A Novel Approach for Template Matching by Nonorthogonal Image Expansion

A novel approach for template matching is presented in this paper. The matching scheme is a specialized implementation of a general method for signal expansion by nonorthogonal basis functions (BF's). The matching principle involves signal expansion into a dense set of nonorthogonal BF's that are all template-similar. Initially, it is proved that both circulant and truncated self-similar BF's in a dense configuration have to satisfy only modest conditions in order to be a complete basis for discrete L-2(R) signals. Next, a novel discriminative signal-to-noise ratio (DSNR) is defined. The DSNR is more relevant to template matching since it even considers as "noise" the filter's off-center response to the signal. Moreover, it is proved that maximization of this DSNR is precisely equivalent to expansion with template-similar BF's. It is also shown that such an expansion matching can be implemented by an operator that is equal to a minimum squared error restoration filter (Wiener filter). In comparison to the widely used correlation matching (also known as matched filtering) that maximizes the traditional SNR and therefore generates broad peaks, expansion matching yields highly localized peaks. Furthermore, it is demonstrated that expansion matching outperforms correlation matching by more than 25-dB DSNR. Expansion has better performance in noise and severe occlusion, and spurious responses are largely attenuated. Since expansion matching is fundamentally a decomposition process, it is also quite suitable for the analysis of superimposed signals such as sound or radar. Expansion matching can be implemented both by restoration techniques and by the adaptive lattice system.