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Discrete Representation of Straight Lines
April 1984 (vol. 6 no. 4)
pp. 450-463
Leo Dorst, Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Delft, The Netherlands.
Arnold W. M. Smeulders, Department of Applied Physics, Delft University of Technology, Delft, The Netherlands; Department of Pathology and Medical Informatics, Free University, Amsterdam, The Netherlands.
If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently than the continuous line segment, but measurements of properties (such as line length) performed on the representation have an intrinsic inaccuracy due to the digitization process. In this paper, two fundamental properties of the quantization of straight line segments are treated. 1) It is proved that every ``straight'' chaincode string can be represented by a set of four unique integer parameters. Definitions of these parameters are given. 2) A mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string. The relation with the chord property is briefly discussed.
Citation:
Leo Dorst, Arnold W. M. Smeulders, "Discrete Representation of Straight Lines," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 450-463, April 1984, doi:10.1109/TPAMI.1984.4767550
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