On the Farey sequence and its augmentation for applications to image analysis

• Autorzy: Pratihar S. , Bhowmick P.

Identyfikatory

DOI

10.1515/amcs-2017-0045

• Języki publikacji: EN

Abstrakty

EN

We introduce a novel concept of the augmented Farey table (AFT). Its purpose is to store the ranks of fractions of a Farey sequence in an efficient manner so as to return the rank of any query fraction in constant time. As a result, computations on the digital plane can be crafted down to simple integer operations; for example, the tasks like determining the extent of collinearity of integer points or of parallelism of straight lines—often required to solve many image-analytic problems—can be made fast and efficient through an appropriate AFT-based tool. We derive certain interesting characterizations of an AFT for its efficient generation. We also show how, for a fraction not present in a Farey sequence, the rank of the nearest fraction in that sequence can efficiently be obtained by the regula falsi method from the AFT concerned. To assert its merit, we show its use in two applications—one in polygonal approximation of digital curves and the other in skew correction of engineering drawings in document images. Experimental results indicate the potential of the AFT in such image-analytic applications.

Słowa kluczowe

EN

Farey sequence; Farey table; fraction rank; theory of fractions; image analysis

PL

sekwencja Fareya; rząd frakcji; analiza obrazu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 637--658
• Opis fizyczny: Bibliogr. 68 poz., rys., tab., wykr.

Twórcy

autor

Pratihar S.

• Department of Computer Science and Engineering, National Institute of Technology Meghalaya, Bijni Complex, Shillong, India

autor

Bhowmick P.

• Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).