Nonorthogonal Image Expansion Related to Optimal Template Matching in Complex Images

Abstract

Expansion matching (EXM) is a novel method for template matching that optimizes a new similarity measure called discriminative signal-to-noise ratio (DSNR). Since EXM is designed to minimize off-center response, it yields results with very sharp matching peaks. 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 presents an extended EXM formulation that matches multiple templates in the complex image domain. Complex template matching is useful in matching frequency domain templates and 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. It is shown that when the complex case is simplified to the case of matching a single real template, the result reduces exactly to the minimum squared error (MSE) restoration filter assuming the template as the blurring function. Here, we introduce a new generalized MSE restoration paradigm based on the analogy to multiple-template EXM. Furthermore, the output of the single-template EXM filter is also shown to be equivalent to a nonorthogonal expansion of the image with basis functions that are all shifted versions of the template. Experimental results prove that EXM is robust to minor rotation and scale distortions.