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Proceedings Paper

Method of incorporating prior information on the structure of random fractal surfaces
Author(s): J. M. Blackledge
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Paper Abstract

Random fractal surfaces (Mandeibrot surfaces) are finding more and more applications in computer graphics, image analysis and the simulation of naturally occurring topologies. A random fractal as a fractional geometry whose statistical properties are scale invarient. In other words, the object looks similar (statistically) at all magnifications. The generation of a random fractal surface involves the user having to input two essential parameters: (i) the Fractal Dimension (a decimal number D where 2 < D < 3) which controls the surface roughness and (ii) the seed of a random number generator which determines the structure of the surface. By changing the seed, the user can generate different surfaces and by increasing the fractal dimension the surface roughness can be increased. In practice, algorithms of this type do not allow the user to construct a random fractal with specific topological features. Hence, in respect of the surface obtained, the user is ultimately at the mercy of a random number generator. In this paper, we address the problem of how to incorporate a priori information into a Mandelbrot surface in such a way that the end product is still fractal. A solution is provided to this problem which provides the user with control over the general topology of the surface. We demonstrate its application for incorporating low resolution data obtained from geographical/geological survey maps on the topology of a given area. Also, we show how the method can be used to generate synthetic terrain databases for the validation of certain surveying algorithms. The technique employs the Fourier Synthesis Method for generating Mandelbrot surfaces and is based on transmitting a predetermined proportion of the complex Fourier coefficients used to describe a given topology. In addition to its use as a complex terrain modeller, it is also shown how the same technique can be used for data compression of general topologies. The idea here is to describe a surface in terms of a few essential coordinate parameters (a prior information), a given seed and a specific fractal dimension.

Paper Details

Date Published: 1 August 1990
PDF: 2 pages
Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); doi: 10.1117/12.19755
Show Author Affiliations
J. M. Blackledge, Cranfield Institute of Technology (United Kingdom)

Published in SPIE Proceedings Vol. 1251:
Curves and Surfaces in Computer Vision and Graphics
Leonard A. Ferrari; Rui J. P. de Figueiredo, Editor(s)

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