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/Automata for the Syntactic Analysis Summary Related Theoretical Results

Character Recognition – Preprocessing Normalization 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 – Preprocessing Elimination 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 – Preprocessing Thinning Algorithms 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 ).

Character Recognition – Preprocessing Result Unitary skeleton on a 20 x 25 grid

Variants of Array Grammars/Automata for 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,

Bounded Parallelism

Bounded Parallelism/Prescribed Teams array productions in team are applied in parallel

Bounded Parallelism/Prescribed Teams derivation modes array productions in team are applied in parallel; the teams themselves may be applied in different derivation modes (variants of co-operation as in co-operating distributed grammar systems): =k, >k, <k, *, t (maximal derivation mode) internally hybrid modes: (t,=k), (t,>k), (t, m,<k)

Bounded Parallelism/Prescribed Teams finite 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 must coincide 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/Automata for 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,

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/Automata for 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,

Variants of Array Grammars/Automata for 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,

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,

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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