modelling of human faces - homepages.laas.frhomepages.laas.fr/adoncesc/wavelet/surface.pdf · the...
TRANSCRIPT
![Page 1: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/1.jpg)
Modelling of Human Faces Andrei Doncescu Jean-Paul Gourret
Laboratoire d’Informatique et d’Imagerie Industrielle University of La Rochelle
FRANCE
![Page 2: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/2.jpg)
The construction of a completely 3D system of subdivision- compression
applied to the points which are 3-connected
![Page 3: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/3.jpg)
P
P1
P2 P3
uses 1-D finite elements 3-connected
The modal analysis gives a number of rigid modes equal to the number of 1-D finite elements assembled to define the face
We avoid the extraordinary points
These organisation of the points allows us an algorithm to obtain the numbering of the vertices at
each level of subdivision
![Page 4: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/4.jpg)
1. L’analyse modale donne un nombre de modes rigides égal au nombre d’éléments assemblés pour définir une surface. Les modes rigides combinés avec le premier mode non-rigide conduisent à l ’obtention d’un modèle moyen appelé PORTRAIT ROBOT
2. Si la connexité uniforme n’est pas respectée, dans le voisinage des points singuliers, le calcul de déformation n’est pas homogène et un CALCUL RECURSIF DE SUBDIVISION est DIFFICILE.
![Page 5: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/5.jpg)
Example of surfaces 3-connected : The Fullerenes
C432
Star-Shaped
![Page 6: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/6.jpg)
Maillage 3-connexe sur un tore
C432
![Page 7: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/7.jpg)
Plan
• Présentation de la transformée en ondelettes • Subdivision par les ondelettes géométriques • Compression des surfaces maillées en 3-connexe • Applications
![Page 8: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/8.jpg)
to have a reversible transform
To modify the detail allowing us to obtain new objects
![Page 9: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/9.jpg)
LA TRANSFORMATION D ’INFORMATION
• La transformation de Fourier (fréquence)
• La transformation de Fourier à fenêtre (temps - fréquence)
• La transformation en ondelettes (temps - échelle)
• Les ondelettes de Malvar (temps - fréquence - échelle)
• Les paquets d ’ondelettes (temps - fréquence)
• Matching Pursuits (temps - fréquence - échelle)
![Page 10: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/10.jpg)
![Page 11: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/11.jpg)
La construction de T. DeRose
![Page 12: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/12.jpg)
Subdivision
![Page 13: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/13.jpg)
• La deuxième génération des ondelettes obtenue par l’algorithme de lifting dans le domaine spatial
• L’applications des ondelettes pour la subdivision et la compression 3D en utilisant les bancs des filtres
![Page 14: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/14.jpg)
La subdivision de Sweldens et Schroder
• Construction de l’algorithme « lifting » • Construction des ondelettes bio-orthogonales « lazy » • Application sur une sphère
![Page 15: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/15.jpg)
Subdivision
![Page 16: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/16.jpg)
La sphère ?
