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On the Number of Digital Straight Line Segments
November 1988 (vol. 10 no. 6)
pp. 880-887

A closed-form expression has been reported in the literature for L/sub N/, the number of digital line segments of length N that correspond to lines of the form y=ax+ beta , O>or= alpha , beta >1. The authors prove an asymptotic estimate for L/sub N/ that might prove useful for many applications, namely, L/sub N/=N/sup 3// pi /sup 2/+O(N/sup 2/ log N). An application to an image registration problem is given.

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Index Terms:
computerized picture processing; digital straight line segments; closed-form expression; asymptotic estimate; image registration; computational complexity; computerised picture processing
C.A. Berenstein, D. Lavine, "On the Number of Digital Straight Line Segments," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 6, pp. 880-887, Nov. 1988, doi:10.1109/34.9109
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