Simant Dube

Affine automata and related techniques for generation of complex images

Abstract In this paper, we introduce probabilistic affine automata (PAA), which are probabilistic finite generators having transitions labeled with affine transformations. It is shown that PAA are capable of generating highly complex images. Barnsleys (1988) IFS method to generate fractals is a special case of PAA when the automaton happens to have only a single state. A number of theoretical results on PAA are shown. The relationship between PAA, mutually recursive function systems (MRFS) and affine regular sets is investigated.

Rational and affine expressions for image description

Abstract In this paper, the representation, generation and inference of images using automata-theoretic techniques is investigated. It is shown that highly complex images, including “fractal” (self-similar) images, can be manipulated by the application of these techniques. Languages and relations over some alphabet are interpreted as images by treating strings as rational coordinates. In particular rational relations, specified by rational expressions, are considered. It is shown how texture of an image can be defined by probabilistic finite generators. Affine expressions are introduced as a generalization of both rational expressions and the IFS method to define images. Finally, two efficient methods to implement rational expressions are presented.

Balancing order and chaos in image generation

Abstract We introduce new techniques to generate real-world images. Many of the natural images exhibit a hierarchical structure and a balanced combination of both order and chaos. We show how a controlled use of deterministic chaos yields a powerful method to concisely describe and to efficiently generate complex realistic images. The basic technique is the use of Mutually Recursive Function Systems (MRFS) possibly with additional control on the order of computations. Then we show that, surprisingly, regular sets of control sequences are convenient but not essential. Some examples are presented illustrating the power of the technique.

L-systems and mutually recursive function systems

In this paper, we investigate the relationship between two different approaches to generate fractal images—L-systems and mutually recursive function systems. We consider two different ways in which L-systems have been used to generate images. The first is the well-known turtle geometry method, and the other is the vector interpretation method as used by Dekking. We show that a uniformly growing D0L-system can be simulated by an MRFS, and any D0L-system can be simulated by a control set produced by an iterative GSM.

ENCODING IMAGES AS WORDS AND LANGUAGES

We present some recently developed methods to describe, generate and encode a wide variety of images, in a mathematical formalism which uses terminology of words and of formal languages. It is shown how complex images including those with fractal (self-similar) geometries can be defined as languages, in particular regular languages, over a code alphabet in which symbols denote affine transformations and words are interpreted as compositions as these transformations. The problem of automatic encoding of images by these methods is addressed which leads to the method of recursive subdivisions.

An efficient solution of the firing mob problem

An efficient solution of the firing mob problem, which is the generalization of the well-known “firing squad synchronization” problem to finite bounded-degree networks, is presented. First, a method of synchronizing tree-connected networks is given. This method is extended to general networks. The total synchronization time is 3.5r where r is the radius of the network. No solution can work in time less than 3r on all networks. Moreover, it is shown why our solution will approach this value in the limit case when the number of states used becomes arbitrarily large.

Affine Automata: A Technique to Generate Complex Images

In this paper, we introduce probabilistic affine automata (PAA) which are probabilistic finite generators having transitions labeled with affine transformations. It is shown that PAA are capable of generating highly complex images. Barnsleys IFS method to generate fractals is a special case of PAA when the automaton happens to have only a single state.

Efficient compression of wavelet coefficients for smooth and fractal-like data

The authors show how to integrate wavelet-based and fractal-based approaches for data compression. If the data is self-similar or smooth, one can efficiently store its wavelet coefficients using fractal compression techniques resulting in high compression ratios. >

New Methods for Image Generation and Compression

We survey new methods in “Computational Fractal Geometry.” We start with M. Barnsleys pioneering Iterative Function Systems and our extension of this method, in particular Mutually Recursive Function Systems. Further we discuss (Probabilistic) Finite Generators, L-systems and other methods as used for image generations.

Implementing Daubechies wavelet transform with weighted finite automata

Abstract.We show that the compactly supported wavelet functions