Dithering

Dithering trades spatial resolution for grey-level depth. A device with few output levels approximates an intermediate intensity by mixing the available levels over a small region, which the eye averages at normal viewing distance.

• Each pixel is divided into sub-pixels, each forced to an available level
• The count of sub-pixels at the higher level encodes the target intensity
• A fixed dither matrix sets the order in which sub-pixels switch on, spreading them to avoid visible clumps

Used in newspaper halftoning, laser printing, and exporting photos to a small fixed palette such as GIF.

Worked Example

A bi-level device with output levels $0$ and $1$. Target intensity $v = 0.5$ across one $2 \times 2$ block, using the Bayer dither matrix.

Sub-pixel $(i,j)$ is set to $1$ iff $v > \dfrac{D_{ij} + 0.5}{4}$.

• $(0,0)$ has threshold $0.125$. Since $0.5 > 0.125$, set to $1$.
• $(0,1)$ has threshold $0.625$. Since $0.5 < 0.625$, set to $0$.
• $(1,0)$ has threshold $0.875$. Since $0.5 < 0.875$, set to $0$.
• $(1,1)$ has threshold $0.375$. Since $0.5 > 0.375$, set to $1$.

2 of the 4 sub-pixels are on, so the block averages $0.5$, matching the target. The on sub-pixels form a checkerboard.