1. TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION Laboratories : INRIA, LJK

2. 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

3. 3D Regularization of Animated Surfaces 1. Type of Data 1.1 Mesh M = { V, E, F } Object File Format

4. 3D Regularization of Animated Surfaces 1. Type of Data 1.2 Animated surface - sequence of meshes Grimage Platform – INRIA Extracting process :

6. 3D Regularization of Animated Surfaces 2. Laplacian operator 2.1 Definitions Relative or Differential or -coordinates ( Image by Olga Sorkine ) Degree matrix DD(i,i) = degree vertex i Adjacency matrix AA(i,j) = 1 (i,j) edge Laplacian matrix LL = D – A = L. X L large but sparse !

7. 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)

8. 3D Regularization of Animated Surfaces 2. Laplacian operator 2.3 Mesh reconstruction and smoothing L-1L-1 constraints + approximation || L.X || 2 : smoothness constraint least-squares solving

9. 3D Regularization of Animated Surfaces 3. Extension to mesh sequences 4D meshing Closest points Isometric 4D Laplacian smoothing3D static & dynamic techniques

10. 3D Regularization of Animated Surfaces 3. Extension to mesh sequences spatial coherent registration Images from Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors by Knossow et al., Perception team, INRIA

11. 3D Regularization of Animated Surfaces Conclusion Laplacian operator : spectral properties My work : libraries, intuitive extensions Future works : mesh registration with real videos

13. 3D Regularization of Animated Surfaces Acknowledgments Thanks to : - Estelle Duveau - Franck Hétroy - Lionel Revéret - Maxime Tournier

14. 3D Regularization of Animated Surfaces Complements Images by Knossow et al.