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