Transcript P Systems with Antiport Rules for Evolution Rules

Syntactical Pattern Recognition
with 2-Dimensional
Array Grammars and
Array Automata
Rudi FREUND
Faculty of Informatics
Vienna University of Technology
Wien, Austria
Overview
Offline Character Recognition
● Preprocessing
- normalization
- elimination of noisy pixels
- thinning
● Syntactic Analysis
Variants of Array Grammars/Automata
for the Syntactic Analysis
Related Theoretical Results
Summary
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 8neighbourhood = 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. 77-80).
Character Recognition – Preprocessing
Result
Unitary skeleton on a 20 x 25 grid
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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, 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 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,<k), (>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
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:
● deviation of lines
● gaps in lines
● superfluous/missing lines
● superfluous (remaining) pixels
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, 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/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, 284-296.
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,
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 contextfee 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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