Multiple template matching using the expansion filter

The paper describes a multiple-template generalization of a newly developed approach for template matching by signal expansion into a set of non-orthogonal template-similar basis functions. The single-template method is proven to be equivalent to "restoration" of undegraded images using the Wiener filter and optimizes a new and more practically defined matching quality criterion that the authors call discriminative signal-to-noise ratio (DSNR). Compared to the widely used matched filtering approach (also known as correlation matching) which is based an projection, expansion matching is based on decomposition and is shown to be more robust in conditions of noise, superposition and severe occlusion. In the paper, the authors extend the DSNR optimization approach to include more than one template. The generalized expansion filter presented is optimal in terms of DSNR and can be designed to elicit any desired response for each of the templates, while optimizing the DSNR criterion. The approach considers additive noise as a parameter and leads to a general formulation, of which many previous approaches (such as the synthetic discriminant function) form special cases. In the case of a single template, the formulation reverts to the previously mentioned Wiener restoration filter