GaussFilter
Gaussfilter, commonly known as the Gaussian filter, is a linear, shift-invariant smoothing filter whose impulse response is a Gaussian function. In one dimension, the kernel is g(x) = (1/(√(2π)σ)) exp(-x^2/(2σ^2)). In two dimensions, the kernel is G(x,y) = (1/(2πσ^2)) exp(-(x^2+y^2)/(2σ^2)). Convolution with this kernel produces a blurred result that attenuates high-frequency components, thereby reducing noise and small details. The filter is isotropic, so the blur is uniform in all directions, and its strength is governed by the standard deviation σ: larger σ yields stronger smoothing.
In practice, the Gaussian kernel is discretized by sampling and then normalized so the sum equals 1.
Applications include noise reduction, pre-processing for edge detection, and general image blurring in photography and computer
Border handling must be considered during implementation (padding, mirroring, or cropping). For large σ or high-resolution images,