2003] [Zheng et al. 2012]

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SLIDE 43

Results

[Desbrun et al. 1999] [Vollmer et al. 1999] [Nealen et al. 2006] [Kim et al. 2005] [Clarenz et al. 2000] [Bajaj and Xu 2003] [Hildebrandt et al. 2004] [Tasdizen et al. 2002] [Yagou et al. 2002] [Fleishman et al. 2003] [Jones et al. 2003] [Zheng et al. 2012]

PMC BNF BF MF

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SLIDE 44

Results

noisy input BF PMC MF BNF

  • ur result
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Results

noisy input BF PMC MF BNF

  • ur result
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Results

noisy input BF PMC MF BNF

  • ur result
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SLIDE 47

Results

noisy input BF PMC MF BNF

  • ur result
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Results

noisy input BF PMC MF BNF

  • ur result
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SLIDE 49

Results

noisy input

  • ur result
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SLIDE 50

A failure case

ground truth

  • ur result

noisy input