1. UMR 5205 C. ROUDETF. DUPONTA. BASKURT Laboratoire 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.fr Tel: +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 study Mesh 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 objectives Improve 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 10 connex patches Original semi-regular mesh (327 680 faces) Resulting 10 connex 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 (2 nd 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° UPDATEUPDATE REMESHREMESH SPLITSPLIT PREDICTPREDICT + 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 ψ m 0, lazy ψ 0, lift m φ m 0 m 1 φ 0-ring update ψ φ φφ φ 0 1 2 3