Recognizing Groups of Curves Based on New Affine Mutual Geometric Invariants, with Applications to Recognizing Intersecting Roads in Aerial Images

This paper treats some of the problem in recognizing the geometry of objects composed of groups of curves that undergo arbitrary affine transformations, providing the objects can be invariantly segmented into groups of curves representable by 3rd degree implicit polynomials. As an illustrative example, we treat the problem of representing and recogniring portions of roads in aerial images. The approach we develop is to represent each road segment in a disc by a third degree implicit-polynomial, and recognition of road geometry is then Bayesian recognition of a vector of mutual algebraic invariants for the polynomials within such a disc. The mutual affine invariants developed and used are for pairs of polynomials. This is a new powerful approach to dealing with the recognition of complex curves.