Recognizing mice, vegetables and hand printed characters based on implicit polynomials, invariants and Bayesian methods

The authors present a robust low-computational-cost system for recognizing freeform objects in 3-D range data or in 2-D curve data in the image plane. Objects are represented by implicit polynomials, i.e., 3-D algebraic surfaces or 2-D algebraic curves of degrees greater than two, and are recognized by computing and matching vectors of their algebraic invariants, which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations. Implicit polynomials of fourth degree can represent complicated asymmetric free-form shapes. A design of Bayesian recognizers for these models and their invariants that results in low-computational-cost recognizers robust to noise, partial occlusion, and other perturbations of the data sets is considered. This work extends the work of D. Keren et al. (1992) by developing and using new invariants for 3-D surface polynomials and applying the Bayesian recognizer to operating on invariants