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.

Spatio-Temporal Shape from Silhouette using Four-Dimensional Delaunay Meshing

Abstract: We propose a novel method for computing a four-dimensional (4D) representation of the spatio-temporal visual hull of a dynamic scene, based on an extension of a recent provably correct Delaunay meshing algorithm. By considering time as an additional dimension, our approach exploits seamlessly the time coherence between different frames to produce a compact and high-quality 4D mesh representation of the visual hull. The 3D visual hull at a given time instant is easily obtained by intersecting this 4D mesh with a temporal plane, thus enabling interpolation of objects' shape between consecutive frames. In addition, our approach offers easy and extensive control over the size and quality of the output mesh as well as over its associated re- projection error. Our numerical experiments demonstrate the effectiveness and flexibility of our approach for generating compact, high-quality, time-coherent visual hull representations from real silhouette image data.

A new approach for categorizing pig lying behaviour based on a Delaunay triangulation method.

Abstract: Machine vision-based monitoring of pig lying behaviour is a fast and non-intrusive approach that could be used to improve animal health and welfare. Four pens with 22 pigs in each were selected at a commercial pig farm and monitored for 15 days using top view cameras. Three thermal categories were selected relative to room setpoint temperature. An image processing technique based on Delaunay triangulation (DT) was utilized. Different lying patterns (close, normal and far) were defined regarding the perimeter of each DT triangle and the percentages of each lying pattern were obtained in each thermal category. A method using a multilayer perceptron (MLP) neural network, to automatically classify group lying behaviour of pigs into three thermal categories, was developed and tested for its feasibility. The DT features (mean value of perimeters, maximum and minimum length of sides of triangles) were calculated as inputs for the MLP classifier. The network was trained, validated and tested and the results revealed that MLP could classify lying features into the three thermal categories with high overall accuracy (95.6%). The technique indicates that a combination of image processing, MLP classification and mathematical modelling can be used as a precise method for quantifying pig lying behaviour in welfare investigations.

Expected time analysis for Delaunay point location

Abstract: We consider point location in Delaunay triangulations with the aid of simple data structures. In particular, we analyze methods in which a simple data structure is used to first locate a point close to the query point. For points uniformly distributed on the unit square, we show that the expected point location complexities are Θ(√n) for the Green-Sibson rectilinear search, Θ(n1/3) for Jump and Walk, Θ(n1/4) for BinSearch and Walk (which uses a 1-dimensional search tree), Θ(n0.056...) for search based on a random 2-d tree, and Θ(log n) for search aided by a 2-d median tree.

Distorted Fingerprint Indexing Using Minutia Detail and Delaunay Triangle

Abstract: This paper is concentrated on an accurate and efficient fingerprint indexing algorithm, which efficiently retrieves the top N possibly matched candidates from a huge database. In order to have ability of coping with distorted fingerprints, the proposed algorithm uses novel features, which are insensitive to distortion, formed by the Delaunay triangulation of minutiae set as the representation unit. These features include minutia detail and Delaunay triangle (its handedness, angles, maximum edge, and related angle between orientation field and edges). Experiments on database FVC 2000 and scanned fingerprints with heavy distortion show our algorithm considerably narrows down the search space in fingerprint databases and is also available for distorted fingerprints. We also compared with other indexing approaches, and results show our algorithm has a better performance, especially on fingerprints with heavy distortion. This algorithm has another significant advantage that is it provides the control points for fingerprint distortion compensation.