Laureηt
69ea7232dc
Co-authored-by: Damien Guillotin <damguillotin@gmail.com> Co-authored-by: pejour <pejour@users.noreply.github.com>
125 lines
3.5 KiB
Markdown
125 lines
3.5 KiB
Markdown
---
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theme: academic
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class: text-white
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coverAuthor: Laurent Fainsin, Damien Guillotin, Pierre-Eliot Jourdan
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coverBackgroundUrl: https://images.unsplash.com/photo-1655720408861-8b04c0724fd9?ixlib=rb-4.0.3&ixid=MnwxMjA3fDB8MHxwaG90by1wYWdlfHx8fGVufDB8fHx8
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coverBackgroundSource: unplash
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coverBackgroundSourceUrl: https://unsplash.com/photos/Vc0CmuIfMg0
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coverDate: '2023-01-05'
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themeConfig:
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paginationX: r
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paginationY: t
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paginationPagesDisabled:
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- 1
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title: Bureau d'étude de PI3D
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---
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# Bureau d'étude de PI3D
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Sujet 6 - Reformulation du MVS par level sets
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---
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## Level sets ?
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<img src="https://upload.wikimedia.org/wikipedia/commons/7/78/Level_set_method.png" class="m-auto -mt-7"/>
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<style>
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span.katex {
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position: absolute;
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top: 48%;
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}
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</style>
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$\mathcal{V}_t = \{ \textbf{Q} \in \mathbb{R}^3, u(\textbf{Q}) = t \}, \quad t\in [0,1], \quad u \colon \mathbb{R}^3 \to [0, 1]$
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<a href="https://en.wikipedia.org/wiki/Level-set_method" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Wikipedia</a>
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---
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## Exemple Level sets 2D
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<img src="figs/lvl7_2D.gif" class="m-auto mt-5"/>
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---
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## Exemple Level sets 3D
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<img src="figs/lvl7_3D.gif" class="m-auto -mt-1 h-125"/>
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---
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## Approximation du volume
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<img src="figs/lvl7_2D.png" class="m-auto h-110"/>
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<a href="https://hal.inria.fr/inria-00073673/document" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Variational principles, surface evolution, PDEs, level set methods, and the stereo problem - Olivier Faugeras, Renaud Keriven, 1998</a>
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---
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## Discrétisation de l'espace
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<img src="https://upload.wikimedia.org/wikipedia/commons/b/bc/Voxels.svg" class="m-auto h-110">
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<a href="https://en.wikipedia.org/wiki/Voxel" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Wikipedia</a>
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---
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## Mise à jour du volume
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- Sélection des voxels sur la bordure du "marbre"
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- Vérification de la visibilité du voxel par toutes les caméras
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- Récupération des couleurs / niveaux de gris visibles par les caméras
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- Consensus sur la couleur / niveau de gris du voxel étudié
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- Remplissage si consensus, creusage sinon
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---
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## Initialisation du volume
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- Définition d'une taille limite:
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- $x \in [-1, 1]$
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- $y \in [-1, 1]$
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- $z \in [-1, 1]$
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- Définition d'une résolution (un pas): $5.10^{-2}$
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- Initialisation des valeurs du marbre:
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- Uniforme (`np.zeros` ou `np.ones`)
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- Shape From Silouhette (BE4)
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---
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## Exemple Shape from Silouhette
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<img src="https://www.researchgate.net/profile/Silvio-Savarese/publication/221625880/figure/fig1/AS:652956261158913@1532688312594/Shape-from-Silhouettes-The-silhouette-and-camera-location-for-each-view-forms-a-cone.png" class="m-auto mt-2 h-110">
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<a href="https://ieeexplore.ieee.org/document/1024034" class="absolute bottom-0 font-extralight mb-1 mr-2 right-0 text-xs">Implementation of a Shadow Carving System for Shape Capture, doi: 10.1109/TDPVT.2002.1024034</a>
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---
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## Raytracing
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<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141883810914427/fvi2.png" class="m-auto -mt-10 h-125"/>
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---
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## Raytracing
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<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141884242931712/fvi4.png" class="m-auto -mt-10 h-125"/>
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---
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## Raytracing
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<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141884679147602/fvi6.png" class="m-auto -mt-10 h-125"/>
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---
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## Raytracing
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<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141885056622661/fvi8.png" class="m-auto -mt-10 h-125"/>
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---
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## Résultats
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