Fractal approximation of surfaces based on projected IFS attractors

Abstract

A method for approximating smooth or rough surfaces defined in R3 is introduced. A fractal model called projected IFS model allows the extension of the iteration space to a barycentric space Rn2 by enriching the classical IFS model with a set of control points (m2 points). This flexible model has good fitting properties for recovering surfaces. The input for the model is single viewpoint range data defined on a fixed grid and also 2D grey-level images considered as surfaces. The model recovery is formulated as a non-linear fitting problem and resolved using a modified LEVENBERG-MARQUARDT minimization method. During the iterative fitting algorithm, all the parameters of the projected IFS model are adjusted simultaneously in order to minimize the overall distance between the models surface and the original data. The final model is very compact and gives satisfactory results on synthetic range data and real geological surfaces. The main applications are surface modeling, shape description and geometric surface compression.