It's a blur operation. Blurs are often defined as transforming input function by convolving it with some kernel function (often a Gaussian, see the Wikipedia pa

It's a blur operation. Blurs are often defined as transforming input function by convolving it with some kernel function (often a Gaussian, see the Wikipedia page on Gaussian blur, similar idea holds for blurring 1d, 2d, 3d, nd signals). Convolution is an operation to combine two functions by integrating then together in a particular way. This defines output at each location that's a weighted average of what values the input function took at neighbouring points to each given location. Integration provides a way of computing averages. The weights used in weighted average are defined by the choice of kernel function. In this case the kernel function is an indicator function that is 1 in some window and 0 everywhere else, instead of a Gaussian function that'd be used for a Gaussian blur. Since the input image is defined as a continuous function that maps a coordinate to a colour (it isn't discretised into pixels) we can apply the blur operation to the input image function and figure out analytically for a new image function that directly evaluates the output smoothed colour value for any coordinate. Then we can just sample that function at each pixel. Blurring removes or damps high frequency components of input leaving lower frequency components, so it can be used to remove or reduce high frequency "noise".