Estimation of fractal surfaces using scale expansion and its applications

This paper treats an estimation method for fractal surfaces (three-dimensio nal fractal signals) and an adaptive technique for cases where the estimati on method is applied. In addition, we present an analysis of the estimation error, an estimate of the fractal dimension, and several applications. Fir st, we assume that the shape of:the fractal surface is represented by the c onvolution of the input signal and the impulse response function which is e xpanded as a set of scale functions. Then we derive an estimation method wh ich uses the self-similarity of the impulse response under the scale expans ion of coordinate axis. The fractal dimension is estimated by using the two -dimensional wavelet transform coefficient on the fractal surface. In the a pproximation of the impulse response function we use an adaptive method to reduce the computation time, where the scale functions are utilized stepwis e. As a numerical example,it is shown that the error of the one-step-ahead estimation is small, and that the error of the n-steps-ahead estimation is limited in range. Then we present real applications such as texture classif ication by surface estimation, and analysis of the spatial distribution of a cloud. (C) 1999 Scripta Technica.