Linear Filters: Heuristic Theory and Stability
Linear filters are among the most widely used tools in image processing for such applications as target detection, localization and classification (or recognition). They are based on correlations between the searched objects (or a linear combination of them) and the analyzed scene. The correlation operation has several advantages in the context of image processing. First, it is an intrinsically position invariant recognition method which makes it possible to recognize an object whatever its location in the image. Second, correlation is quite robust to noise, and thus often constitutes an efficient way of processing very noisy images. Finally, it can be computed at a relatively low computational cost if fast methods are available, based for example on Fast Fourier Transform (FFT).
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