Rees, David Baxter Treharne; (1993) Evaluation of the Fractional Brownian Motion Model of Terrain. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The goal of this research is to evaluate a commonly applied statistically self-similar model of two-dimensional height fields. Fractional Brownian motion was chosen as such a model, due to the large body of literature supporting its application as an analysis tool and a terrain simulation technique. The measurement process used - variogram analysis - has also inspired a significant body of research detailing its application. Previous studies have, almost exclusively, used the model in the context of entire datasets. However, the serious application of this technique demands the analysis of local areas over large regions, in order to determine variations in the behaviour of different surfaces. Accordingly, one aspect of the research concentrated on automating analysis, and attaining realistic processing times to make such a study possible. The constraints that determine fractional Brownian motion behaviour have been tested. The datasets analysed indicate such behavior to be a poor model of terrain. Thus, doubt is cast upon its application to determine surface roughness, and upon its general use in the characterisation and generation of terrain. However, terrain is shown to be scaling, implying that a valid fractal model of terrain behaviour does exist. Results indicate that the variogram technique is not ideally suited to determining the fractal dimension of terrain. Such analysis appears vulnerable to periodicity and other behaviour which may occur within the data. Conversely, this behaviour has highlighted poor data and, if errors can be discriminated from natural features, might be used as a quality assessment tool.

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