• représente un solide avec l’énergie zéro de déformation
• utilisée dans les algorithmes d’éclairage • utilisée pour la projection radiale
![Page 17: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/17.jpg)
Les différentes méthodes de subdivision
• Khamlichi-Gourret • Doncescu-Gourret
![Page 18: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/18.jpg)
Avantage :
côtés
approximativement égaux
Inconvénient :
les barycentres ne sont pas conservés
![Page 19: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/19.jpg)
La subdivision par insertion des barycentres
![Page 20: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/20.jpg)
• Linéarisation de la rotation
• Rotation
![Page 21: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/21.jpg)
Première étape : rotation-contraction
![Page 22: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/22.jpg)
Construction d ’un hexagone devant chaque noeud
Deuxième étape : contraction
![Page 23: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/23.jpg)
![Page 24: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/24.jpg)
Subdivision des surfaces 3-connexe en utilisant la base de Haar
![Page 25: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/25.jpg)
Le résultat de la subdivision par la base de Haar
Sphère : niveau 3 de subdivision Sphère : niveau 4 de subdivision
![Page 26: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/26.jpg)
Construction des filtres associés à une base
d’ondelettes
![Page 27: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/27.jpg)
![Page 28: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/28.jpg)
![Page 29: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/29.jpg)
![Page 30: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/30.jpg)
L’erreur de reconstruction
![Page 31: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/31.jpg)
L’erreur de reconstruction pour a=0.017
![Page 32: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/32.jpg)
Le module du filtre passe-haut G pour a=0.017
![Page 33: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/33.jpg)
Le module du filtre passe-bas H pour a=0.017
![Page 34: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/34.jpg)
Les fonctions ϕ et ψ obtenues par l’algorithme en cascade
![Page 35: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/35.jpg)
Implémentation
![Page 36: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/36.jpg)
![Page 37: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/37.jpg)
![Page 38: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/38.jpg)
![Page 39: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/39.jpg)
12 pentagones
Les hexagones
La construction des nouveaux
hexagones
![Page 40: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/40.jpg)
Le niveau 3 de subdivision
Le niveau 4 de subdivision
![Page 41: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/41.jpg)
Subdivision par les ondelettes rotationnelles
![Page 42: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/42.jpg)
![Page 43: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/43.jpg)
• HTH + GTG=I • GHT = HGT = 0 • HHT = GGT = I
• HT RT R H + GT RT R G=I
![Page 44: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/44.jpg)
![Page 45: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/45.jpg)
Level 3 of subdivision
Level 4 of subdivision
Subdivision using rotational wavelets
![Page 46: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/46.jpg)
Construction de la base de données
![Page 47: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/47.jpg)
• V0 = 20 ( level 0)
• V1= 60 (level 1) • Vi = 3 * Vi-1 = 20 * 3i ( level i) • Pi = 12 ( level i) • H0 = 0 ( level 0)
• H1 = 20 (level 1) • Hi = Hi-1 + Vi-1 = 10 ( 3i-1) ( level i) • Ei = 10*3i+1 ( level i)
Vertices
Hexagons
Edges
Pentagons
![Page 48: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/48.jpg)
![Page 49: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/49.jpg)
Vertices Numbering
![Page 50: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/50.jpg)
Construction de la numérotation des points
Construction de la nouvelle liste
![Page 51: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/51.jpg)
L ’organisation du fichier contenant les points
![Page 52: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/52.jpg)
La transformée inverse
![Page 53: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/53.jpg)
The Inverse Transform
Originality : 3 LEVELS OF SUBDIVISION
Level i
Level i+1
Level i+2
![Page 54: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/54.jpg)
![Page 55: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/55.jpg)
![Page 56: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/56.jpg)
Modélisation du visage par le maillage 3-connexe
![Page 57: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/57.jpg)
![Page 58: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/58.jpg)
![Page 59: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/59.jpg)
![Page 60: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/60.jpg)
N=6
N=7
![Page 61: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/61.jpg)
Ns=6
Ns=7
TD
TI
![Page 62: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/62.jpg)
![Page 63: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/63.jpg)
Modification du détail pour des objets 3D
![Page 64: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/64.jpg)
Signal obtained by combination of resumes from Signal1 with
details of Signal2
New signal
![Page 65: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/65.jpg)
![Page 66: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/66.jpg)
Detail Modification resume
details
![Page 67: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/67.jpg)
![Page 68: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/68.jpg)
N2 N8
N2
![Page 69: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/69.jpg)
![Page 70: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/70.jpg)
La méthode des milieux extérieurs MPE
![Page 71: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/71.jpg)
![Page 72: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/72.jpg)
![Page 73: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/73.jpg)
La méthode des milieux des milieux MMM
![Page 74: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/74.jpg)
![Page 75: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/75.jpg)
![Page 76: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/76.jpg)
![Page 77: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/77.jpg)
La méthode des milieux rotationnels MMROT
![Page 78: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/78.jpg)
![Page 79: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/79.jpg)
![Page 80: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/80.jpg)
![Page 81: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/81.jpg)
![Page 82: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/82.jpg)
La méthode des barycentres MB
![Page 83: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/83.jpg)
![Page 84: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/84.jpg)
1. Les filtres d’Adelsson et Simoncelli [1 2 1] et [-1 2 -1]
Le résumé est :
Le signal est :
![Page 85: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/85.jpg)
2. Les ondelettes splines d ’ordre trois
Le signal est :
Pour la transformée directe, les deux filtres sont [1,2,1] et [-1,-2,-1]
Pour la transformée inverse, les deux filtres sont [-1,2,1] et [-1,2,-1]
![Page 86: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/86.jpg)
![Page 87: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/87.jpg)
Construction du système de compression
![Page 88: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/88.jpg)
MÉTHODEs CONSERVATIONDU
BARYCENTRE
RECONSTRUCTION POSSIBILITÉD’UTILISATION
DE LA T. O.
