On Synthesizing Discrete Fractional Brownian Motion with Applications to Image Processing
✍ Scribed by W.M. Krueger; S.D. Jost; K. Rossi; U. Axen
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 419 KB
- Volume
- 58
- Category
- Article
- ISSN
- 1077-3169
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✦ Synopsis
wavelets for fractal modulation on a noisy communication channel. Voss [18, 19] and Saupe [15] use various syntheses This paper evaluates the following four methods for synthesizing discrete fractional Brownian motion (dfBm): sampled of fBm to render fractal landscapes.
fBm, displaced interpolation, spectral synthesis, and Karhu-
Of particular interest to us is the application of dfBm nen-Loeve-like wavelet expansion with respect to the following to image processing, in particular to texture analysis. Fracquestions: Does the candidate dfBm have the correct secondtional Brownian motion has associated to it a single paramorder statistics? Does the candidate dfBm have the correct eter H, the Hurst exponent, which controls its roughness fractal dimension? To estimate the fractal dimension we apply via the formula D ϭ 2 Ϫ H, where D is the Hausdorff spectral linear regression, multiresolution energy analysis, and dimension. Smoothness varies inversely with D. maximum likelihood estimation. Running an estimation routine Mandelbrot and van Ness [8] defined fractional on synthesized data raises the final question: How do the as-Brownian motion as the fractional derivation of ordinary sumptions of the estimation method interact with the assump-Brownian motion. Specifically, let B be ordinary Brownian tions of the synthesis method to produce the results of the motion and 0 Յ H Յ 1. Then B H (0) ϭ 0 and