Splines as embeddings for generalized cylinders

Generalized cylinders are an attractive representation for three-dimensional objects. One of their principal features is that the representation contains an intrinsic coordinate frame. The intrinsic (object-centered) frame computed from image data facilitates the matching of an object with a similarly represented stored prototype. The definitions of generalized cylinders are loose and do not specify how a generalized cylinder is to be represented digitally. Previous digital representations have tended to be either nonparametric renditions, which makes them computationally cumbersome, or parametric simplifications, which limit the class of objects that can be represented. It is shown that splines provide an attractive representation technique for generalized cylinders. In fact splines provide a parametric representation for the full generalization of the generalized cylinders concept.

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