Multilevel Algebraic Invariants Extraction by Incremental Fitting Scheme

Abstract

Algebraic invariants extracted from coefficients of implicit polynomials (IPs) have been attractive because of its convenience for solving the recognition problem in computer vision. However, traditional IP fitting methods fixed the polynomial degree and thus lead to the difficulty for obtaining appropriate invariants according to the complexity of an object. In this paper, we propose a multilevel method for invariant extraction based on an incremental fitting scheme. Because this fitting scheme incrementally determines the IP coefficients in different degrees, we can extract the invariants from different degree forms of IP coefficients during the incremental procedure. Our method is effective, not only because it adaptively encodes the appropriate invariants to different shapes, but also we encodes the information evaluating the contribution of shape representation to each degree invariant set, so as to have better discriminability. Experimental results demonstrate the better effectiveness of our method compared with prior methods.