LINÉARISATIONDE LA
ROTATION
M. DESMILIEUXEXTÉRIEURS
MPE N IMPOSSIBLE N O
M. DESMILIEUX DESMILIEUX
MMM N SEULEMENT POUR LESFACETTES UTILISÉES ET
EXACTE
O O
M. DESMILIEUXROTATIONNELS
MMROT N SEULEMENT POUR LESFACETTES UTILISÉES ET
EXACTE
O N
M. DESBARYCENTRES
MB O SEULEMENT POUR LESFACETTES UTILISÉES ET
INEXACTE POUR LESSOMMETS, EXACTES POUR
LES BRYCENTRES
O O
![Page 89: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/89.jpg)
Le maillage obtenu par la transformée inverse
![Page 90: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/90.jpg)
![Page 91: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/91.jpg)
![Page 92: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/92.jpg)
• F.E.M : Synthesize a mean model of the face named a photo-fit identikit
• Fast and progressive visualisation • Morphing 3D • Multimedia applications
![Page 93: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/93.jpg)
![Page 94: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/94.jpg)
Le diagramme de Schlegel associé au fullerène C60
![Page 95: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/95.jpg)
The construction of 3-connected organized points from unorganized points
First step
![Page 96: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/96.jpg)
The construction of 3-connected organized points from unorganized points
The future pentagons The future hexagons
Second step
![Page 97: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/97.jpg)
Bh=10(3i-1) T=20 * 3i
H=10(3i+1-1)
Generalisation
![Page 98: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/98.jpg)
B2 B1
B3
Reconstruction of 3-Connected Surfaces from Unorganized Points
![Page 99: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/99.jpg)
Interpolation by spheres
![Page 100: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/100.jpg)
Interpolation by spheres
Radial Projection
![Page 101: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/101.jpg)
![Page 102: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/102.jpg)
ray
ray
object1
object2
sphere
Morphing 3D applied to the objects with homogeneous mesh and 3-connected vertices
![Page 103: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/103.jpg)
![Page 104: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/104.jpg)
Applications multimedia
![Page 105: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/105.jpg)
server
![Page 106: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/106.jpg)
server
![Page 107: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/107.jpg)
Level 5
Level 6
![Page 108: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/108.jpg)
Parallélisation de l’algorithme
![Page 109: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/109.jpg)
![Page 110: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/110.jpg)
Calculus parallel
Calculus non parallel
Level of subdivision
![Page 111: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/111.jpg)
Conclusion
![Page 112: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/112.jpg)
Perspective de recherche • Subdivision locale 3-connexe
♦Mise au point d’un nouveau système de numérotation pour la connexion de sphères ♦Construction de différentes pièces mécaniques maillées en 3-connexe
• Comparaison entre les surfaces obtenues par les ondelettes sur des surfaces 3-connexes et les nurbs
![Page 113: Modelling of Human Faces - homepages.laas.frhomepages.laas.fr/adoncesc/Wavelet/surface.pdf · The modal analysis gives a number of rigid modes equal to the ... • E i = 10*3i+1 (](https://reader031.vdocuments.us/reader031/viewer/2022030501/5aadd0b17f8b9a190d8b5d15/html5/thumbnails/113.jpg)