Syntactical Pattern Recognition with 2-Dimensional

Array Grammars and Array Automata

Faculty of Informatics Vienna University of Technology

Wien, Austria

Rudi FREUND

Offline Character Recognition

Overview

● Preprocessing - normalization - elimination of noisy pixels - thinning● Syntactic Analysis

Variants of Array Grammars/Automatafor the Syntactic Analysis

Summary

Related Theoretical Results

Character Recognition – PreprocessingNormalization

The scanned characters first are normalized to fill out a 320×400 grid in order to get comparable patterns. Then noisy pixels are eliminated. After noise elimination, the resulting arrays on the 320×400 grid are mapped on a 20×25 grid.

Character Recognition – PreprocessingElimination of Noisy Pixels

Algorithms are based on parallel array grammars

eliminate pixel if number of pixels in the 8-neighbourhood = 0,iterate this algorithm until no more changes

Character Recognition – PreprocessingThinningAlgorithms are based on parallel array grammars. Reduction to a unitary skeleton (e.g., J. H. Sossa, An improved parallel algorithm for thinning digital patterns, Pattern Recognition Letters 10 (1989), pp. 77-80).

Character Recognition – PreprocessingResult

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Œ Œ Œ ŒŒ Œ Œ Œ Œ

Œ ŒŒ Œ Œ Œ Œ ŒŒ Œ Œ Œ Œ Œ Œ ŒŒ ŒŒ ŒŒ Œ

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Unitary skeleton on a 20 x 25 grid

Variants of Array Grammars/Automatafor the Syntactic Analysis (SSPR’96)

Henning Fernau, Rudolf Freund: Bounded parallelism in array grammars used for character recognition. In: Petra Perner, Patrick Shen-Pei Wang, Azriel Rosenfeld (Eds.): Advances in Structural and Syntactical Pattern Recognition, 6th International Workshop, SSPR'96, Leipzig, Germany, August 20-23, 1996, Proceedings. LNCS 1121, Springer, Berlin, 1996, 40-49.

Bounded Parallelism

Bounded Parallelism

Bounded Parallelism

Bounded Parallelism

Bounded Parallelism

Bounded Parallelism

Bounded Parallelism/Prescribed Teams

array productions in team are applied in parallel

Bounded Parallelism/Prescribed Teamsderivation modes

array productions in team are applied in parallel;the teams themselves may be applied in differentderivation modes (variants of co-operation as inco-operating distributed grammar systems):

=k, >k, <k, *, t (maximal derivation mode)

internally hybrid modes: (t,=k), (t,>k), (t,<k), (>m,<k)

Bounded Parallelism/Prescribed Teamsfinite index restriction/pattern analysis

Finite index restriction:by applying the array productions of a team in parallel, all non-terminal symbols in the current sentential form must be affected

Analysis of a given pattern:whenever a terminal symbol is generated, it mustcoincide with the symbol in the pattern (character) to be analysed

Syntactic Pattern Analysis – Distance from Ideal Cluster

● deviation of lines● gaps in lines● superfluous/missing lines● superfluous (remaining) pixels

During the analysis of a given pattern, its distance from the ideal cluster of arrays representing a specific character is computed.

Features to be taken into account:

Variants of Array Grammars/Automatafor the Syntactic Analysis (SSPR’98,k-head finite automata)

Henning Fernau, Rudolf Freund, Markus Holzer: Character recognition with k-head finite array automata. In: Adnan Amin, Dov Dori, Pavel Pudil, Herbert Freeman (Eds.): Advances in Pattern Recognition, Joint IAPR International Workshops SSPR '98 and SPR '98, Sydney, NSW, Australia, August 11-13, 1998, Proceedings. LNCS 1451, Springer, Berlin, 1998, 282-291.

k-head finite automata

The k heads in a k-head finite array automaton are the counterparts of the k non-terminal symbols in array grammars with prescribed teams and finite index. In each step, every head has to move.The automaton has a „head sensing ability“, i.e., two heads can never occupy the same position.Moreover, a position carrying a terminal symbol in the array to be parsed can only be visited once by one of the k heads (and then is marked as „forbidden position“ for the rest of the parsing procedure).

Variants of Array Grammars/Automatafor the Syntactic Analysis (regulated array grammars of finite index)

Henning Fernau, Rudolf Freund, Markus Holzer: Regulated array grammars of finite index. II: Syntactic pattern recognition. In: Gheorghe Păun, Arto Salomaa (Eds.): Grammatical Models of Multi-Agent Systems. Topics in Computer Mathematics 8, Gordon and Breach Science Publishers, 1999, 284-296.

Variants of Array Grammars/Automatafor the Syntactic Analysis (SSPR 2000)

Rudolf Freund, Markus Neubauer, Martin Summerer, Stefan Gruber, Jürgen Schaffer, Roland Swoboda: A hybrid system for the recognition of hand-written characters. In: Francesc J. Ferri, José Manuel Iñesta Quereda, Adnan Amin, Pavel Pudil (Eds.): Advances in Pattern Recognition, Joint IAPR International Workshops SSPR 2000 and SPR 2000, Alicante, Spain, August 30 - September 1, 2000, Proceedings. LNCS 1876, Springer, Berlin, 2000, 67-76.

Hybrid Systems

Pre-selection by neural network(for a given pattern, only a few pre-selected array grammars have to analyse it)

Application of teams controlled by additional mechanism (programmed, matrix)

Look-ahead instead of inefficient backtracking(larger neighbourhoods)

Related Theoretical Results

Henning Fernau, Rudolf Freund, Markus Holzer: Regulated array grammars of finite index. I: Theoretical Investigations. In: Gheorghe Păun, Arto Salomaa (Eds.): Grammatical Models of Multi-Agent Systems. Topics in Computer Mathematics 8, Gordon and Breach Science Publishers, 1999, 260-283.

Regulated Array Grammars of Finite Index

Restricted by the finite index condition, with the control mechanisms of using variants of context-fee array productions in prescibed teams, matrices or a control graph, the corresponding families of generated array languages coincide, even in the appearance checking case. The corresponding models of k- head automata accept the same families of array languages, too.With respect to k, we obtain infinite hierarchies for dimensions n > 1.

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