Fractal Surface Reconstruction with Uncertainty Estimation: Modeling Natural Terrain

Abstract

This report develops a systematic method, based on fractal gemmetry, for modeling natural terrain. The method consists of two main parts: reconstructing dense surfaces from sparse data while preserving roughness, and estimating the uncertainty of each reconstructed point. In earlier work, Szeliski developed stochastic ngularization techniques to reconstruct natural surfaces. We found that these methods did not provide sufficient control over the roughness of the reconstructed surfaces. We present a modified version in which a temperature parameter, determined as a function of the fractal dimension, plays a critical role in controlling roughness. Reconstructing dense, rough surfaces is seldom useful without assigning some measure of confidence to the surface points. This is particularly challenging for the reconstructed points. We revisit Szeliski's approach of Monte Carlo estimation of uncertainty, and report quantitative accuracy results for both synthetic data and real range data.