Abstract
A spatial point pattern is a collection of points irregularly located within a bounded area (2D) or space (3D) that have been generated by some form of stochastic mechanism. Examples of point patterns include locations of trees in a forest, of cases of a disease in a region, or of particles in a microscopic section of a composite material. Spatial Point pattern analysis is used mostly to determine the absence (completely spatial randomness) or presence (regularity and clustering) of spatial dependence structure of the locations. Methods based on the space domain are widely used for this purpose, while methods conducted in the frequency domain (spectral analysis) are still unknown to most researchers. Spectral analysis is a powerful tool to investigate spatial point patterns, since it does not assume any structural characteristics of the data (ex. isotropy), and uses only the autocovariance function, and its Fourier transform. There are some methods based on the spectral frameworks for analyzing 2D spatial point patterns. There is no such methods available for the 3D situation and, therefore, the aim of this work is to develop new methods based on spectral framework for the analysis of three-dimensional point patterns. The emphasis is on relating periodogram structure to the type of stochastic process which could have generated a 3D observed pattern. The results show that the methods based on spectral analysis developed in this work are able to identify patterns of three typical three-dimensional point processes, and can be used, concurrently, with analyzes in the space domain for a better characterization of spatial point patterns.
Highlights
In the study of spatial point processes, each event can be idealized as a point, and the irregular distribution of the events generated by the point process within a bounded region (2D or 3D) is called a spatial point pattern
Figura 6 - Periodogram of the simulated regular three-dimensional spatial point pattern. These results show that the spectral analysis can be competitive with the analysis based on the space domain for the characterization of three-dimensional spatial point patterns, some problems must be kept in mind that may limit a wider diffusion of its application
This paper aimed both: to present theoretical aspects involved in spectral analysis of three-dimensional spatial point patterns, and to show how this theory can be used in the exploratory analysis of such patterns
Summary
In the study of spatial point processes, each event can be idealized as a point, and the irregular distribution of the events generated by the point process within a bounded region (2D or 3D) is called a spatial point pattern. The primary stochastic component is the spatial location of the event and, the data of interest is the coordinate of each of these events in the study region (BADDELEY et al, 2015; DIGGLE, 2003). The main aim of the spatial point pattern analysis is to characterize how individuals are located with respect to each other over the space. The analysis is conducted to characterize the three fundamental spatial point patterns: complete spatial randomness (CSR), regularity and clustering (DIGGLE, 2003)
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