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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.
