Rational and affine expressions for image description

Čulík, Karel; Dube, Simant

doi:10.1016/0166-218x(93)90031-i

Cited by 37 publications

(8 citation statements)

References 7 publications

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“…contributes another 1 16 , adding up to 7 16 , which is the average of (all the numbers from the interval delimited by) 3 8 and 1 2 .…”

Section: Proofmentioning

confidence: 99%

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Binary operations on automatic functions

Karhumäki¹,

Kari²,

Kupke³

2007

RAIRO-Theor. Inf. Appl.

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Real functions on the domain [0, 1) n-often used to describe digital images-allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomlyused full Cartesian product. We show, however, the infeasibility of functional composition; simple examples yield that the class of automatic functions (i.e., functions computable by automata) is not closed under this operation.

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“…contributes another 1 16 , adding up to 7 16 , which is the average of (all the numbers from the interval delimited by) 3 8 and 1 2 .…”

Section: Proofmentioning

confidence: 99%

“…The use of finite automata for image representation (and, ideally, compression and even manipulation) was proposed in [1] and [3]. Later, the model of weighted finite automata and their basic properties were discussed in [5].…”

Section: Introductionmentioning

confidence: 99%

Binary operations on automatic functions

Karhumäki¹,

Kari²,

Kupke³

2007

RAIRO-Theor. Inf. Appl.

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“…photographs) and there is a good theoretical reason for it. Indeed, in contrast to (nonprobabilistic) generators for black and white images discussed in [7], the nondeterministic ap-WFA are much more powerful than the deterministic one. We show a simple example of linear greyness function that can be generated by a nondeterministic but not by a deterministic ap-WFA.…”

Section: F(paq)fl(q))mentioning

confidence: 99%

“…The WFA's are a modification of probabilistic finite generators from [7]. A nonprobabilistic version of equivalent devices, describing black and white images, were independently studied in [4,5,16,17].…”

Section: Introductionmentioning

confidence: 99%

Image compression using Weighted Finite Automata

Čulík

Kari

1993

Lecture Notes in Computer Science

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We introduce Weighted Finite Automata (WFA) as a tool to define real functions, in particular, the greyness functions of greytone images. Mathematical properties and the definition power of WFA have been studied by Culik and KarhumsTheir generative power is incomparable with Barnsley's Iterative Function Systems. Here, we give an automatic encoding algorithm that converts an arbitrary grey-toneimage (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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“…w2A n fDiam(w(X))g = k n p N: (7) 3.2 Statistics on symbolic sequences Let S = s 1 s 2 ::: 2 A 1 be a sequence generated by a stationary information source 12]. Denote the (empirical) probability of nding an n-block w 2 A n in S by P n (w).…”

Section: Preliminary Examplesmentioning

confidence: 99%

Spatial representation of symbolic sequences through iterative function systems

Tiňo

1999

IEEE Trans. Syst., Man, Cybern. A

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Je rey 10] proposed a graphic representation of DNA sequences using Barnsley's iterative function systems. In spite of further developments in this direction 19, 2 5 , 1 3 ], the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Je rey's graphic representation to accommodate (possibly in nite) sequences over an arbitrary nite number of symbols, 2) establish a direct correspondence between the statistical characterization of symbolic sequences via R enyi entropy spectra and the multifractal characteristics (R enyi generalized dimensions) of the sequences' spatial representations, 3) show that for general symbolic dynamical systems, the multifractal f H -spectra in the sequence space coincide with the f H -spectra on spatial sequence representations.

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Rational and affine expressions for image description

Cited by 37 publications

References 7 publications

Binary operations on automatic functions

Binary operations on automatic functions

Image compression using Weighted Finite Automata

Spatial representation of symbolic sequences through iterative function systems

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