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.

[1]  T. Kanade,et al.  The theory of straight homogeneous generalized cylinders and A taxonomy of generalized cylinders , 1983 .

[2]  Donald P. Greenberg,et al.  An interactive computer graphics approach to surface representation , 1977, SIGGRAPH '77.

[3]  Richard Franklin Riesenfeld,et al.  Applications of b-spline approximation to geometric problems of computer-aided design. , 1973 .

[4]  Henry Fuchs,et al.  Optimal surface reconstruction from planar contours , 1977, CACM.

[5]  Ruzena Bajcsy,et al.  Generalised cylinders from local aggregation of sections , 1981, Pattern Recognit..

[6]  Samuel D. Conte,et al.  Elementary Numerical Analysis: An Algorithmic Approach , 1975 .

[7]  Aristides A. G. Requicha,et al.  The PADL-1.0/2 system for defining and displaying solid objects , 1978, SIGGRAPH.

[8]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[9]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[10]  D. Marr,et al.  Representation and recognition of the spatial organization of three-dimensional shapes , 1978, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  Gerald J. Agin Representation and description of curved objects , 1972 .

[12]  Robert F. Sproull,et al.  Principles in interactive computer graphics , 1973 .


[14]  Rodney A. Brooks,et al.  The ACRONYM Model-Based Vision System , 1979, IJCAI.

[15]  Sargur N. Srihari,et al.  Representation of Three-Dimensional Digital Images , 1981, CSUR.

[16]  R. Brooks Solving the Find-Path Problem by Representing Free Space as Generalized Cones , 1982 .

[17]  Ramakant Nevatia,et al.  Description and Recognition of Curved Objects , 1977, Artif. Intell..

[18]  Rodney A. Brooks,et al.  Symbolic Reasoning Among 3-D Models and 2-D Images , 1981, Artif. Intell..

[19]  Thomas O. Binford,et al.  Computer Description of Curved Objects , 1973, IEEE Transactions on Computers.

[20]  Uri Shani Understanding three-dimensional images: the recognition of abdominal anatomy from computed axial tomograms (cat) , 1980 .