UMR 5205

C. ROUDET F. DUPONT A. BASKURTLaboratoire d'InfoRmatique en Image et Systèmes d'information

UMR5205 CNRS/INSA de Lyon/Université Claude Bernard Lyon 1/Université Lumière Lyon 2/Ecole Centrale de Lyon,Université Claude Bernard Lyon1 - Bâtiment Nautibus, 8 boulevard Niels Bohr - 69622 Villeurbanne Cedex, France

http://liris.cnrs.frTel: +33 4 26 23 44 64 ; fax: +33 4 72 43 15 36 ; e-mail : croudet@liris.cnrs.fr

Conclusion and future work

The wavelet coefficients norm and polar angle are relevant measures to reflect the 3D objects surface roughness

The boundaries of the segmented regions could be improved by considering the high discrete curvatures

The produced hierarchy of segmentations are of particular interest for adaptive mesh compression, denoising and watermarking where different marks or wavelets could be applied according to the visual aspect of the surface

Objectives of this studyMesh segmentation based on multiresolution (MR) analysis Distribution of the wavelet coefficients used to reflect the

roughness of the surface Series of segmentations for all meshes resulting from the

wavelet decomposition

General objectivesImprove the QoS during the exchange of 3D data

Resources : adapt to the heterogeneity of the terminals and networks involved

Waitings : allow user interaction with 3D objects, transmitted at his/her request

Propose a new scalable and adaptive compression scheme

Multiresolution mesh segmentation based on

surface roughness and wavelet analysis

Related work in MR analysis & mesh segmentation

Existing scalable compression methods apply a global wavelet decomposition (same scheme & quantization on the entire surface)

Most mesh segmentation algorithms are based on the discrete curvature computed in each vertex

Experimental results

The produced histograms reveal a non uniform distribution

The distribution of the wavelet coefficients norm is comparable to the one obtained from discrete curvature tensors

The Butterfly analysis provides a better differentiation between the smooth and rough parts than the midpoint one

The Butterfly analysis is on the other hand less revealing with regard to the polar angle distribution

It can be explained because the Normal remesher uses the Butterfly scheme

The distribution of the polar angle, ranging from 0° to 180°, tends to emphasize the high curvatures

The classification in 2 clusters has given the best results

The high frequencies are globally well partitioned The results could be improved by considering a propagation of the roughness

into all the resolution levels

Proposed method

Global MR analysis with subdivision wavelets & the lifting scheme Study of the decomposition produced with various prediction operators

Mesh segmentation in surface patches with different roughness Vertices classified in K clusters according to their roughness value Connex groups of triangles produced by region growing & merging algorithms

Keywords : Mesh segmentation, classification, multiresolution analysis, geometric wavelets, lifting scheme, region growing, region merging.

Analysis of the high-frequency details on the Venus head model

Midpoint analysis(Normal mesh)

Midpoint analysis(MAPS)

Butterfly analysis(Normal mesh)

Midpoint analysis(Normal mesh)

Butterfly analysis(Normal mesh)

Midpoint analysis(Normal mesh)

Midpoint analysis(MAPS)

Resulting K-Means(2 clusters)

Resulting 10connex patches

Original semi-regular mesh (327 680 faces)

Resulting 10connex patches

Log of coefficients norm (x5)

Log of coefficients polar angle (α)

Min Max

Classification and segmentation based on the wavelet coefficients norm and polar angle(Second resolution level : 20 480 faces - Midpoint analysis – Normal mesh)

Normalized distribution of the wavelet coefficients norm and polar angle (2nd resolution level)

Roughness

Standard deviation of the discrete curvature

even

odd

Coarser mesh

Wavelet coefs

+

Butterfly scheme

Extraordinary points

Mesh segmentation scheme based on multiresolution analysis

0° ≤ α ≤ 90° 0° ≤ α ≤ 180°

UPDATE

REMESH

SPLIT

PREDICT

+

Norm value x5 – Midpoint analysis – Normal mesh 0° ≤ polar angle ≤ 90° – Midpoint analysis – Normal mesh 0° ≤ polar angle ≤ 180° – Midpoint analysis – Normal mesh

K-MEANS

REGION GROWING

REGION MERGING

Clusters

Connex surface patches

ψm

0, lazy

ψ0, lift

m

φm

0m1

φ

0-ring update

ψ

φ

φ φ

φ

01

2

3