Title

Fractal Image Error Analysis

Document Type

Article

Publication Date

10-1-1998

Department

Mathematics

Abstract

Fractal techniques which assess the spatial component of an image use the observation that image complexity is a direct consequence of the operation of many different spatial processes acting to produce images over a wide range of spatial scales. Precisely because fractals inherently involve enormous levels of multiple scale phenomenon, fractal analysis techniques afford new prospects for dealing with spatial images and fractal geometry is now bring applied to a variety of spatial problems, and to a limited extent, to remote sensing data. In this study the focus is on assessing the utility of fractal dimension to investigating applications involving imaging of spatial. multi-scale image data. This means understanding quantitatively the effects of discretization errors and signal noise on the determination of the fractal dimension of an image set. The accuracy and efficiency of three methods for estimating the fractal dimension of an image are evaluated: Images of the Cantor set are used to measure accuracy of the isarithm, the triangular prism method and the variogram method. Overall, of these methods, the triangular prism is found to be the most robust in regard to noise rejection and accuracy while at the same time. this algorithm also was computationally the most efficient. (C) 1998 Elsevier Science Ltd. All rights reserved.

Publication Title

Computers & Geosciences

Volume

24

Issue

8

First Page

785

Last Page

795