Image compression using weighted finite automata

doi:10.1016/0097-8493(93)90079-O

Computers & Graphics

Volume 17, Issue 3, May–June 1993, Pages 305-313

https://doi.org/10.1016/0097-8493(93)90079-O Get rights and content

Abstract

We introduce Weighted Finite Automata (WFA) as a tool to define real functions, in particular, greyness functions of grey-tone images. Mathematical properties and the definition power of WFA have been studied by Culik and Karhumäki. Their generative power is incomparable with Barnsley's Iterative Function Systems. Here, we given an automatic encoding algorithm that converts an arbitrary grey-tone-image (a digitized photograph) into a WFA that can regenerate it (with or without information loss). The WFA seems to be the first image definition tool with such a relatively simple encoding algorithm.

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The mathematical theory behind WFAs, that of rational power series, has been extensively studied in the past [31,54,39,17] and has been more recently the topic of a dedicated handbook [28]. WFAs are widely used in modern applications, perhaps most prominently in image processing and speech recognition where the terminology of weighted automata seems to have been first introduced and made popular [24,46,52,44,48], in several other speech processing applications such as speech synthesis [56,3], in phonological and morphological rule compilation [36,37,50], in parsing [53,47], machine translation [25,2], bioinformatics [30,4], sequence modeling and prediction [22], formal verification and model checking [6,5], in optical character recognition [20], and in many other areas. The recent developments in spectral learning [34,8] have triggered a renewed interest in the use of WFAs in machine learning, with several recent successes in natural language processing [10,11] and reinforcement learning [19,33].
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^☆: Research was supported by the National Science Foundation under Grant No. CCR-9202396.

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Technical sectionImage compression using weighted finite automata☆

Abstract

Disc. Appl. Math.

Comp. & Graph.

Quadtrees generated by finite automata

Compact Representation of Pattern by Finite Automata

Quadtrees and the Hausdorff dimension of pictures

Fractal Everywhere

Recurrent iterated function systems

Constructive Approximation

Harnessing chaos for image synthesis

Technical section
Image compression using weighted finite automata☆