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Outline

Title
Abstract
Key Takeaways
Introduction
Background: The Flow Complex and Its Hasse Diagram
Results
References

Reconstruction d'ensembles compacts 3D

Profile image of Frederic CazalsFrederic Cazals

2009

Abstract

Reconstruire un modèleà partir d'échantillons est un problème central se posant en médecine numérique, en ingénierie inverse, en sciences naturelles, etc. Ces applications ont motivé une recherche substantielle pour la reconstruction de surfaces, la question de la reconstruction de modèles plus généraux n'ayant paś eté examinée. Ce travail présente an algorithme visantà changer le paradigme de reconstruction en 3D comme suit. Premièrement, l'algorithme reconstruit des formes générales-des ensembles compacts et non plus des surfaces. Sous des hypothèses appropriées, nous montrons que la reconstruction a le type d'homotopie de l'objet de départ. Deuxièmement, l'algorithme ne génère pas une seule reconstruction, mais un ensemble de reconstructions plausibles. Troisièmement, l'algorithme peutêtre coupléà la persistance topologique, afin de sélectionner les traits les plus stables du modèle reconstruit. Enfin, en cas d'échec de la reconstruction, la méthode permet une identification aisée des régions sous-echantillonnées, afinéventuellement de les enrichir. Ces points clefs sont illustrés sur des modèles difficiles, et devraient permettre de mieux tirer parti de leurs caractéristiques dans les application sus-citées.

Key takeaways
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  1. The algorithm reconstructs general 3D compact sets, not just smooth surfaces, enhancing flexibility.
  2. It generates multiple plausible reconstructions, addressing the ambiguity in point cloud data.
  3. The algorithm integrates topological persistence to prioritize stable features in reconstructions.
  4. Reconstruction operates effectively on challenging datasets, including non-manifold shapes like intersecting hemi-spheres.
  5. Key experiments involve models with 3,000 to 20,956 points, demonstrating practical efficiency and robustness.

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  29. Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex (France) Éditeur INRIA -Domaine de Voluceau -Rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) ❤tt♣✿✴✴✇✇✇✳✐♥r✐❛✳❢r ISSN 0249-6399

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Reconstruire un modèleà partir d'échantillons est un problème central se posant en médecine numérique, en ingénierie inverse, en sciences naturelles, etc. Ces applications ont motivé une recherche substantielle pour la reconstruction de surfaces, la question de la reconstruction de modèles plus généraux n'ayant paś eté examinée. Ce travail présente an algorithme visantà changer le paradigme de reconstruction en 3D comme suit. Premièrement, l'algorithme reconstruit des formes générales-des ensembles compacts et non plus des surfaces. Sous des hypothèses appropriées, nous montrons que la reconstruction a le type d'homotopie de l'objet de départ. Deuxièmement, l'algorithme ne génère pas une seule reconstruction, mais un ensemble de reconstructions plausibles. Troisièmement, l'algorithme peutêtre coupléà la persistance topologique, afin de sélectionner les traits les plus stables du modèle reconstruit. Enfin, en cas d'échec de la reconstruction, la méthode permet une identification aisée des régions sous-echantillonnées, afinéventuellement de les enrichir. Ces points clefs sont illustrés sur des modèles difficiles, et devraient permettre de mieux tirer parti de leurs caractéristiques dans les application sus-citées.

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