To cite this version:Dobrina Boltcheva, Bruno Levy. Surface reconstruction by computing restricted Voronoi cells in parallel. Computer-Aided Design, Elsevier, 2017, 90, pp.123 -134. 10.1016/j.cad.2017 Surface reconstruction by computing restricted Voronoi cells in parallel
AbstractWe present a method for reconstructing a 3D surface triangulation from an input point set. The main component of the method is an algorithm that computes the restricted Voronoi diagram. In our specific case, it corresponds to the intersection between the 3D Voronoi diagram of the input points and a set of disks centered at the points and orthogonal to the estimated normal directions. The method does not require coherent normal orientations (just directions). Our algorithm is based on a property of the restricted Voronoi cells that leads to an embarrassingly parallel implementation. We experimented our algorithm with scanned point sets with up to 100 million vertices that were processed within few minutes on a standard computer. The complete implementation is provided.
Abstract. The problem of generating realistic computer models of objects represented by 3D segmented images is important in many biomedical applications. Labelled 3D images impose particular challenges for meshing algorithms because multi-material junctions form features such as surface pacthes, edges and corners which need to be preserved into the output mesh. In this paper, we propose a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations.
International audienceThis paper describes a new semi-automatic method to cluster TLS data into meaningful sets of points to extract plant components. The approach is designed for small plants with distinguishable branches and leaves, such as tree seedlings. It first creates a graph by connecting each point to its most relevant neighbours, then embeds the graph into a spectral space, and finally segments the embedding into clusters of points. The process can then be iterated on each cluster separately. The main idea underlying the approach is that the spectral embedding of the graph aligns the points along the shape's principal directions. A quantitative evaluation of the segmentation accuracy, as well as of leaf area estimates, is provided on a poplar seedling mock-up. It shows that the segmentation is robust with false positive and false negative rates around 1%. Qualitative results on four contrasting plant species with three different scan resolution levels each are also shown
We propose a new iterative algorithm for computing the homology of arbitrary shapes discretized through simplicial complexes, We demonstrate how the simplicial homology of a shape can be effectively expressed in terms of the homology of its sub-components. The proposed algorithm retrieves the complete homological information of an input shape including the Betti numbers, the torsion coefficients and the representative homology generators.To the best of our knowledge, this is the first algorithm based on the constructive Mayer-Vietoris sequence, which relates the homology of a topological space to the homologies of its sub-spaces, i.e. the sub-components of the input shape and their intersections. We demonstrate the validity of our approach through a specific shape decomposition, based only on topological properties, which minimizes the size of the intersections between the sub-components and increases the efficiency of the algorithm.
Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multimaterial junctions forming features such as surface patches, edges and corners. The resulting meshes should preserve these features to ensure the visual quality and the mechanical soundness of the models. We present a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations.
Surgical planning in oncological liver surgery is based on the location of the liver segments and tumours inside these structures. The detection of the boundaries between the segments is then the first step of the preoperative planning. The proposed method, devoted to binary images of livers segmented from CT-scans, has been designed to delineate these segments. It automatically detects a set of landmarks using a priori anatomical knowledge and differential geometry criteria. These landmarks are then used to position planes delineating the 8 liver anatomical segments according to Couinaud's definition. The results of validations on 7 clinical cases tend to prove that the method is reliable for most of these separation planes.
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