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The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields.
The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications.
List of contents
I Fractal Image Encoding.- 1 Why Fractal Block Coders Work.- 2 On Fractal Compression and Vector Quantization.- 3 On the Use of Subsampling in Fractal Image Compression.- 4 On the Benefits of Basis Orthogonalization in Fractal Compression.- 5 On the Dimension of Fractally Encoded Images.- 6 Fractal Image Compression via Nearest Neighbor Search.- 7 Fractal Image Coding: Some Mathematical Remarks on Its Limits and Its Prospects.- 8 Linear Time Fractal Quadtree Coder.- 9 Fractal Encoding of Video Sequences.- 10 Theory of Generalized Fractal Transforms.- 11 Inverse Problem Methods for Generalized Fractal Transforms.- 12 Fractal Compression of ECG Signals.- II Fractal Image Analysis.- 13 Dimensions of Fractals and Multifractals.- 14 Velocity, Length, Dimension.- 15 A Local Multiscale Characterization of Edges Applying the Wavelet Transform.- 16 Local Connected Fractal Dimension Analysis of Early Chinese Landscape Paintings and X-Ray Mammograms.- 17 Introduction to the Multifractal Analysis of Images.- List of Participants.
