A Novel Skeleton Extraction Algorithm for 3d Wireless Sensor Networks

Wireless sensor network design is critical and resource allocation is a major problem which remains to be solved satisfactorily. The discrete nature of sensor networks renders the existing skeleton extraction algorithms inapplicable. 3D topologies of sensor networks for practical scenarios are considered in this paper and the research carried out in the field of skeleton extraction for three dimensional wireless sensor networks. A skeleton extraction algorithm applicable to complex 3D spaces of sensor networks is introduced in this paper and is represented in the form of a graph. The skeletal links are identified on the basis of a novel energy utilization function computed for the transmissions carried out through the network. The frequency based weight assignment function is introduced to identify the root node of the skeleton graph. Topological clustering is used to construct the layered topological sets to preserve the nature of the topology in the skeleton graph. The skeleton graph is constructed with the help of the layered topological sets and the experimental results prove the robustness of the skeleton extraction algorithm introduced. Provisioning of additional resources to skeletal nodes enhances the sensor network performance by 20% as proved by the results presented in this paper

Medial Axis Approximation with Constrained Centroidal Voronoi Diagrams On Discrete Data

International audienceIn this paper, we present a novel method for me-dial axis approximation based on Constrained Centroidal Voronoi Diagram of discrete data (image, volume). The proposed approach is based on the shape boundary subsampling by a clustering approach which generates a Voronoi Diagram well suited for Medial Axis extraction. The resulting Voronoi Diagram is further filtered so as to capture the correct topology of the medial axis. The resulting medial axis appears largely invariant with respect to typical noise conditions in the discrete data. The method is tested on various synthetic as well as real images. We also show an application of the approximate medial axis to the sizing field for triangular and tetrahedral meshing

Classification topologique locale d'images 3D

L'objectif de ce travail est de proposer une méthode d'analyse locale des formes des objets contenus dans une image 3D. Nous nous intéressons plus particulièrement aux formes de type cylindre ou plaque. Notre approche est basée sur l'analyse des points du squelette 3D et se déroule en deux étapes. Premièrement, 4 types de points du squelette sont identifiés : régulier, arc, bord et multiple. Un point du squelette est classé en fonction des propriétés topologique d'une région d'intérêt locale autour de ce point. La taille de cette région est réglée en fonction de l'épaisseur locale de la structure en ce point. Ensuite, la réversibilité du squelette est utilisée pour en déduire une classification du volume entier. Après avoir obtenu des résultats sur des images simulées 3D, nous présentons une application de la méthode dans l'identification des structures osseuses à partir d'images tomographiques hautes- résolution 3D

A novel procedure for medial axis reconstruction of vessels from Medical Imaging segmentation

A procedure for reconstructing the central axis from diagnostic image processing is presented here, capable of solving the widespread problem of stepped shape effect that characterizes the most common algorithmic tools for processing the central axis for diagnostic imaging applications through the development of an algorithm correcting the spatial coordinates of each point belonging to the axis from the use of a common discrete image skeleton algorithm. The procedure is applied to the central axis traversing the vascular branch of the cerebral system, appropriately reconstructed from the processing of diagnostic images, using investigations of the local intensity values identified in adjacent voxels. The percentage intensity of the degree of adherence to a specific anatomical tissue acts as an attraction pole in the identification of the spatial center on which to place each point of the skeleton crossing the investigated anatomical structure. The results were shown in terms of the number of vessels identified overall compared to the original reference model. The procedure demonstrates high accuracy margin in the correction of the local coordinates of the central points that permits to allocate precise dimensional measurement of the anatomy under examination. The reconstruction of a central axis effectively centered in the region under examination represents a fundamental starting point in deducing, with a high margin of accuracy, key informations of a geometric and dimensional nature that favours the recognition of phenomena of shape alterations ascribable to the presence of clinical pathologies

Voronoi Cells in Metric Algebraic Geometry of Plane Curves

Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach. In each case, we provide algebraic equations defining the object and, where possible, give formulas for the degrees of these algebraic varieties. We show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.Comment: 23 pages, 14 figure