Topic
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.
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TL;DR: A sequential multiresolution surface modeling technique that preserves the topology of the triangulation and surface orientation discontinuities and builds from complex multipart objects with holes.
135 citations
TL;DR: In this article, various models for homogeneous random division of three-dimensional space are surveyed, mostly Voronoi tessellations of random convex polyhedra and Delaunay tetrahedra, generated by random points in space.
Abstract: Various models for the homogeneous random division of three-dimensional space are surveyed. They are mostly 'tessellations' of random convex polyhedra. First, the partitioning of space by random planes is considered; then the Voronoi tessellation, and the dual Delaunay tessellation of tetrahedra, generated by random points in space. Three-dimensional sections of higher dimensional Voronoi tessellations afford an interesting source of models. Another ample source results when an inhomogeneous time element is introduced into the Voronoi structure, to yield a generalized Johnson-Mehl model. GEOMETRICAL PROBABILITY; RANDOM DIVISION OF SPACE INTO CELLS; SPATIAL STOCHASTIC HOMOGENEITY; ERGODIC DISTRIBUTIONS; POISSON POINT AND PLANE PROCESSES; RANDOM CONVEX POLYHEDRA; VORONOI, DELAUNAY AND JOHNSON-MEHL DIVISIONS
135 citations
18 Apr 2011
TL;DR: A scalable logo recognition approach that extends the common bag-of-words model and incorporates local geometry in the indexing process and represents triangles by signatures capturing both visual appearance and local geometry.
Abstract: We propose a scalable logo recognition approach that extends the common bag-of-words model and incorporates local geometry in the indexing process. Given a query image and a large logo database, the goal is to recognize the logo contained in the query, if any. We locally group features in triples using multi-scale Delaunay triangulation and represent triangles by signatures capturing both visual appearance and local geometry. Each class is represented by the union of such signatures over all instances in the class. We see large scale recognition as a sub-linear search problem where signatures of the query image are looked up in an inverted index structure of the class models. We evaluate our approach on a large-scale logo recognition dataset with more than four thousand classes.
134 citations
TL;DR: A new greedy algorithm for surface reconstruction from unorganized point sets that achieves topologically correct reconstruction in most cases and can handle surfaces with complex topology, boundaries, and nonuniform sampling.
Abstract: In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.
133 citations
TL;DR: An algorithm for computing the medial surface of a large class of B-rep solids is presented, based on the domain Delaunay triangulation of a relatively sparse distribution of points, which are generated on the boundary of the object.
Abstract: The medial surface is a skeletal abstraction of a solid that provides useful shape information, which compliments existing model representation schemes. The medial surface and its associated topological entities are defined, and an algorithm for computing the medial surface of a large class of B-rep solids is then presented. The algorithm is based on the domain Delaunay triangulation of a relatively sparse distribution of points, which are generated on the boundary of the object. This strategy is adaptive in that the boundary point set is refined to guarantee a correct topological representation of the medial surface.
132 citations