This is a bit confusing so here is a high-pass sharpening filter that computes output values by subtracting surrounding pixel values from the current calculation point and adding the eight differences to the current calculation point pixel value:

Here is another example that results in less sharpening—often more visually appealing.

High-pass sharpening filters are characterized by taps that have a positive center tap with some or all of the surrounding taps having negative values. Here are a few other typical sharpening filters:

The last two filters are similar but the second of the two is scaled by six since the center tap would otherwise have a value of 10, leaving a tap total sum of 6, rather than the required value of 1. This diminishes the sharpening effect. Finally, when images consist of two interlaced fields, one interlaced field should not be sharpened using data from the other interlaced field. Here is a filter that solves the problem:

Smoothing

Smoothing reduces intensity transitions within images. Using the sandbox analogy, smoothing processes remove sand from ridges and peaks and places it in neighboring lower-elevation areas. This attenuates differences between the original sand surface features. In images, this visually blurs detail, producing a soft “out-of-focus” effect which grows as the spatial filter increases in row and column count.

Image smoothing uses spatial filters called low-pass filters. Low-pass filtering calculations reduce pixel value differences by averaging local intensities. Like sharpening, adding the filter coefficients always produces a sum value of 1. Here is a low-pass smoothing filter: