# Fractal Image Compression: Theory and Application (Inquiries in Social Construction)

Language: English

Pages: 342

ISBN: 0387942114

Format: PDF / Kindle (mobi) / ePub

One half of the book is authored by Yuval Fisher himself, while articles from another 12 experts in the field present material from different points of view. The focus here is solely on fractal image encoding, with the aim of providing a working code that is usable in applications, while containing the *complete* details of how to encode and decode images. An indispensable "how to" guide, combining the very latest results in the field. Of interest to a very wide audience, ranging from experts in image processing to high school students.

libraries - D\, D2 , and D3 . The first has a roughly equal number of domains of each size. The second domain library has more larg domains and fewer small domains, the idea being that it is more important to find a good domain-range fit for larger ranges, since then the encoding will require fewer transformations. The third domain library has more small domains than large domains. The domains are selected as subsquares of the image whose upper-left comers are positioned on a lattice determined

specification of T would indirectly yield an exact description of XT, provided we have a way of finding fixed points of arbitrary operators. This is the essence of fractal modeling of images and other signals. Formally, fractal signal modeling may be described as follows: I. We consider signals of fixed length M, generated from an information source. Let S C ]RM consist of all signals the particular source can possibly generate. I 2. We define a family T = {Ta : ]RM --+ ]RM la E A of piecewise

computationally very efficient structure. Also, a coder offering non-iterative decoding and direct attractor optimization in the encoder is included as a special case. Other benefits of the proposed coder class include more optimal quantization and an improved Collage Theorem. The encoder/decoder structure in a fractal image coder is depicted in Figure 8.1. The encoder optimizes a mapping T such that the distance between the image x to be coded, and the collage T x of x with respect to T is

provides direct attractor optimization in the encoder. This is a simple consequence of the fact that the encoding algorithm produces a collage error which is blockwise orthogonal to the translation space, and of specific constraints made on the domain-to-range decimation factor. We illustrate this by a simple example. Let the constraints stated earlier in this chapter be fulfilled. It can be shown that the attractor error e in pixel m can be written as em = ec,m + L (8.43) fmjej, jEIm where

to measure how much blocks resemble each other, we need a function that expresses how good a set of cluster centers is, and we need a procedure for finding good cluster centers. Each of these problems is treated in this chapter. 9.2. Complexity Reduction in the Encoding Step 9.2 179 Complexity Reduction in the Encoding Step A set of cluster centers implies a clustering of the original blocks as well as of the codebook blocks (cluster Xm of original blocks consists of the blocks that most