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.

Geometrically invariant watermarking using feature points

Abstract: This paper presents a new approach for watermarking of digital images providing robustness to geometrical distortions. The weaknesses of classical watermarking methods to geometrical distortions are outlined first. Geometrical distortions can be decomposed into two classes: global transformations such as rotations and translations and local transformations such as the StirMark attack. An overview of existing self-synchronizing schemes is then presented. Theses schemes can use periodical properties of the mark, invariant properties of transforms, template insertion, or information provided by the original image to counter geometrical distortions. Thereafter, a new class of watermarking schemes using the image content is presented. We propose an embedding and detection scheme where the mark is bound with a content descriptor defined by salient points. Three different types of feature points are studied and their robustness to geometrical transformations is evaluated to develop an enhanced detector. The embedding of the signature is done by extracting feature points of the image and performing a Delaunay tessellation on the set of points. The mark is embedded using a classical additive scheme inside each triangle of the tessellation. The detection is done using correlation properties on the different triangles. The performance of the presented scheme is evaluated after JPEG compression, geometrical attack and transformations. Results show that the fact that the scheme is robust to these different manipulations. Finally, in our concluding remarks, we analyze the different perspectives of such content-based watermarking scheme.

Surface reconstruction by Voronoi filtering

Abstract: We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs.

Coverage in wireless ad hoc sensor networks

Abstract: Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking. One of the fundamental problems in sensor networks is the calculation of the coverage. In Meguerdichian et al. (2001), it is assumed that the sensor has uniform sensing ability. We provide efficient distributed algorithms to optimally solve the best-coverage problem raised in the above-mentioned article. In addition, we consider a more general sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption and how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed above that uses the Delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

Guaranteed-quality mesh generation for curved surfaces

Abstract: For several commonly-used solution techniques for partial differential equations, the first step is to divide the problem region into simply-shaped elements, creating a mesh. We present a technique for creating high-quality triangular meshes for regions on curved surfaces. This technique is an extension of previous methods we developed for regions in the plane. For both flat and curved surfaces, the resulting meshes are guaranteed to exhibit the following properties: (1) internal and external boundaries are respected, (2) element shapes are guaranteed—all elements are triangles with angles between 30 and 120 degrees (with the exception of badly shaped elements that may be required by the specified boundary), and (3) element density can be controlled, producing small elements in “interesting” areas and large elements elsewhere. An additional contribution of this paper is the development of a practical generalization of Delaunay triangulation to curved surfaces.

Voronoi diagrams and Delaunay triangulations

Abstract: The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site The dual of the Voronoi diagram the Delaunay triangulation is the unique triangulation so that the circumsphere of every triangle contains no sites in its interior Voronoi diagrams and Delaunay triangulations have been rediscovered or applied in many areas of math ematics and the natural sciences they are central topics in computational geometry with hundreds of papers discussing algorithms and extensions Section discusses the de nition and basic properties in the usual case of point sites in R with the Euclidean metric while section gives basic algorithms Some of the many extensions obtained by varying metric sites environment and constraints are discussed in section Section nishes with some interesting and nonobvious structural properties of Voronoi diagrams and Delaunay triangulations