Jen-Chang Liu, Wen L. Hwang and Ming-Syan Chen
The 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 1-D fBm estimation method. This method does not perform well when the image size is small (say 128x128). 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 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 near 1/f process. Numerical simulation shows the performance for our algorithm in both the fractal parameter and image estimation. Applications on coastline detection and texture segmentation in noisy environment are also demonstrated.