Efficient two-dimensional pattern matching with scaling and rotation and higher-order interpolation

Abstract

Two-dimensional pattern matching with scaling and rotation for given pattern P and text T is the computational problem of finding a subtext in T such that a scaled and rotated transformation of P most accurately resembles the subtext. Applications of pattern matching are found, for instance, in computer vision, medical imaging, pattern recognition and watermarking. All known approaches to find a globally optimal matching depend on the basic nearest-neighbor interpolation. To use higher-order interpolations, current algorithms apply numerical techniques that provide only locally optimal solutions. This paper presents the first algorithm to find an optimal match under a large class of higher-order interpolation methods including bilinear and bicubic. The algorithm exploits a discrete characterization of the parameter space for scalings and rotations to achieve a polynomial time complexity. © 2012 Springer-Verlag.