Discrete Gaussian filters Discuss the following issues with implementing a discrete Gaussian filter:
• If you just sample the equation of a continuous Gaussian filter at discrete locations, will you get the desired properties, e.g., will the coefficients sum up to 0? Similarly, if you sample a derivative of a Gaussian, do the samples sum up to 0 or have vanishing higher-order moments?
• Would it be preferable to take the original signal, interpolate it with a sinc, blur with a continuous Gaussian, then pre-filter with a sinc before re-sampling? Is there a simpler way to do this in the frequency domain?
• Would it make more sense to produce a Gaussian frequency response in the Fourier domain and to then take an inverse FFT to obtain a discrete filter?
• How does truncation of the filter change its frequency response? Does it introduce any additional artifacts?
• Are the resulting two-dimensional filters as rotationally invariant as their continuous analogs? Is there some way to improve this? In fact, can any 2D discrete (separable or non-separable) filter be truly rotationally invariant?