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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\u2014often required to solve many image-analytic problems\u2014can 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<jats:italic>nearest fraction<\/jats:italic>in that sequence can efficiently be obtained by the<jats:italic>regula falsi<\/jats:italic>method from the AFT concerned. To assert its merit, we show its use in two applications\u2014one 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.<\/jats:p>","DOI":"10.1515\/amcs-2017-0045","type":"journal-article","created":{"date-parts":[[2017,9,25]],"date-time":"2017-09-25T10:00:43Z","timestamp":1506333643000},"page":"637-658","source":"Crossref","is-referenced-by-count":2,"title":["On the Farey sequence and its augmentation for applications to image analysis"],"prefix":"10.61822","volume":"27","author":[{"given":"Sanjoy","family":"Pratihar","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering , National Institute of Technology Meghalaya , Bijni Complex, Shillong , India"}]},{"given":"Partha","family":"Bhowmick","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering , Indian Institute of Technology , Kharagpur , India"}]}],"member":"37438","published-online":{"date-parts":[[2017,9,23]]},"reference":[{"key":"2021040808473540930_j_amcs-2017-0045_ref_001_w2aab3b7c14b1b6b1ab1ab1Aa","unstructured":"Amin, A. and Fischer, S. 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Skew angle detection of digitized Indian script documents, IEEE Transactions on Pattern Analysis and Machine Intelligence19(2): 182\u2013186.10.1109\/34.574803"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_008_w2aab3b7c14b1b6b1ab1ab8Aa","unstructured":"Chou, C., Chu, S. and Chang, F. (2007). Estimation of skew angles for scanned documents based on piecewise covering by parallelograms, Pattern Recognition40(2): 443\u2013455.10.1016\/j.patcog.2005.10.030"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_009_w2aab3b7c14b1b6b1ab1ab9Aa","unstructured":"Chung, K.L., Liao, P.H. and Chang, J.M. (2008). Novel efficient two-pass algorithm for closed polygonal approximation based on LISE and curvature constraint criteria, Journal of Visual Communication and Image Representation19(4): 219\u2013230.10.1016\/j.jvcir.2008.01.004"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_010_w2aab3b7c14b1b6b1ab1ac10Aa","unstructured":"Cormen, T.H., Leiserson, C.E. and Rivest, R.L. (2000). 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Detection of circular arcs in images, 4th Alvey Vision Conference, Manchester, UK, pp. 259\u2013263."},{"key":"2021040808473540930_j_amcs-2017-0045_ref_050_w2aab3b7c14b1b6b1ab1ac50Aa","unstructured":"Rosin, P.L. and West, G.A.W. (1995). Non-parametric segmentation of curves into various representations, IEEE Transactions on Pattern Analysis and Machine Intelligence17(12): 1140\u20131153.10.1109\/34.476507"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_051_w2aab3b7c14b1b6b1ab1ac51Aa","doi-asserted-by":"crossref","unstructured":"Routledge, N. (2008). Computing Farey series, Mathematical Gazette92(523): 55\u201362.","DOI":"10.1017\/S002555720018252X"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_052_w2aab3b7c14b1b6b1ab1ac52Aa","unstructured":"Sarkar, B., Singh, L.K. and Sarkar, D. (2004). 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Hough transform based fast skew detection and accurate skew correction methods, Pattern Recognition41(12): 3528\u20133546.10.1016\/j.patcog.2008.06.002"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_055_w2aab3b7c14b1b6b1ab1ac55Aa","doi-asserted-by":"crossref","unstructured":"Srihari, S.N. and Govindraju, V. (1989). Analysis of textual images using the Hough transform, Machine Vision Applications2(3): 141\u2013153.","DOI":"10.1007\/BF01212455"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_056_w2aab3b7c14b1b6b1ab1ac56Aa","doi-asserted-by":"crossref","unstructured":"Teh, C.H. and Chin, R.T. (1989). On the detection of dominant points on digital curves, IEEE Transactions on Pattern Analysis and Machine Intelligence2(8): 859\u2013872.","DOI":"10.1109\/34.31447"},{"key":"2021040808473540930_j_amcs-2017-0045_ref_057_w2aab3b7c14b1b6b1ab1ac57Aa","unstructured":"Van, T.T. and Le, T.M. (2016). 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