Polynomial-Time Geometric Matching for Object Recognition

Abstract

This paper considers the task of recognition and position determination, by computer, of a 2D or 3D object where the input is a single 2D brightness image, and a model of the object is known a priori. The primary contribution of this paper is a novel formulation and methods for local geometric feature matching. This formulation is based on analyzing geometric constraints on transformations of the model features which geometrically align it with a substantial subset of image features. Specifically, the formulation and algorithms for geometric feature matching presented here provide a guaranteed method for finding all feasible interpretations of the data in terms of the model. This method is robust to measurement uncertainty in the data features and to the presence of spurious scene features, and its time and space requirements are only polynomial in the size of the feature sets. This formulation provides insight into the fundamental nature of the matching problem, and the algorithms commonly used in computer vision for solving it.