Clustered dot ordered dither

In order to generate the spots in a clustered dot dithered image, a grid is super-imposed on the original image.

Fig 1: 16x16 grid over the image

The image is divided into cells by the grid - each cell will ultimately hold a single spot made up of multiple device pixels in order to approximate the darkness of the original image in that cell.

Fig 2: image after dithering

As you can see, a large cell size results in a heavy loss in resolution! Note also that the spots in the cells start off as circles, and grow to be diamond shaped. This change in shape is controlled by a spot function. By using different spot functions, the evolution in the shape of the spots as the cell goes from fully black to fully white may be controlled.

Fig 3: reference greyscale gradient

Fig 4: Euclidean dot, 0° screen angle

Figure 4 displays the Euclidean spot function as the tone changes from black to white. Notice how these spots are clearly defined compared to the slightly smudged look of those in Figure 2 above. This is because the spot function defines a threshold value for each pixel in the cell, and this threshold value is compared against the image to discover what the output device pixel should be. The output pixel is illuminated only if the image's pixel is above the threshold. This means that sharp edges in the image are not lost, but the spots are less regular. In practice, the cell sizes used here are rather large in order to emphasise these effects; normally they are less perceptible.

The Euclidean dot is not the only spot function available. The merits and detractions of a variety of spot functions are covered on the spot function reference page.

So far, the screen has been aligned with the horizonal and vertical axes. It turns out that the human eye is very good at discerning horizontal and vertical lines, but the screen should ideally have the minimum impact on the image possible. This is the reason that screens aligned to 0° (or equivalently 90°) are not normally used by themselves, whereas 45° is favoured as being minimally visible:
(a) 0° screen
(b) 45° screen
Fig 5: screen angle and visibility

In fact any screen angle may be used, with positive angles being anti-clockwise rotations, as demonstrated by Figure 6.
Fig 6: screen angles increase anti-clockwise

[ On to spot reference . . . > ]
(c) 1998 Austin Donnelly <Austin_Donnelly@yahoo.co.uk>
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