Multiresolution Analysis of Irregular Meshes with Multiple Attributes

Multiresolution Analysis of Irregular Meshes with Multiple Attributes Michaël Roy

3 D Models High quality 3 D models High density meshes High resolution textures Available ressources are always constrained CPU, space, graphics speed, network bandwidth We need an efficient mesh representation 2

Motivations (1) Level of Detail Representation Adaptive representation Varies with context Picture of the original object Level 0 117, 564 faces (initial scan) Level 5 25, 100 faces Level 10 5, 232 faces Level 15 1, 066 faces Level 20 212 faces 3

Motivations (2) Multiresolution Analysis Space / Frequency analysis of 3 D models Filtering min max Small scale detail: high frequency Large scale detail: low frequency 4

V 0 V 1 V 2 V 3 W 1 W 2 W 3 Vi Approximation Wi Details Analysis (Decomposition) Synthesis (Reconstruction) Wavelet Transform (1) 5

Wavelet Transform (2) Decomposition A 0 V 0 A 1 V 1 B 0 V 2 Vj-1 B 1 Aj-1 Vj Bj-1 W 1 Wj W 2 Reconstruction Vj Wj Pj Qj Vj-1 W 1 Pj-1 Qj-1 Vj-2 V 1 Wj-1 P 1 V 0 Q 1 6

Previous Work (1) Coarse-to-fine hierarchies Lounsbery 1995 Multiresolution for surface of arbitrary topological type Zorin 1997 Interactive Multiresolution Mesh Editing 7

Previous Work (2) Fine-to-coarse hierarchies Bonneau 1998 Multiresolution Analysis on Irregular Meshes Guskov 1999 Multiresolution Signal Processing for Meshes 8

Multiresolution Analysis Framework 3 D model with attributes Level of detail representation Detail extraction Multiresolution Analysis Multiresolution model Intelligent visualization Filtering Denoising Characterisation 9

Level of detail representation Simplification Level 0 117, 564 faces Level 5 25, 100 faces Level 10 5, 232 faces Level 15 1, 066 faces Level 20 212 faces Subdivision 10

Progressive Mesh (Hoppe 1996) Edge contraction Vertex split M 0 econ 0 vsplit 0 M 1 econ 1 vsplit 1 . . . econj-2 vsplit j-1 M j-2 econj-1 vsplitj-1 Mj 11

Progressive Mesh (Hoppe 1996) Edge contraction Vertex split Pro: Nested mesh hierarchy Vj Vj-1 . . . V 1 V 0 12

Progressive Mesh (Hoppe 1996) Edge contraction Vertex split Con: only one vertex removed per level 13

Global Downsampling Create distinct levels of detail Select an independent set of vertices and remove them by a serie of edge contractions Fine mesh Select vertices to remove Coarse mesh 14

Detail Computation Details are the difference between a fine mesh and a smoothed version of that mesh Original Smoothed Difference 15

Surface Relaxation Smooth the surface using a relaxation operator minimizing the curvature 16

Attribute Details What about the attributes ? Attribute details are the difference between the attributes of a fine mesh and the smoothed attributes of that mesh Original Smoothed Difference 17

Surface Attribute Relaxation Smooth the attributes using a relaxation operator minimizing the curvature Assume the attributes are linked to the surface 18

Multiresolution Mesh Decomposition Fine model with attributes Vertex Selection Simplification Attribute Surface Relaxation + Coarse model _ Details 19

Multiresolution Mesh Reconstruction Coarse model Details Subdivision Attribute Surface Relaxation + + Fine model 20

Applications 3 D model with attributes Level of detail representation Detail extraction Multiresolution Analysis Multiresolution model Intelligent visualization Filtering Denoising Characterisation 21

Filtering 22

Denoising (1) We extend the concept of soft thresholding (AKA wavelet shrinkage) to 3 D multiresolution model 23

Denoising (2) Initial model Laplacian smoothing Soft thresholding 24

Denoising (3) 25

Characterization (1) Thresholding the detail allows highlight of important features of a model 26

Characterization (2) Impulse Noise Detection Impulse noise Geometric analysis Normal analysis Noise detection 27

Intelligent Visualization (1) Level Vs Threshold Reconstruction Threshold reconstruction selects vertices according to their details 28

Intelligent Visualization (2) 131 242 faces (6. 8 MB) 36 772 faces (1. 9 MB) 29

Intelligent Visualization (3) Initial model (73. 000 faces) Level reconstruction (17. 000 faces) Threshold reconstruction (16. 000 faces) 30

Conclusion Multiresolution decomposition for irregular meshes with attributes Global downsampling Attribute surface relaxation Applications Filtering Denoising using soft thresholding Characterization / feature detection Adaptive reconstruction 31

Future Work Improve characterization Use the angle between the normal and the detail vector Visualization of meshes with multiple attributes Management of multiple attributes Investigation for better detail metrics e. g. HSI space for colors 32

Multiresolution Mesh Analysis Thank you for your attention ! Questions ? 33