Fractal Simplification of Lines Using Convex Hulls

Abstract

We investigate the problem of the simplification of a curve from a geometric viewpoint. Starting from a fractal hypothesis, we consider that the best methods are those that keep an estimated value of the fractal dimension constant, before and after simplification. We propose a simplification rule based on the use of local convex hulls that corresponds to a new algorithm for computing fractal dimension. This algorithm is both accurate and universal, and does not imply the need to make arbitrary hypotheses regarding the structure of the curve. A comparison is made with other fractal approaches and with the well‐known Douglas‐Peucker method. 1993 The Ohio State University