Blur

Blur is image processing's most common operation: it softens backgrounds, frosts interface glass and underlies glows, sharpening and drop shadows. This effect offers four kinds: Gaussian, motion, a camera zoom and a spin around a centre.

How it works

A Gaussian blur averages each point's neighbourhood with the weights of Gauss's bell curve. The kernel has two rare properties. It is the only one both round and separable into 1D factors, so a 2D blur is two passes, horizontal then vertical: about 4R samples instead of 4R². And two Gaussian blurs in a row make another Gaussian — the variances add. That lets a large radius come cheap: the effect halves the picture until σ is at most six texels, blurs there and comes back up with a cubic B-spline. A blur a quarter of the frame wide costs about as much as a two-pixel one, in the preview and at 8K alike.

Motion, zoom and spin average points along a path — a segment, a ray from the centre or an arc. Three passes of 8 taps, each 8 times finer than the last, give 512 samples with no ghosting. The smear is sized so its σ equals the Gaussian one at the same “Radius”: a segment of length ℓ has σ = ℓ/√12. Finally the result is lightly dithered, so smooth gradients show no banding in 8 bits.

A bit of history

The curve now called Gaussian was first derived by Abraham de Moivre in 1733; in 1809 Gauss made it the law of errors in astronomical measurement. Physicists know it as the solution of the heat equation: a Gaussian blur of σ is diffusion for a time σ²/2. Computer vision adopted it as “scale space”: Andrew Witkin (1983) and Jan Koenderink (1984) showed that blurring this way creates no new detail as the scale grows. In 1983, too, Peter Burt and Edward Adelson proposed the pyramid of shrinking copies — the ladder this effect climbs down.

What to tweak

• “Radius” is in frame units: 0.005 is a slight softening, 0.05 fog, 0.2 nothing but patches of colour.
• “Zoom” with an “Amount” of 0.3–0.6 is the jump to hyperspace: everything flies out of the centre.
• “Motion” at a “Radius” of 0.03–0.06 is a photo from a train window; “Direction” sets the heading.
• “Spin” is a long exposure of a carousel, or the swirl round the eye of a storm.
• A heavy blur turns Fractal flames and Strange attractors into glowing fog, and a spin over Quasicrystal or Phyllotaxis into a whirlpool.