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Filtering Closed Curves
May 1986 (vol. 8 no. 5)
pp. 665-668
B. K. P. Horn, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139.
E. J. Weldon, Department of Electrical Engineering, University of Hawaii, Honolulu, HI 96822.
A closed curve in the plane can be described in several ways. We show that a simple representation in terms of radius of curvature versus normal direction has certain advantages. In particular, convolutional filtering of the extended circular image leads to a closed curve. Similar filtering operations applied to some other representations of the curve do not guarantee that the result corresponds to a closed curve. In one case, where a closed curve is produced, it is smaller than the original. A description of a curve can be based on a sequence of smoothed versions of the curve. This is one reason why smoothing of closed curves is of interest.
B. K. P. Horn, E. J. Weldon, "Filtering Closed Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 5, pp. 665-668, May 1986, doi:10.1109/TPAMI.1986.4767839
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