TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck...

TER - ENSIMAG 2009

3D Regularization of Animated Surfaces

Simon Courtemanche

Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau

Team : EVASION Laboratories : INRIA, LJK

3D Regularization of Animated Surfaces

Introduction

1. Type of Data

1.1 Mesh

1.2 Animated Surface

2. Laplacian operator

2.1 Definitions

2.2 Basic smoothing

2.3 Mesh reconstruction & smoothing

3. Extension to mesh sequences

3D Regularization of Animated Surfaces

1. Type of Data

1.1 Mesh

M = { V, E, F }

Object File Format

3D Regularization of Animated Surfaces

1. Type of Data

1.2 Animated surface

- sequence of meshes

Grimage Platform – INRIA

Extracting process :

3D Regularization of Animated Surfaces

2. Laplacian operator

2.1 Definitions

Relative or Differential or -coordinates

( Image by Olga Sorkine )

Degree matrix D D(i,i) = degree vertex i

Adjacency matrix A A(i,j) = 1 <=> (i,j) edge

Laplacian matrix L L = D – A

= L . X

L

large but sparse !

3D Regularization of Animated Surfaces

2. Laplacian operator

2.2 Basic smoothing

- eigenbasis of the Laplacian matrix

λ=0 (low frequence) λ=3 (high frequences)

3D Regularization of Animated Surfaces

2. Laplacian operator

2.3 Mesh reconstruction and smoothing

L-1 constraints + approximation

|| L.X ||2 : smoothness constraint

least-squares solving

3D Regularization of Animated Surfaces

3. Extension to mesh sequences

4D meshing

Closest points Isometric

4D Laplacian smoothing 3D static & dynamic techniques

3D Regularization of Animated Surfaces

3. Extension to mesh sequences

spatial coherent registration

Images from Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectorsby Knossow et al., Perception team, INRIA

3D Regularization of Animated Surfaces

Conclusion

Laplacian operator : spectral properties

My work : libraries, intuitive extensions

Future works : mesh registration with real videos

3D Regularization of Animated Surfaces

Acknowledgments

Thanks to :

- Estelle Duveau

- Franck Hétroy

- Lionel Revéret

- Maxime Tournier

3D Regularization of Animated Surfaces

Complements

Images by Knossow et al.