Análise espacial espectral em processos pontuais

Abstract

The spatial analysis of point processes has a prominent placing in many knowledge areas. Most of the methods available for this type of analysis are based on techniques focused on “space domain” which involve the analysis between points. The spectral analysis, though applied in various areas, is not yet widespread in the analysis of space point processes. The spectral analysis is based on the autocovariance function and its Fourier transformation (the spectrum). The objective of this dissertation is to explore the spectral analysis in order to analyze the point processes in plane and volume. Basing on the two-dimensional spectral analysis theory available in literature, we developed programs using the R software. The spectral methods were applied in classic point configurations and in composite material samples. This dissertation also developed a theory for three-dimensional spectral analysis. The three-dimensional spectral methods are applied in three-dimensional configurations simulated using programs constructed in the R software. The polar spectrum and Monte Carlo methods are used to test the complete two and threedimensional spatial randomness hypothesis. The results showed that the spectral analysis is a good tool to investigate the complete spatial randomness, since it does not assume any structural disposition (ex. isotropy) over the stochastic process which generated the point configuration.