Linear noise smoothing

Linear (spatial) filtering is a function with a weighted sum of pixel values (in a neighborhood). It is a linear operation on an image that can be used for blurring/noise reduction. Blurring is used in pre-processing steps; for example, in the removal of small (irrelevant) details. A few popular linear filters are the box filter and the Gaussian filter. The filter is implemented with a small (for example, 3 x 3) kernel (mask), and the pixel values are recomputed by sliding the mask over the input image and applying the filter function to every possible pixel in the input image (the input image's center pixel value corresponding to the mask is replaced by the weighted sum of pixel values, with the weights from the mask). The box filter (also called the averaging filter), for example, replaces each pixel with an average of its neighborhood and achieves a smoothing effect(by removing sharp features; for example, it blurs edges, whereas spatial averaging removes noise...