TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck...
-
Upload
reynard-floyd -
Category
Documents
-
view
213 -
download
0
Transcript of TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck...
![Page 1: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/1.jpg)
TER - ENSIMAG 2009
3D Regularization of Animated Surfaces
Simon Courtemanche
Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau
Team : EVASION Laboratories : INRIA, LJK
![Page 2: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/2.jpg)
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
![Page 3: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/3.jpg)
3D Regularization of Animated Surfaces
1. Type of Data
1.1 Mesh
M = { V, E, F }
Object File Format
![Page 4: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/4.jpg)
3D Regularization of Animated Surfaces
1. Type of Data
1.2 Animated surface
- sequence of meshes
Grimage Platform – INRIA
Extracting process :
![Page 5: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/5.jpg)
![Page 6: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/6.jpg)
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 !
![Page 7: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/7.jpg)
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)
![Page 8: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/8.jpg)
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
![Page 9: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/9.jpg)
3D Regularization of Animated Surfaces
3. Extension to mesh sequences
4D meshing
Closest points Isometric
4D Laplacian smoothing 3D static & dynamic techniques
![Page 10: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/10.jpg)
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
![Page 11: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/11.jpg)
3D Regularization of Animated Surfaces
Conclusion
Laplacian operator : spectral properties
My work : libraries, intuitive extensions
Future works : mesh registration with real videos
![Page 12: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/12.jpg)
![Page 13: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/13.jpg)
3D Regularization of Animated Surfaces
Acknowledgments
Thanks to :
- Estelle Duveau
- Franck Hétroy
- Lionel Revéret
- Maxime Tournier
![Page 14: TER - ENSIMAG 2009 3D Regularization of Animated Surfaces Simon Courtemanche Supervisors : Franck Hétroy, Lionel Revéret, Estelle Duveau Team : EVASION.](https://reader035.fdocuments.in/reader035/viewer/2022062806/56649ea15503460f94ba5000/html5/thumbnails/14.jpg)
3D Regularization of Animated Surfaces
Complements
Images by Knossow et al.