Regular Article: On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves

Authors:
Mustafa Unel;William A. Wolovich
Affiliations:
Division of Engineering, Brown University, Providence, Rhode Island, 02912, f1{mu or waw}@lems.brown.eduf1;Division of Engineering, Brown University, Providence, Rhode Island, 02912, f1{mu or waw}@lems.brown.eduf1
Venue:
Advances in Applied Mathematics
Year:
2000

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Abstract

We provide a solution to the important problem of constructing complete independent sets of Euclidean and affine invariants for algebraic curves. We first simplify algebraic curves through polynomial decompositions and then use some classical geometric results to construct functionally independent sets of invariants. The results presented here represent some new contributions to algebraic curve theory that can be used in many application areas, such model-based vision, object recognition, graphics, geometric modeling, and CAD.