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

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coverAuthor: Laurent Fainsin, Damien Guillotin, Pierre-Eliot Jourdan
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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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$\mathcal{V}_t = \{ \textbf{Q} \in \mathbb{R}^3, u(\textbf{Q}) = t \}, \quad t\in [0,1], \quad u \colon \mathbb{R}^3 \to [0, 1]$

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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"/>

<Footnotes separator>
  <Footnote>
    Variational principles, surface evolution, PDEs, level set methods, and the stereo problem - Olivier Faugeras, Renaud Keriven, 1998
  </Footnote>
</Footnotes>

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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">

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## Mise à jour du volume

consensus blabla

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## Initialisation du volume

ones ou alors shape from silouhette

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## Exemple Shape from Silouhette

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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