Computational fractal methods for image analysis and compression

We presents the following methods for image compression and signal and image analysis: (1) An efficient method for fractal image compression based a triangular Sierpinski scan path algorithm, which results in a binary triangulation tree structure and facilitates multiresolution block matching. (2) Wavelet based multifractal signal segmentation and spectral estimation for signals applied to an important class of electrocardiogram (ECG) signals known as Heart Rate Variability (HRV) signals and (3) A new method for image analysis and compression based on (i) using the fast wavelet transformation or multifractal segmentation to isolate edge information; (ii) saving trend information as low-pass or low frequency wavelet coefficients and (iii) analyzing the remaining texture information by multifractal texture segmentation. A local fractal dimension (local Hurst exponent) is estimated from the either the wavelet method or rescaled range (R/S) analysis. For example, by calculating local R/S values over multiscale Quincunx neighborhoods of each pixels, we form a "slope image" whose intensity levels represents textures in the original image.