2D object description and recognition based on contour matching by implicit polynomials

This work deals with 2D object description and recognition based on coefficients of implicit polynomials (IP). We first improve the description abilities of recently published Min-Max and Min-Var algorithms by replacing algebraic distances by geometric ones in the relevant cost function. We propose a new recognition approach that is based on deriving linear rotation invariants from several polynomials of different degrees, fitted to the object shape, as well as on their fitting errors. This approach is found to considerably improve the recognition and is denoted as Multi Order (degree) and Fitting Errors Technique (MOFET). We also use a Shape Transform, based on the Scatter Matrix of the objects' shape, to allow Affine invariant classification. Finally, we compare the performance of our approach with the Curvature Scale Space (CSS) method and find that it has an advantage over CSS, at about the same complexity.