Automated Sphere Segmentation from Point Clouds

Nowadays huge datasets can be collected in a relatively short time. After capturing these data sets the next step is their processing. Automation of the processing steps can contribute to efficiency increase, to reduction of the time needed for processing, and to reduction of interactions of the user. The paper brings a short review of the most reliable methods for sphere segmentation. An innovative algorithm for automated detection of spheres and for estimating their parameters from 3D point clouds is introduced. The algorithm proposed was tested on complex point clouds. In the last part of the paper, the implementation of the algorithm proposed to a standalone application is described.

A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media

The complex traveltime solutions of the complex eikonal equation are the basis of inhomogeneous plane-wave seismic imaging methods, such as Gaussian beam migration and tomography. We have developed analytic approximations for the complex traveltime in transversely isotropic media with a titled symmetry axis, which is defined by a Taylor series expansion over the anisotropy parameters. The formulation for the complex traveltime is developed using perturbation theory and the complex point-source method. The real part of the complex traveltime describes the wavefront, and the imaginary part of the complex traveltime describes the decay of the amplitude of waves away from the central ray. We derive the linearized ordinary differential equations for the coefficients of the Taylor-series expansion using perturbation theory. The analytical solutions for the complex traveltimes are determined by applying the complex point-source method to the background traveltime formula and subsequently obtaining the coefficients from the linearized ordinary differential equations. We investigate the influence of the anisotropy parameters and of the initial width of the ray tube on the accuracy of the computed traveltimes. The analytical formulas, as outlined, are efficient methods for the computation of complex traveltimes from the complex eikonal equation. In addition, those formulas are also effective methods for benchmarking approximated solutions.

Decomposition of Repulsive Clusters in Complex Point Processes with Heterogeneous Components

The decomposition of a point process is useful for the analysis of spatial patterns and in the discovery of potential mechanisms of geographic phenomena. However, when a local repulsive cluster is present in a complex heterogeneous point process, the traditional solution, which is based on clustering, may be invalid for decomposition because a repulsive pattern is not subject to a specific probability distribution function and the effects of aggregative and repulsive components may be counterbalanced. To solve this problem, this paper proposes a method of decomposing repulsive clusters in complex point processes with multiple heterogeneous components. A repulsive cluster is defined as a set of repulsive density-connected points that are separated by a certain distance at a small scale and aggregated at a large scale simultaneously. The H-function is used to identify repulsive clusters by determining the repulsive distance and extracting repulsive points for further clustering. Through simulation experiments based on three datasets, the proposed method has been shown to effectively perform repulsive cluster decomposition in heterogeneous point processes. A case study of the point of interest (POI) dataset in Beijing also indicates that the method can identify meaningful repulsive clusters from types of POIs that represent different service characteristics of shops in different local regions.

Using Internet Streamed Data for Sport Visualization

<p><strong>Abstract.</strong> In many modern sports, athlete tracking for athlete performance analysis is a common practice. Most of the time this athlete tracking is done during training sessions. At some World Tour cycling races the broadcasting company and race organizers use athlete tracking data during race events for various graphical for fans of the sport. This research attempt to use the race real time broadcast of data to produce a web mapping application that will show detailed cycling race tactics and other mapping forms in near real time. This research focuses on data flow and processing for dynamic mapping of complex point data patterns.</p>

Point processes on the complex plane with applications

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] A point process is a random collection of points from a certain space, and point process models are widely used in areas dealing with spatial data. However, studies of point process theory in the past only focused on Euclidean spaces, and point processes on the complex plane have been rarely explored. In this thesis we introduce and study point processes on the complex plane. We present several important quantities of a complex point process (CPP) that investigate first and second order properties of the process. We further introduce the Poisson complex point process and model its intensity function using log-linear and mixture models in the corresponding 2-dimensional space. The methods are exemplified via applications to density approximation and time series analysis via the spectral density, as well as construction and estimation of covariance functions of Gaussian random fields.