Wm. Krueger et al., ON SYNTHESIZING DISCRETE FRACTIONAL BROWNIAN-MOTION WITH APPLICATIONSTO IMAGE-PROCESSING, Graphical models and image processing, 58(4), 1996, pp. 334-344
Citations number
22
Categorie Soggetti
Computer Sciences, Special Topics","Computer Science Software Graphycs Programming
This paper evaluates the following four methods for synthesizing discr
ete fractional Brownian motion (dfBm): sampled fBm, displaced interpol
ation, spectral synthesis, and Karhunen-Loeve-like wavelet expansion w
ith respect to the following questions: Does the candidate dfBm have t
he correct second-order statistics? Does the candidate dfBm have the c
orrect fractal dimension? To estimate the fractal dimension we apply s
pectral linear regression, multiresolution energy analysis, and maximu
m likelihood estimation, Running an estimation routine on synthesized
data raises the final question: How do the assumptions of the estimati
on method interact with the assumptions of the synthesis method to pro
duce the results of the various trials? Our main conclusions relative
to these questions are: (1) Sampled fBm is the only one of the four me
thods which has the correct second-order statistics, but only spectral
synthesis produces a stationary signal, (2) The fractal dimension of
signals produced by sampled fBm, displaced interpolation, and spectral
synthesis can be estimated with reasonable accuracy, On the other han
d, the wavelet signals are only slightly sensitive to the input values
of H. (3) Analysis routines which make assumptions not made by the sy
nthesis routine generally yield poor estimates of H, whereas a match o
f assumptions generally produces good estimates. (C) 1996 Academic Pre
ss,Inc.