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.

Generating cancellable fingerprint templates based on Delaunay triangle feature set construction

Abstract: In this study, the authors propose a novel fingerprint template protection scheme that is developed using Delaunay triangulation net constructed from the fingerprint minutiae. The authors propose two methods namely FS_INCIR and FS_AVGLO to construct a feature set from the Delaunay triangles. The feature set computed is quantised and mapped to a 3D array to produce fixed length 1D bit string. This bit string is applied with a DFT to generate a complex vector. Finally, the complex vector is multiplied by user's key to generate a cancellable template. The proposed computation of feature set maintained a good balance between security and performance. These methods are tested on FVC 2002 and FVC 2004 databases and the experimental results show satisfactory performance. Further, the authors analysed the four requirements namely diversity, revocability, irreversibility and accuracy for protecting biometric templates. Thus, the feasibility of proposed scheme is depicted.

Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes

Abstract: We present a constructive proof of Alexandrov's theorem regarding the existence of a convex polytope with a given metric on the boundary. The polytope is obtained as a result of a certain deformation in the class of generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a relation with the weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of a positively curved generalized convex polytope. The latter is shown to be equal to the Hessian of the volume of the dual generalized polyhedron. We prove the non-degeneracy by generalizing the Alexandrov-Fenchel inequality. Our construction of a convex polytope from a given metric is implemented in a computer program.

Map Generalization with a Triangulated Data Structure

Abstract: Automation of map generalization requires facilities to monitor the spatial relationships and interactions among multiple map objects An experimental map generalization system has been developed which addresses this issue by representing spatial objects within a simplicial data structure (SDS) based on constrained Delaunay triangulation of the source data Geometric generalization operators that have been implemented include object exaggeration, collapse, amalgamation, boundary reduction and displacement The generalization operators exploit a set of primitive SDS functions to determine topological and proximal relationships, measure map objects, apply transformations, and detect and resolve spatial conflicts Proximal search functions are used for efficient analysis of the structure and dimensions of the intervening spaces between map objects Because geometric generalization takes place within a fully triangulated representation of the map surface, the presence of overlap conflicts, resulting from indi

Online Routing in Convex Subdivisions

Abstract: We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.