A [[Convolution]] is a [[Binary Operation|binary operation]] $*$ between two [[Function|Functions]] $f,g$ equal to the [[Integration|Integral]] (or a certain [[Summation|summation]] for discrete functions / [[Matrix|matrices]]) of $f$ multiplied by a reflected $g$ over the $y$ axis. $\huge (f*g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)d \tau $ If the function has limited [[Domain]], then the integral can be truncated to only teh value of the [[Domain]], as long said domain is bounded with no holes. ![[convolution.gif]] In Image Processing, convolution(s) are discrete, involving some [[Image]] and a [[02 Areas/Math/Kernel|Kernel]] (typically smaller than the Image). $\huge (f*\kappa)[x] = \sum_{n=-N}^{N} f[x-n]g[n] \\ $ With two dimensions, $\huge (f*\kappa)[x,y] = \sum_{n=-N}^{N} \sum_{m=-M}^{M} f[x-n,y-n]g[x,y] \\ $