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

This paper presents a new robust low-computational-cost system for recognizing freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i. e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, 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 4th degree can represent complicated asymmetric free-form shapes. This paper deals with the design of Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants that results in low computational cost recognizers that are robust to noise, partial occlusion, and other perturbations of the data sets. This work extends the work by developing and using new invariants for 3D surface polynomials and applying the Bayesian recognizer to operating on invariants.