projet-probleme-inverse-3D/docs/slides.md

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title: Bureau d'étude de PI3D
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# Bureau d'étude de PI3D

Sujet 6 - Reformulation du MVS par level sets

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## Level sets ?

<img src="https://upload.wikimedia.org/wikipedia/commons/7/78/Level_set_method.png" class="m-auto -mt-7"/>

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$\mathcal{V}_t = \{ \textbf{Q} \in \mathbb{R}^3, u(\textbf{Q}) = t \}, \quad t\in [0,1], \quad u \colon \mathbb{R}^3 \to [0, 1]$

<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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## Exemple Level sets 2D

<img src="figs/lvl7_2D.gif" class="m-auto mt-5"/>

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## Exemple Level sets 3D

<img src="figs/lvl7_3D.gif" class="m-auto -mt-1 h-125"/>

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## Approximation du volume

<img src="figs/lvl7_2D.png" class="m-auto h-110"/>

<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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## Discrétisation de l'espace

<img src="https://upload.wikimedia.org/wikipedia/commons/b/bc/Voxels.svg" class="m-auto h-110">

<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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## Mise à jour du volume

- Sélection des voxels sur la bordure du "marbre"
- Vérification de la visibilité du voxel par toutes les caméras
- Récupération des couleurs / niveaux de gris visibles par les caméras
- Consensus sur la couleur / niveau de gris du voxel étudié
- Remplissage si consensus, creusage sinon

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## Initialisation du volume

- Définition d'une taille limite:
  - $x \in [-1, 1]$
  - $y \in [-1, 1]$
  - $z \in [-1, 1]$
- Définition d'une résolution (un pas): $5.10^{-2}$
- Initialisation des valeurs du marbre:
  - Uniforme (`np.zeros` ou `np.ones`)
  - Shape From Silouhette (BE4)


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## Exemple Shape from Silouhette

<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">

<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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## Raytracing

<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141883810914427/fvi2.png" class="m-auto -mt-10 h-125"/>

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## Raytracing

<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141884242931712/fvi4.png" class="m-auto -mt-10 h-125"/>

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## Raytracing

<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141884679147602/fvi6.png" class="m-auto -mt-10 h-125"/>

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## Raytracing

<img src="https://cdn.discordapp.com/attachments/953586522572066826/1068141885056622661/fvi8.png" class="m-auto -mt-10 h-125"/>

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## Résultats