On the construction of complete sets of geometric invariants for algebraiccurves

We provide a solution to the important problem of constructing complete ind ependent sets of Euclidean and affine invariants for algebraic curves. We f irst simplify algebraic curves through polynomial decompositions and then u se some classical ge geometric results to construct functionally independen t sets of invariants. The results presented here represent some new contrib utions to algebraic curve theory that can be used in many application areas , such model-based vision, object recognition, graphics, geometric modeling , and CAD. (C) 2000 Academic Press.