Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology

We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time. We introduce the notion of a persistence field as a statistical summary of persistence data and we show how these fields can be used to identify different stages of reionisation. We identify two new stages common to all bubble ionisation scenarios. Following an initial pre-overlap and subsequent overlap stage, the topology is first dominated by neutral filaments (filament stage) and then by enclosed patches of neutral hydrogen undergoing outside-in ionisation (patch stage). We study how these stages are affected by the degree of galaxy clustering. We also show how persistence fields can be used to study other properties of the ionisation topology, such as the bubble size distribution and the fractal-like topology of the largest ionised region.Comment: 18 pages, 12 figures, 1 table. Submitted to MNRA

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd

AN ADAPTIVE LOCALIZATION SYSTEM USING PARTICLE SWARM OPTIMIZATION IN A CIRCULAR DISTRIBUTION FORM

Tracking the user location in indoor environment becomes substantial issue in recent research High accuracy and fast convergence are very important issues for a good localization system. One of the techniques that are used in localization systems is particle swarm optimization (PSO). This technique is a stochastic optimization based on the movement and velocity of particles. In this paper, we introduce an algorithm using PSO for indoor localization system. The proposed algorithm uses PSO to generate several particles that have circular distribution around one access point (AP). The PSO generates particles where the distance from each particle to the AP is the same distance from the AP to the target. The particle which achieves correct distances (distances from each AP to target) is selected as the target. Four PSO variants, namely standard PSO (SPSO), linearly decreasing inertia weight PSO (LDIW PSO), self-organizing hierarchical PSO with time acceleration coefficients (HPSO-TVAC), and constriction factor PSO (CFPSO) are used to find the minimum distance error. The simulation results show the proposed method using HPSO-TVAC variant achieves very low distance error of 0.19 mete

Heuristic 3d Reconstruction Of Irregular Spaced Lidar

As more data sources have become abundantly available, an increased interest in 3D reconstruction has emerged in the image processing academic community. Applications for 3D reconstruction of urban and residential buildings consist of urban planning, network planning for mobile communication, tourism information systems, spatial analysis of air pollution and noise nuisance, microclimate investigations, and Geographical Information Systems (GISs). Previous, classical, 3D reconstruction algorithms solely utilized aerial photography. With the advent of LIDAR systems, current algorithms explore using captured LIDAR data as an additional feasible source of information for 3D reconstruction. Preprocessing techniques are proposed for the development of an autonomous 3D Reconstruction algorithm. The algorithm is designed for autonomously deriving three dimensional models of urban and residential buildings from raw LIDAR data. First, a greedy insertion triangulation algorithm, modified with a proposed noise filtering technique, triangulates the raw LIDAR data. The normal vectors of those triangles are then passed to an unsupervised clustering algorithm – Fuzzy Simplified Adaptive Resonance Theory (Fuzzy SART). Fuzzy SART returns a rough grouping of coplanar triangles. A proposed multiple regression algorithm then further refines the coplanar grouping by further removing outliers and deriving an improved planar segmentation of the raw LIDAR data. Finally, further refinement is achieved by calculating the intersection of the best fit roof planes and moving nearby points close to that intersection to exist at the intersection, resulting in straight roof ridges. The end result of the aforementioned techniques culminates in a well defined model approximating the considered building depicted by the LIDAR data