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Semi-regular 3D mesh progressive compression and transmission based on
an adaptive wavelet decomposition
21st January 2009
Wavelet Applications in Industrial Processing VIIS&T/SPIE Symposium on Electronic Imaging
C. ROUDET, F. DUPONT & A. BASKURTcroudet, fdupont, abaskurt @liris.cnrs.fr
2
Context
3D objects Used in various applications Lots of different models
Triangular meshes More and more detailed Adapted to heterogeneous resources Irregularly sampled
3
Triangular meshes
4 bytes x3 coordinates
4 bytes x3 indexes
Mesh regularity Link to vertex valence (σ)
V : {Vi = (xi, yi, zi) є R3 / 0 ≤ i <|V|}
F : {Fi = j, k, l є Z3 / 0 ≤ i <|F|}
I - Context II - WT III – Our approach IV - Results
irregular regularsemi-regular
Mesh M = (V, F)
Geometry
Connectivity
Triangular mesh36 bytes / vertex288 bits / vertex
3 types of meshes :1. irregular
2. semi-regular : W V | Vi ,Vj є W : σ(Vi ) ≠ σ(Vj )
3. regular : Vi ,Vj є V : σ(Vi ) = σ(Vj )
∩
4
Progressive representations
Advantages : Efficient rendering Data adapted to heterogeneous devices and networks
Various possible representations : Subdivision surfaces [Doo & Sabin, 78] + wavelets [Lounsbery, 97] ≈ 2 - 4 bits / v
Irregular refinements [Hoppe, 96], [Gandoin & Devillers, 02] ≈ 2 bytes / v
5
Multiresolution analysis
L 2
H
L
L H
1/4 1/2 f
L
H
L
H
L
H
…
details details details
M0Mm-
1
Mm
H
[½ ½]
[1 -1]
2
2 2
2 2
2
2
2 2
6
Geometric wavelets
Filter bank generalization Spatial multiresolution analysis
Advantages : Reduce computation costs Simplified filters Analysis & synthesis in linear time
[Sweldens, 95]
[Lounsbery, 97]
S : Split
P : Predict
U : Update
reconstructedsignal
coarsesignal
details
signal
even
odd
[Mallat, 89]
coarsesignal
details
signal reconstructedsignal
7
MnMn-1
On meshes Update
Predict
even
odd
coarsesignal
details
reconstructedsignal
8
Overview of our approach
CHANNEL
Globalanalysis
Multiresolutionsegmentation
Localanalysis
Localencoding
Localdecoding
binaryflow
Remesh
waveletcoefficients
irregular 3Dmodel
semi-regular3D model
clusterspatches
Coarsegluing
Localsynthesis
binaryflow
resolution levels
Visualization
Classification
9
An-3
Mn
An-2
An-1 Dn-1
Dn-2
Dn-3
Multiresolution representation
Level n-1 Level n-2 Level n-3 Level n-1…Level noriginal
112 642 vertices 28 162 vertices 7 042 vertices 1 762 vertices
Multiresolution weighting
0 1
Wavelet magnitude
x10
10
Classification and region growing
Magnitude
Pol
ar a
ngle
vertices
Classification (K-means)2 clusters
Magnitude
Pol
ar a
ngle
Magnitude
Polar angle
vertices facets
K=2
Regiongrowing
Globalanalysis
Level noriginal
Level n-1 Level n-1
11
Cluster « coarse » projection
Coarse projection Region extraction
Level n (original)Level n-1 Level n-5
Level n-2 … Level n-4 Level n-5
Fine projection
t0t2
12
Cluster « fine » projection
Initial classification
Level n-2Level n-4 …Level n-5
Coarse projection Region extraction
Level n (original)Level n-1 Level n-5
Fine projection
13
14
Different possible segmentations
Multiresolution weighting on the finest approximation + « coarse » & « fine » projections
Multiresolution weighting on the coarsest level + « fine » projection
5 regions
6 regions6 regions
5 regions
11 regions
9 regions
15
Independent analysis and coding
CHANNEL
+ Coding of partitioning information : nb regions, cluster type, filters used, … : losslessly compressed
zerotree
Connectivity Arithmeticcoding
symbollist
00110101
Quantization110110
Geometry [Touma & Gotsman, 98]
…
[Khodakovsky et al., 00]
Arithmeticcoding
Arithmeticcoding
symbollist
Quantization
[Touma & Gotsman, 98]
Arithmeticcoding
Connectivity
Geometry
01010001
100101
16
Global vs local analysis
PSNR = 20.log10 BBdiag / d BBdiag = Bounding Box diagonal d = Hausdorff distance
Rate / distortion curves(unique prediction scheme used)
Local analysis (2nd weighting)
additional cost
Local analysis (1st weighting)
Global analysis
Remeshing error
Bitrate (bits / irregular vertex)
17
Progressivity of the reconstruction
0,23 bit / vertex 0,68 bit / vertex 1,66 bit / vertex 6,54 bit / vertex
18
Other applications
Adaptive denoising & watermarking View-dependent transmission & reconstruction (ROI)Error-resilient coding
e : error (x 10-4)
Globalanalysis
ClassificationAdaptive reconstructions:with prédiction without
554 KBe: 0,203
36% rough 218 KBe: 10,3
218 KBe: 17,4
11 967 bytes
5 181 bytes
19
Conclusion and future work
Adaptive multiresolution framework Used to propose view-dependent transmission & visualization Based on a multiresolution segmentation Patch-independent analysis, quantization & encoding
Future work: Design new prediction schemes adapted to non-smooth regions Optimize patch-quantization and binary allocation