Wavelet-based Compression of 3D Mesh Sequences

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Wavelet-based Compression of 3D Mesh Sequences

• Frédéric Payan
• Coauthor Marc Antonini
• I3S laboratory - CReATIVe Research Group
• Universite de Nice Sophia Antipolis FRANCE

2nd ACIDCA-ICMI, Tozeur, Tunisia, november, 2005.
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Motivations

• Design a compression algorithm for mesh sequences
  (with a fixed connectivity).

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Problem Statement

• Raw representation set of irregular meshes
• Talking Face 10001 meshes of 539 vertices
• Each frame defined by the coordinates of its
  vertices
• VRML more than 137 Mb! Compression needed

. . . . .
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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Main Related Works
I. Background

• Principal component analysis (PCA) Alexa
  Müller (2000)
• exploit the temporal correlation of sequence
  geometry
• but very complex and long analysis step and
  efficient only when few shape deformations
• PCAlinear prediction coding (LPC) Karni
  Gotsman (2004)
• more efficient than PCA
• but same problem than PCA!
• Spatial multiresolution analysis Guskov
  Khodakovsky (2004)
• efficient to capture local shape deformations
• but less efficient when global deformations

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Contributions
I. Background

• Observation no temporal wavelet-based coder !
• Proposed approach
• Temporal lifting scheme
• to exploit the temporal coherence
• fast and low complex synthesis but also analysis
• Bit allocation process
• optimal coding

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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Lifting scheme principle
II. Proposed temporal lifting scheme

• 3 steps
• split gt two cosets
• Prediction operator gt set of details
• Update operator gt low frequency (LF) signal
• defined by a pair n,m

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Temporal Lifting scheme principle
II. Proposed temporal lifting scheme
TLS
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Temporal Lifting Scheme for mesh sequences
II. Proposed temporal lifting scheme

• Principle for each vertex, apply a 1D lifting
  scheme on its successive positions along the time
  axis

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Temporal Lifting Scheme for mesh sequences
II. Proposed temporal lifting scheme

• Example filter 2,0, with 2 levels of
  decomposition

Successive positions of the vertex V(i)
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Temporal Lifting Scheme for mesh sequences
II. Proposed temporal lifting scheme

• gt Multiresolution decomposition

time
Input sequence

First set of temporal details

h(1)(4)
h(1)(2)
h(1)(3)
h(1)(1)
Second set of temporal details

h(2)(1)
h(2)(2)

LF sequence
Decomposition level
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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Bit allocation principle
III. Bit allocation
D

• Compression optimize the rate-distortion
  tradeoff
• Multiresolution representation gt how dispatching
  the bits across the different sets of details ?

R
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Proposed bit allocation
III. Bit allocation

• Objective find the quantization steps (used to
  encode the different set of details) that
  minimize the MSE of the reconstructed mesh
  sequence for a user-given target bitrate.
• This problem can be modeled by

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How solving this problem?
III. Bit allocation

• Find the quantization steps and lambda that
  minimize the following lagrangian criterion
• Method first order conditions
• Algorithm iterative and model-based

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Overall coding scheme
III. Bit allocation
connectivity encoding
Sequence connectivity
MUX
1011
Entropy Coding
Temporal DWT
Geometry encoding
q
Bit Allocation
Target Bitrate

• SQ scalar quantization
• Connectivity encoding valence-based coder of
  Touma Gotsman

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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Distortion measure
III. Simulation results

• KG in 2 gt relative discrete L2-norm both in
  time and space
• with
• matrix G geometry of the sequence
• matrix hat G quantized geometry
• Matrix E(G) mean coordinates of each frame

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Different models!
III. Simulation results

• Talking face
• Few global motion
• Surprised chicken
• high global motion
• high local deformations
• Mad cow
• high global motion
• few local deformations

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Different lifting schemes
III. Simulation results

• Filter 4,2 less computing resources in time
  and memory

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Different numbers of decomposition
III. Simulation results

• high motion gt few decomposition levels (4)
• few motion gt a lot of decomposition levels (7)

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Comparison with
III. Simulation results

• TG (Touma Gotsman)
• Dynapack (Ibarria Rossignac)
• PCA (Alexis Müller)
• KG (PCALPC, Karni Gotsman)
• WCA (Guskov Khodakovsky)

on
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The talking face!
III. Simulation results

• few global motion

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the surprised chicken!
III. Simulation results

• high global motion and local deformations

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the mad cow!
III. Simulation results

• high global motion and few local deformations

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Summary

• Background
• Related works
• Contributions
• Proposed temporal lifting scheme
• Bit allocation
• Simulation results
• Conclusion perspectives

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Conclusions
IV. Conclusions and perspectives

• Temporal lifting scheme for mesh sequences
• simpler and faster than other analysis tools (for
  analysis and synthesis) like PCA
• Optimal encoding of the different subbands
• Model-based bit allocation
• gt Efficient and fast compression method for mesh
  sequences

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Perspectives
IV. Conclusions and perspectives

• Additional spatial multiresolution analysis on LF
  sequences
• Explicit motion estimation technique (like in
  video coding) ?
• should reduce geometry information
• transmit side information (motion vectors)

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This is the end

• My Email fpayan.i3s.unice.fr
• My webpage www.i3s.unice.fr/fpayan/
• Acknowledgement
• Microsoft Inc. For the surprised chicken
• D. Terzopoulos For the talking face
• Z. Karni for providing us with these data
• I. Guskov for providing us with mad cow
• Results extracted from
• paper of Z. Karni C. Gotsman
• provided by I. Guskov