Optimal template matching by nonorthogonal image expansion using restoration

In this paper we present a novel approach for template matching. The basic principle is expansion matching and it entails signal expansion into a set of nonorthogonal templatesimilar basis functions. The coefficients of this expansion signify the presence of the template in the corresponding locations in the image. We demonstrate that this matching technique is robust in conditions of noise, superposition, and severe occlusion. A new and more practical discriminative signal-to-noise ratio (DSNR) for matching is proposed that considers even the filter's off-center response to the template as “noise”. We show that expansion yields the optimal linear operator that maximizes the DSNR and results in a sharp response to the matched template. Theoretical and experimental comparisons of expansion matching and the widely used correlation matching demonstrate the superiority of our approach. Correlation matching (also known as matched filtering) yields broad peaks and spurious responses, both of which hamper good detection. We also show that the special case of expansion with a dense set of self-similar basis functions is equivalent to signal restoration. Expansion matching can be implemented by restoration techniques and also by our recently developed lattice architecture.