Title: MSE%20Approximation%20for%20model-based%20compression%20of%20multiresolution%20semiregular%20meshes
1MSE Approximationfor model-based compression of
multiresolution semiregular meshes
- Frederic Payan, Marc Antonini
I3S laboratory - CReATIVe Research
Group Universite de Nice Sophia Antipolis - FRANCE
13th European Conference on Signal Processing,
Antalya, Turkey, 2OO5
2Motivations
- Design an efficient wavelet-based lossy
compression method for the geometry of
semiregular meshes
- DWT discrete wavelet transform
- Q quantization
3Summary
4Wavelet transform
I. Background
Details
Details
Details
Details
One-level decomposition
- N-level multiresolution decomposition
- low frequency (LF) mesh connectivity geometry
- N sets of wavelet coefficients (3D vectors)
geometry
5Compression principle
I. Background
D
- Compression ? Optimization of the rate-distortion
(RD) tradeoff
R
- Multiresolution data ? how dispatching
pertinently the bits across the subbands in
order to obtain the highest quality for the
reconstructed mesh? - gt Solution bit allocation process
6Proposed bit allocation
I. Background
- find the set of optimal quantization steps
that minimizes the total distortion at one
user-given target bitrate . - Distortion criterion Mean Square Error
semiregular vertices
Quantized vertices
Number of vertices
7Problem statement
I. Background
- The distortion is measured on the vertices
(Euclidean Space) - The quantization is done on the coefficient
subbands (Transformed space)
In order to speed the allocation process up,
how expressing MSEsr directly from the
quantizationerrors of each coefficient subband?
8Summary
- Background
- MSE approximation for semiregular meshes
9Previous works
II. MSE approximation for semiregular meshes
- The MSE of data quantized by a wavelet coder can
be approximated by a weighted sum of the MSE of
each subband - The weights depend on the coefficients of the
synthesis filters - But shown only for data sampled on square grids
and not for the mesh geometry!
Challenge develop an MSE approximation for a
data sampled on a triangular grid
10II. MSE approximation for semiregular meshes
MSE approximation for meshes
- Triangular sampling
- Principle of a wavelet coder/decoder for meshes
LF coset (0)
HF coset 1
HF coset 2
HF coset 3
11Method global steps
II. MSE approximation for semiregular meshes
- We follow a deterministic approach
-
- quantization error ? additive noise
- We exploit the polyphase notations
with
Polyphase notation of the synthesis filters
the polyphase components
12Solution
II. MSE approximation for semiregular meshes
- For a one-level decomposition
- MSE approximation for a N-level decomposition
with
MSE of the coset i
with
13Model-based algorithm
II. MSE approximation for semiregular meshes
- Probability density Function of the coordinate
setsGeneralized Gaussian Distribution (GGD)
- gt Model-based algorithm
- Complexity 12 operations / semiregular vertex
- Example 0.4 second (PIII 512 Mb Ram)
- gt Fast allocation process
14Summary
- Background
- MSE approximation for semiregular meshes
- Experimental results
15Simulations
- Two versions of our algorithm are proposed
- for MAPS meshes Lifted butterfly scheme
- for Normal meshes Unlifted butterfly scheme
- Comparison with the zerotree coders PGC (for MAPS
meshes) and NMC (for Normal meshes) - Comparison criterion PSNR based on the Hausdorff
distance (computed with MESH)
16Curves PSNR-Bitrate for our MAPS Coder
17Curves PSNR-Bitrate for the Normal Coder
18Summary
- Background
- MSE approximation for semiregular meshes
- Experimental results
- Conclusion
19Conclusions
V. Conclusions and perspectives
- Contribution
- derivation of an MSE approximation for the
geometry of semiregular meshes - Interest
- fast model-based bit allocation optimizing the
quality of the quantized mesh
An efficient compression method for semiregular
meshes outperformingthe state of the art
zerotree methods(up to 3.5 dB)
20This is the end.
- My homepage
- http//www.i3s.unice.fr/fpayan/
21MSE approximation for meshes
II. MSE approximation for semiregular meshes
- Proposed MSE approximation is well-adapted for
the lifting schemes because the polyphase
components of such transforms depend on only the
prediction and update operators
22Geometrical comparison
IV. Experimental results
NMC (62.86 dB)
Proposed algorithm (65.35 dB)
Bitrate 0.71 bits/iv
23MSE of one subband i
III.Optimization of the Rate-Distorsion trade-off
MSE relative to the tangential components
MSE relative to the normal components
24Optimization of the Rate-Distorsion trade-off
III.Optimization of the Rate-Distorsion trade-off
- Objective
- find the quantization steps that maximize the
quality of the reconstructed mesh - Scalar quantization (less complex than VQ)
- 3D Coefficients gt data structuring?
25How solving the problem?
III.Optimization of the Rate-Distorsion trade-off
- Find the quantization steps and lambda that
minimize the following lagrangian criterion - Method
- gt first order conditions
26Solution
III.Optimization of the Rate-Distorsion trade-off
- Need to solve (2N 4) equations with (2N 4)
unknowns
PDF of the component setsGeneralized Gaussian
Distribution (GGD)gt model-based algorithm (C.
Parisot, 2003)
27Model-based algorithm
III.Optimization of the Rate-Distorsion trade-off
compute the variance and a for each subband
compute the bitratesfor each subband
?
Target bitratereached?
Look-up tables
new ?
compute the quantizationstep of each subband