Our recently developed Expansion Matching (EXM) is an effective method for matching templates and optimizes a new similarity measure called Discriminative Signal-to-Noise Ratio (DSNR). DSNR optimization leads to sharp matching peaks and minimal off-center response in the matching result. Consequently, EXM yields superior performance to the widely used correlation matching (also known as matched filtering), especially in conditions of noise, superposition and severe occlusion. This paper extends the real-valued EXM formulation for simultaneous matching of multiple templates in the complex image domain. Complex-valued template matching is relevant to matching frequency domain templates, edge gradient images and can be extended to multispectral images as well. Here, a single filter is designed to simultaneously match a set of given complex templates with optimal DSNR, while eliciting user-defined center responses for each template. For the simplified case of matching a single real-valued template, this EXM result reduces exactly to the Minimum Squared Error restoration filter assuming the template as the blurring function. In addition, the single- template EXM matching result also corresponds to the coefficients of a non-orthogonal expansion of the input image using shifted versions of the template as basis functions.
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