Fractal-Based Description

Abstract

This paper addresses the problems of (I) representing natural ~h a p cs 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 r <:> quires a good model of natural surface shapes. Fractal functions are good a choice for modeling natural surfaces because (I) many physical processes produce a fractal surface shape, (2) fractal s are widely used as a graphics tool for generating naturallooking shape s, and (3) a survey of natural imagery has shown t.hat th e 3-D fractal surface model, transformed by the image form ation proce~ s, furnishes an accurate description of both textured and shaded image regions. This characterization of image regions has be en shown to be stable over transformations of scale and linear tran sforms or intensity. Murh work has been accomplished that is relevant to comput ing 3-D information from the image data, and the computation of a 3-D fract al-based representation from actual image data has been de monstrated 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.