Delaunay triangulation

About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.

Object skeletons from sparse shapes in industrial image settings

Abstract: Presents a method for computing the shape skeleton of planar objects in presence of noise occurring inside the image regions. Such noise may be due to poor control of lighting conditions, incorrect thresholding or image subsampling. Binary images of objects with such noise exhibit sparseness (lack of connectivity), within their image regions. Such non-contiguity may also be observed in thresholded images of objects which consist of regions having varying albedo. The problem of obtaining the skeletal description of sparse shapes is ill posed in the sense of conventional skeletonization techniques. We propose a skeletonization method which is based on obtaining the shape skeleton by evolving an approximation of the principal curve of the shape distribution. Our method is implemented as a batch mode Kohonen self-organizing map algorithm and involves iterating the following two steps: (1) Voronoi tessellation of the data, (2) kernel smoothing on the Voronoi centroids. Adjacency relationships between the Voronoi regions are obtained by computing a Delaunay triangulation of the centroids. The Voronoi centroids are connected by a minimum spanning tree after each iteration. The final shape skeleton is obtained by joining centroids which are disjoint in the spanning tree, but have adjacent Voronoi regions. The skeletal descriptions obtained with the method are invariant to translation, rotation, and scale changes of the shape. The potential of the method is demonstrated on industrial objects having varying shape complexity under different imaging conditions.

AUTOCLUST+: Automatic Clustering of Point-Data Sets in the Presence of Obstacles

Abstract: Wide spread clustering algorithms use the Euclidean distance to measure spatial proximity. However, obstacles in other GIS data-layers prevent traversing the straight path between two points. AUTOCLUST+ clusters points in the presence of obstacles based on Voronoi modeling and Delaunay Diagrams. The algorithm is free of usersupplied arguments and incorporates global and local variations. Thus, it detects high-quality clusters (clusters of arbitrary shapes, clusters of different densities, sparse clusters adjacent to high-density clusters, multiple bridges between clusters and closely located high-density clusters) without prior knowledge. Consequently, it successfully supports correlation analyses between layers (requiring high-quality clusters) and more general locational optimization problems in the presence of obstacles. All this within O(n log n+[m+R] log n) expected time, where n is the number of data points, m is the number of line-segments that determine the obstacles and R is the number of Delaunay edges intersecting some obstacles. A series of detailed performance evaluations illustrates the power of AUTOCLUST+ and confirms the virtues of our approach.

A new tracking algorithm of PIV and removal of spurious vectors using Delaunay tessellation

Abstract: A new algorithm of Delaunay Tessellation Particle Tracking Velocimetry (DT-PTV in abbreviation) is proposed for tracking particles in images of a PIV system by making use of the Delaunay tessellation (DT). The algorithm is tested by using numerically simulated particle images. The calculation results based on DT are compared with those obtained by a conventional algorithm of Binary Image Cross-correlation method (BICC). The new algorithm shows higher performance of obtaining more identical particles in two consecutive images correctly with shorter computation time even if the images contain many particles. A further application of DT to elimination of spurious vectors is also discussed.

Delaunay conforming iso-surface, skeleton extraction and noise removal

Abstract: Iso-surfaces are routinely used for the visualization of volumetric structures. Further processing (such as quantitative analysis, morphometric measurements, shape description) requires volume representations. The skeleton representation matches these requirements by providing a concise description of the object. This paper has two parts. First, we exhibit an algorithm which locally builds an iso-surface with two significant properties: it is a 2-manifold and the surface is a subcomplex of the Delaunay tetrahedrization of its vertices. Secondly, because of the latter property, the skeleton can in turn be computed from the dual of the Delaunay tetrahedrization of the iso-surface vertices. The skeleton representation, although informative, is very sensitive to noise. This is why we associate a graph to each skeleton for two purposes: (i) the amount of noise can be identified and quantified on the graph and (ii) the selection of the graph subpart that does not correspond to noise induces a filtering on the skeleton. Finally, we show some results on synthetic and medical images. An application, measuring the thickness of objects (heart ventricles, bone samples) is also presented.

Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids

Abstract: When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, accurate simulation requires quality Delaunay meshes and the use of circumcentric pressures. Second, meshes must align with potentially complex moving surfaces and boundaries, necessitating continuous remeshing. Unfortunately, sacrificing mesh quality in favour of speed yields inaccurate velocities and simulation artifacts. We describe how to eliminate the boundary-matching constraint by adapting recent embedded boundary techniques to tetrahedra, so that neither air nor solid boundaries need to align with mesh geometry. This enables the use of high quality, arbitrarily graded, non-conforming Delaunay meshes, which are simpler and faster to generate. Temporal coherence can also be exploited by reusing meshes over adjacent timesteps to further reduce meshing costs. Lastly, our free surface boundary condition eliminates the spurious currents that previous methods exhibited for slow or static scenarios. We provide several examples demonstrating that our efficient tetrahedral embedded boundary method can substantially increase the flexibility and accuracy of adaptive Eulerian fluid simulation.