Multiresolution Signal Processing for Meshes

1
Multiresolution Signal Processing for Meshes

• Igor Guskov, Princeton University
• Wim Sweldens, Bell Labs
• Peter Schröder, Caltech

2
Meshes are important

• Progress in shape acquisition
• Meshes abound
• highly detailed
• Applications
• CAGD
• entertainment
• medicine

3
Processing

• Huge meshes are difficult to
• render
• store
• transmit
• edit
• Multiresolution is crucial

4
Multiresolution

• predict/subdivide

• downsample

• details/wavelets

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Regular Multiresolution

• downsample
• subdivision
• Catmull Clark 78Doo Sabin 78Loop 94
• wavelets
• Lounsbery 94 Eck et al 95 Schröder Sweldens
  95

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Irregular Multiresolution

• downsample
• mesh simplification
• progressive meshHoppe 96
• Garland Heckbert 97
• many others
• subdivision, wavelets ??

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Our contribution

• subdivision on irregular hierarchies
• multiresolution toolbox for meshes
• applications

8
Related work

• Taubin 95 - irregular
• signal processing
• Zorin et al. 97 - regular
• Burt-Adelson pyramid
• Kobbelt et al. 98 - irregular
• multiresolution editing

9
Our approach

• Novel smoothing operation
• smoothes geometry
• preserves sampling

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Scalar setting
f1
f(u,v)
f3
f0
f2
v
u
1
e
3
2
0
Second difference
D2f(e) ? f 0,1,2 - ? f 1,2,3
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Relaxation
minfi Sedges D2f2

• Properties
• local linear functional
• coefficients depend on (u,v)-areas and edge
  lengths
• preserves f A B u C v

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Relaxation 3d

• Original mesh plays two roles
• source of local (u,v)
• data

x
y
z
13
Smoothing
14
Enhance
smoothed 2 (original - smoothed) enhanced
15
Subdivision scheme
Runs on top of the progressive mesh reconstruction

• edge uncollapse

• predict position of the new vertex using
  relaxation

• update positions of its neighbors using
  relaxation

16
Rabbit Simplify Subdivide
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Multiresolution Pyramid
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Filtering
19
Preserving Sampling
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Multiresolution Enhance
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Editing
22
Sitting Horse
23
Edit Enhance
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• Conclusion
• multiresolution toolbox on progressive mesh
  hierarchies
• Future work
• compression
• genus changing
• tetrahedralizations

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Design Khrysaundt Koenig
ivguskov_at_cs.caltech.edu
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reconstruction
Smooth
27
Parameterization
Local
28
Multi-resolution Enhance