Computationally fast Bayesian recognition of complex objects based on mutual algebraic invariants

An effective approach has appeared in the literature for recognizing a 2D curve or 3D surface objects of modest complexity based on representing an object by a single implicit polynomial of 3/sup rd/ or 4/sup th/ degree, computing a vector of Euclidean or affine invariants which are functions of the polynomial coefficients, followed by Bayesian object recognition of the invariants, thus producing a low computational cost robust recognition. This paper extends the approach, as well as an initial work on mutual invariants recognizers, to the recognition of objects too complicated to be represented by a single polynomial. Hence, an object to be recognized is partitioned into patches, each patch is represented by a single implicit polynomial, mutual invariants are computed for pairs of polynomials for pairs of patches, and the object recognition is via a Bayesian recognition of vectors of self and mutual invariants. We discuss why the complete object geometry can be captured by the geometry of pairs of patches, how to design mutual invariants, and how to match patches in the data with those in the database at a low computational cost. The approach is a low computational cost recognition of partially occluded articulated objects in an arbitrary position and in noise by recognizing the self or joint geometry of one or more patches.