Introductory Remarks
The recognition of patterns will be here considered as a cybernetical subdiscipline investigating the general principles of decision making in transmission systems with stationary information sources, under the assumption that the set of decisions is enum
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No. 85
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JULIUSZ KULIKOWSKI AC:\DEMY OF SCIENCES - WARSAW
ALGEBRAIC METHODS IN PATTERN RECOGNITION
COURSE HELD :\.T THE DEPARTMENT OF AUTOMATION AND INFORMATION JULY 1971
Springer-Verlag Wien GmbH 1971
This work is I!Uqect to copynght
All rights are reserved, whether the whole or part of the material is concerned specifically those of translation. reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1972 by Springer-Verlag Wien Originally published by Springer-Verlag Wien-New York in 1972
ISBN 978-3-211-81128-3 DOI 10.1007/978-3-7091-2884-8
ISBN 978-3-7091-2884-8 (eBook)
P R E F A C E
During the last years electronic computation and data processing methods have reached a comparatively high level of maturity. More and more complicated forms of input data: numerical, alpha-numerical, textual can be handled automatically and processed by electronic computers. Last time a growing attention is paid to the picture processing. Graphical and pictorial forms of information play an important role anywhere a human individuum is linked on an informational system as its element. This is a consequence of the fact that a human visual tract is distinguished by its possibility to parallel information processing and by its flexibility to changing circumstances. That is why the problem of immediate visual information exchange between man and computer arises as a very actual one. The recognition of patterns by specialized automata or by electronic computers is a first step toward the solution of this problem. The pictures being of interest in many practical applications are not only typewritten or handwritten texts, but also graphics, electronic sahemas, graphs, fingerprints, meteorogio~l charts, miarophotos eta. Under certain assumptions they can be divided into less or more formalized classes to be discriminated automatically. It seems to us reasonable to consider the pia-
4
Preface
tures as some expressions of a "planar" language~ subjected to a certain number of morphological and syn~ tactical rules. An identification of the sets of grammatical rules corresponding to the given classes of patterns is a problem of interest if a pattern recognition algorithm is to be chosen. No universal "planar" language seems to exist and no universal pattern recognition algorithm for a computer seems to be possible~ as well. Nevertheless~ the linguistic approach turns out as a more effective one when composite patterns are dealt with. The other methods based on geostatistical or functional models of patterns recognition can be included as fragmentary ones in the structural-linguistic anaZusis of a composite pattern. A need of an universal meta-language for the description and theoretical investigation of "planar" languages that are used in particular situations arised. In our opinion~ this can be reached on the basis of a general approach offered by a general theory of relations. This last can be specified in such a
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