For a monitor, at every row and column position, the assigned output pixel value is 255 when the input pixel value exceeds a threshold which the algorithm specifies for each pixel position. Otherwise the output value is zero. (For printers, the strategy is the reverse since the output medium is already white and colorant must darken it. So, for printers, the colorant is applied when the input pixel value is less than a threshold to darken the corresponding pixel.) The following is one actual 4x4 square algorithm’s thresholds:

Pictorially, the following simple diagram describes the algorithm:

So, if all input pixel values within a square have a value of 230, only output pixels (0, 0) and (0, 3) have a value of zero because their corresponding threshold values (243 and 231, respectively) exceed 230. The assigned output values for all the other pixels is 255. The following diagram orders the pixel thresholds—1 has the lowest threshold with 16 having the highest.

For uniform intensities across the square, (1, 1) is the first pixel to assume a value of 255, followed by (1, 2), (2, 2), etc., in that order. Over an image, the transition values for pixel positions within an area can vary but usually do not.

The preceding example discussed a 4x4 tile which provides 17 different intensities for the square—all can have zero output values or one to 16 total output values can assume a value of 255. However, remember that determining output values is performed independently on a tile-by-tile basis by pixel position within a tile.

Clustered Dot Ordered Dither

Various ordered dither algorithms illuminate pixels (assign a maximum intensity value) on displays using different strategies. In some instances, isolated pixels are set to the maximum value. Because of monitor slew rate considerations, this can cause problems with low-cost displays which do not have the necessary slew rate to display isolated pixels at high intensity. Applying isolated ink spots also causes problems for many printers. Hence, a popular form of ordered dither is the clustered dot ordered dither while the other forms are known as disbursed dither.

Clustered dot ordered dither algorithms attempt to avoid illuminating or printing isolated pixels by specifying “seed” pixel positions that have the lowest threshold values. The threshold sequence pattern then spirals around the seed position. As in the previous example, consider the following spiral threshold order:

Note that the upper left 3x3 square and the lower right 3x3 square are identical. Note also the upper right and lower left 3x3 squares are also identical. This actually depicts a 3x6 rectangular tiling which is offset by three columns every three input scan-line rows as depicted by the following:

Now consider the example in a different light that reveals the way the offset rectangle patterns interact and the resulting output diamond pattern more fully: