Estimation of fractal surfaces using scale expansion and its applications
Yoshikazu Ikeda, Shozo Tokinaga, Akio Miyazaki · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1999
This paper treats an estimation method for fractal surfaces (three-dimensional fractal signals) and an adaptive technique for cases where the estimation method is applied. In addition, we present an analysis of the estimation error, an estimate of the fractal dimension, and several applications. First, we assume that the shape of the fractal surface is represented by the convolution of the input signal and the impulse response function which is expanded as a set of scale functions. Then we derive an estimation method which uses the self-similarity of the impulse response under the scale expansion of coordinate axis. The fractal dimension is estimated by using the two-dimensional wavelet transform coefficient on the fractal surface. In the approximation of the impulse response function we use an adaptive method to reduce the computation time, where the scale functions are utilized stepwise. 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 classification by surface estimation, and analysis of the spatial distribution of a cloud. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(9): 10–17, 1999