高斯滤波器

A bell instead of a plateau

Discretizing, normalizing, truncating

A Gaussian transforms into a Gaussian

Blurs that add, in the continuous world

A discrete Gaussian is built with $\sigma = 2$ using the unnormalized form $g[n,m] = e^{-(n^2+m^2)/2\sigma^2}$ and truncated at $\pm 3\sigma$. Which half-width is used, and why that bound?

Two Gaussian filters have $\sigma_1 = 1$ and $\sigma_2 = 2$. Comparing their frequency responses $G = e^{-w^2\sigma^2/2}$, which statement is right?

An image is blurred with a Gaussian of variance $\sigma_1^2 = 4$ and then with an independent Gaussian of variance $\sigma_2^2 = 9$. Using the closure law $\sigma_3^2 = \sigma_1^2 + \sigma_2^2$, compute the combined variance $\sigma_3^2$ and write it as an integer.