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 : [email protected]
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