Optimal operators for template and shape recognition by nonorthogonal image expansion

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Abstract
This paper presents a novel approach for template recognition by signal expansion into a set of non-orthogonal template-similar basis functions (wavelets). It is shown that expansion matching is a special case of the general non-orthogonal expansion which is equivalent to 'restoration' of undegraded images. Expansion matching also maximizes a new and more practically defined Discriminative signal-to-noise ratio (DSNR). It is proved that maximizing the DSNR is equivalent to minimum squared error restoration by Wiener filters. The widely used matched filtering (also known as correlation matching) maximizes the conventional SNR and generates broad peaks since the SNR imposes no constraint on the sharpness of the filter response to the template itself. In comparison, maximizing our newly defined DSNR ensures that expansion matching yields much sharper peaks, with the ideal response quested being a delta (impulse) function. Furthermore, it is demonstrated that expansion matching outperforms correlation matching by more than 20 dB DSNR. This results in much less spurious responses and a more robust performance in noise and severe occlusion. Since expansion matching is fundamentally a decomposition process, it is also quire suitable for the analysis of superimposed signals, such as sound and radar signals. The filters generated by expansion matching have a multi-pole structure with amplitudes approximately proportional to the curvature of edges in the template. Analytically, they confirm previous conjectures about shape perception.

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