Fractal-based description

Abstract

This paper addresses the problems of (1) representing natural shapes such as mountains, trees and clouds, and (2) computing such a description from image data. In order to solve these problems we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are good a choice for modeling natural surfaces because (1) many physical processes produce a fractal surface shape, (2) fractals are widely used as a graphics tool for generating naturallooking shapes, and (3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. This characterization of image regions has been shown to be stable over transformations of scale and linear transforms of intensity. Much work has been accomplished that is relevant to computing 3-D information from the image data, and the computation of a 3-D fractal-based representation from actual image data has been demonstrated using an image of a mountain. This example shows the potential of a fractal-based representation for efficiently computing good 3-D representations of natural shapes, including such seemingly-difficult cases as mountains, clumps of leaves and clouds. I