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The Gaussian distribution is separable. Apply your transformation to each coordinate separately and you will get a 2D Gaussian. If $G(x)$ is a 1D Gaussian, then $G(x) G(y)$ is a 2D Gaussian. …

m00 says something about the intensity scaling, m01 and m10 give the origin of the Gaussian, and mu20 and mu02 give the variances along the axes. … If the Gaussian can be rotated, you need to include mu11 in the mix. These three last values then form the covariance matrix of the Gaussian. …

The (continuous-domain) FT of a Gaussian is a Gaussian, as OP knows. … approximately the sampled FT of that Gaussian. …

There are two ways to compute the Laplace of Gaussian operator: As Royi suggests, by computing $f * \nabla^2 * g$,where we take the operator $\nabla^2$ as a convolution kernel created using the finite … Approach 2 is more precise: it doesn't use any discrete approximations to the derivative, instead using a sampled Gaussian derivative as a kernel. …

I don’t know of any method that can measure sharpness in an arbitrary image, and presume it is impossible to distinguish a sharp picture of a smooth color transition form a blurry picture of a sharp c …

Instead, integrate the part of the Gaussian from -3𝜎 to 3𝜎, this gives 0.9973. This means that at most 0.27% of the Gaussian weight is missing. …

Ndimage generates a Gaussian kernel by sampling a Gaussian and normalizing it to 1. … Indeed, one can not just sample a derivative of Gaussian to obtain a convolution kernel, because the Gaussian function is not band-limited, and so sampling causes aliasing. …