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Gaussian blur applies convolution with $G_{\sigma }(x)=(2\pi {\sigma }^2{)}^{-n/2}{e}^{-|x{|}^2/(2{\sigma }^2)}$ to an image signal. It averages over a spatial scale $\sigma$, suppressing rapid variation while also blurring image edges. The heat-kernel convolution realizes this filter at time $t={\sigma }^2/2$.