Estimation of 2-D Noisy Fractional Brownian Motion and Its Applications Using Wavelets
Journal
IEEE Transactions on Image Processing
Journal Volume
9
Journal Issue
8
Pages
1407-1419
Date Issued
2000
Date
2000
Author(s)
Abstract
The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorithms for 2-D isotropic fBm images are simple extensions of the one-dimensional (1-D) fBm estimation method. This method does not perform well when the image size is small (say, 32 × 32). We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coefficients across scales. Our method places no restriction on the wavelets. Also, it provides a robust parameter estimation for small noisy fractal images. For image denoising, a Wiener filter is constructed by our algorithm using the estimated parameters and is then applied to the noisy wavelet coefficients at each scale. We show that the averaged power spectrum of the denoised image is isotropic and is a nearly 1/f process. The performance of our algorithm is shown by numerical simulation for both the fractal parameter and the image estimation. Applications on coastline detection and texture segmentation in noisy environment are also demonstrated.
SDGs
Other Subjects
Algorithms; Brownian movement; Computer simulation; Digital filters; Fractals; Image analysis; Parameter estimation; Regression analysis; Two dimensional; Wavelet transforms; Denoising; Fractal images; Fractal parameter estimation algorithm; Fractional Brownian motion; Wiener filter; Image enhancement
Type
journal article
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