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Sayre's paradox
Sayre’s Paradox is a dilemma encountered in the design of automated handwriting recognition systems. A standard statement of the paradox is that a cursively written word cannot be recognized without being segmented and cannot be segmented without being recognized.〔See the PhD thesis by Alessandro Vinciarelli “Offline Cursive Handwriting: From Word to Text Recognition” (http://infoscience.epfl.ch/record/82879). See also Machine Learning: Theory and Applications, Vol. 31 of Handbook of Statistics, B. V. Elsevier, ed., p. 422 (https://one.overdrive.com/media/1358341/machine-learning-theory-and-applications).〕 The paradox was first articulated in a 1973 publication by Kenneth M. Sayre, after whom it was named.〔Kenneth M. Sayre, “Machine Recognition of Handwritten Words: A Project Report,” Pattern Recognition, Pergamon Press, Vol. 5, 1973, pp. 213-228.〕
==Nature of the Problem==
It is relatively easy to design automated systems capable of recognizing words inscribed in a printed format. Such words are segmented into letters by the very act of writing them on the page. Given templates matching typical letter shapes in a given language, individual letters can be identified with a high degree of probability. In cases of ambiguity, probable letter sequences can be compared with a selection of properly spelled words in that language (called a lexicon).〔Alessandro Vinciarelli, “A Survey on () Off-line Cursive Word Recognition,” Pattern Recognition, Vol. 35, issue 7. July 2002, pp. 1433-1446.〕 If necessary, syntactic features of the language can be applied to render a generally accurate identification of the words in question.〔See “Introduction of Statistical Information in a Syntactic analyzer for Document Image Recognition,” by André O. Maroneze, Bertrant Coüashon, and Aurélie Lemaitre (http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=731511).〕 Printed-character recognition systems of this sort are commonly used in processing standardized government forms, in sorting mail by zip code, and so forth.
In cursive writing, however, letters comprising a given word typically flow sequentially without gaps between them. Unlike a sequence of printed letters, cursively connected letters are not segmented in advance. Here is where Sayre’s Paradox comes into play. Unless the word is already segmented into letters, template-matching techniques like those described above cannot be applied. Prior segmentation, that is to say, is necessary for word recognition. On the other hand, there are no reliable techniques for segmenting a word into letters unless the word itself has been previously identified. Word recognition requires letter segmentation, and letter segmentation requires word recognition. There is no way a cursive writing recognition system employing standard template-matching techniques can do both simultaneously.
Advantages to be gained by use of automated cursive writing recognition systems include routing mail with handwritten addresses, reading handwritten bank checks, and automated digitalization of hand-written documents.〔See Alessandro Vinciarelli, “Offline Cursive Handwriting: From Word to Text Recognition,” op. cit.〕 These are practical incentives for finding ways of circumventing Sayre’s Paradox.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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