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Filtering Closed Curves

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2 Author(s)
Horn, B.K.P. ; Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139. ; Weldon, E., Jr.

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.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-8 ,  Issue: 5 )