HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Fig. 1. Surface meshes. Left: Meshing the boundaries of brain tissues with a tissue-dependent resolution. We requested the cortical surface (colored in dark gray) to have a resolution twice higher than other tissues. As a result, output surface meshes of other anatomical structures have a coarse resolution except in local regions where they neighbor gray matter. This is apparent in the magnified view of the white matter mesh (in light gray), in which the gray matter interface has been partially removed for visualization purposes. Right: The quality of the obtained surface meshes is much higher than with the marching cubes algorithm.

In this paper, we propose a robust and efficient Lagrangian approach, which we call Delaunay Deformable Models, for modeling moving surfaces undergoing large deformations and topology changes. Our work uses the concept of restricted Delaunay triangulation, borrowed from computational geometry. In our approach, the interface is represented by a triangular mesh embedded in the Delaunay tetrahedralization of interface points. The mesh is iteratively updated by computing the restricted Delaunay triangulation of the deformed objects. Our method has many advantages over popular Eulerian techniques such as the level set method and over hybrid Eulerian-Lagrangian techniques such as the particle level set method: localization accuracy, adaptive resolution, ability to track properties associated to the interface, seamless handling of triple junctions. Our work brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as Tsnakes.

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