# Changeset 2174Tweet

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Timestamp:
Dec 29, 2007, 11:35:48 PM (14 years ago)
Message:
• Omni-directional error diffusion (a dot diffusion rip-off).
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www/study
Files:
3 edited

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• ## www/study/part3.html

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3.3. Changing image parsing direction

The usual way to parse an image is one pixel after the other, following their order in memory. When reaching the end of a line, we automatically jump to the beginning of the next line:

to the beginning of the next line. Error diffusion methods using this parsing order are called raster error diffusion:

Dot diffusion is an error diffusion method by Donald E. Knuth that uses tileable matrices just like ordered dithering, except that only the cell uses tileable matrices just like ordered dithering, except that the cell value order is taken into account for error propagation. Diagonal cells get half as much error as directly adjacent cells.

much error as directly adjacent cells:

For instance, in the following example, cell 25’s error is propagated to

class="matrix" alt="Dot diffusion matrix sample" />

Dot diffusion was reinvented 14 years later by Arney, Anderson and Ganawan without crediting Knuth. They call their method omni-directional error diffusion. Instead of using a clustered dot matrix like dot diffusion, they use a dispersed dot matrix. This is a 16×12 portion of that matrix:

The recommended implementation of omni-directional error diffusion uses a slightly different propagation matrix, where top and bottom neighbours get more error than the others:

3.4. Variable coefficients error diffusion

And this is block Floyd-Steinberg using a modified, weighed intra-block error distribution matrix:

And this is block Floyd-Steinberg using the same full set of blocks and a modified, weighed intra-block error distribution matrix. The picture still looks sharpened, but is significantly less noisy:

• ## www/study/part5.html

 r2152

Shaked, Arad, Fitzhugh and Sobel introduce the minimum brightness variation criterion (MBVC), stating that in order to reduce halftone noise, the halftone set which should be used to render the desired colour should be the one whose brightness variation is minimal.