Use of Fourier and Karhunen-Loeve Decomposition for Fast Pattern Matching With a Large Set of Templates

Abstract

We present a fast pattern matching algorithm with a large set of templates. The algorithm is based on the typical template matching speeded up by the dual decomposition; the Fourier transform and the Karhunen-Loeve transform. The proposed algorithm is appropriate for the search of an object with unknown distortion within a short period. Patterns with different distortion differ slightly from each other and are highly correlated. The image vector subspace required for effective representation can be defined by a small number of eigenvectors derived by the Karhunen-Loeve transform. A vector subspace spanned by the eigenvectors is generated, and any image vector in the subspace is considered as a pattern to be recognized. The pattern matching of objects with unknown distortion is formulated as the process to extract the portion of the input image, find the pattern most similar to the extracted portion in the subspace, compute normalized correlation between them at each location in the input image, and find the location with the best score. Searching for objects with unknown distortion requires vast computation. The formulation above makes it possible to decompose highly correlated reference images into eigenvectors, as well as to decompose images in frequency domain, and to speed up the process significantly.