Algebraic Geometry and Computational Algebraic Geometry for Image Database Indexing, Image Recognition, And Computer Vision

摘要

This work provides a general framework for the use of geometric invariants in image recognition and computer vision. The theory yields a feature dependent system of equations in variables which represent the 3D invariants of certain features on an object and the 2D invariants of those same features in an image. These equations (called object/image equations) will be satisfied whenever the object produces the image up to suitable transformations of both the object and the image. The significant new contribution of our work is in the use of the theory of correspondences to produce relatively simple 'equivariant' polynomial equations to precisely describe these geometric constraints between an object and the images it can produce or an image and the objects that can produce it. A minimal set of generator for the ideal of all such polynomial relations provides an important tool that can be used in recognition algorithms.