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Gaussian filtering in one
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In the given text, Gaussian filtering in one, two, or three dimensions is mentioned as one of the most commonly required tasks in signal and image processing. Implementing finite impulse response filters in the time domain with Gaussian masks is relatively simple in both floating-point and fixed-point arithmetic, as Gaussian kernels are strictly positive and bounded. However, these implementations tend to be slow when dealing with large images or kernels. Fortunately, there are at least two alternative methods to perform Gaussian filtering in a faster manner: recursive IIR filters and FFT-based methods. Unfortunately, these methods can only be applied when there is access to floating-point hardware.
In this paper, the focus is on a fixed-point implementation of recursive Gaussian filtering. This approach is discussed and applied to both isotropic and anisotropic image filtering. The key idea is to utilize a non-orthogonal separation scheme for the Gaussian filter.
