Fractal Modeling of Natural Terrain: Analysis and Surface Reconstruction with Range Data

Abstract

In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fractal surface reconstruction, we extend Szeliski's regularization with fractal priors method to use a temperature parameter that depends on fractal dimension. We demonstrate both estimation and reconstruction with noisy range imagery of natural terrain.