Blur softens the image just before it is cut, so that grain, paper texture and noise melt into their surroundings instead of turning into ragged edges and specks. It is a trade of detail for calm, and it softens every edge, the ones you want as well as the ones you do not.
What it does
“Blur” runs from 0 to 10 px in steps of 0.5, and starts at 0, which is off. It works on the score image after levels and before the threshold, so the ink layer of the histogram includes it and the “Adjusted” preview shows it.
The radius is measured in pixels of the working copy of the photo, the copy at most 2048 pixels on its long side that “Trace” uses. The preview works on a copy at most 1024 pixels across and scales the radius down to match, so that it shows roughly the same softening at its own size. The radius is rounded to whole pixels, so the half steps matter less than they look: at Trace, 0.5 and 1 give the same blur, as do 1.5 and 2, and at the lowest settings the preview can show a little more or less blur than Trace will make.
The blur itself is a box blur, run three times. One pass replaces every pixel with the plain average of a window of pixels around it, first along each row and then down each column; the window is twice the radius plus one pixel wide. At the edges of the image the edge pixels are repeated outwards, so the border neither darkens nor lightens. Three passes of this crude average come very close to a Gaussian blur, the smooth, bell-shaped softening of a lens slightly out of focus.
What blur does to the two-tone result:
- Grain, noise and texture average out, so the edges between front and back run smoothly instead of fraying.
- Corners round off. A sharp point is blunted and a sharp inside corner fills in, on about the scale of the radius.
- Thin lines fade. A dark line narrower than the blur is averaged with the light around it, and once its darkest value rises above the threshold it vanishes.
- Narrow gaps close, and small shapes shrink or run into their neighbors.
Around a skewed photo, the pixels that are not photo are set to back before the blur, so they are not smeared into the photo's edge.
Why it works this way
A threshold is merciless with noise. Where an edge is soft or a surface is textured, pixels side by side fall on opposite sides of the cut, and the result is a fringe of specks and a ragged edge, which the tracer will then faithfully follow. Blur takes the noise out before the decision is made.
It is a box blur three times over because that is fast. A box average can be kept as a running sum: as the window slides one pixel along, add the pixel coming in and subtract the one going out. The cost per pixel is the same whatever the radius, so a 10 px blur on a 2048-pixel photo costs no more than a 1 px one, and the preview keeps up while you drag.
And it is only one of two ways to clean up, on purpose. Blur rounds every edge, including the ones you want sharp. When the trouble is small shapes rather than rough edges, Detail removes whole small shapes and leaves the edges of the rest exactly as they were.
The metaphor
Blur borrows the painter's squint. Look at a subject through half-closed eyes and the detail dissolves: the stripes on a shirt, the texture of bark, the glitter on water. What is left is the arrangement of big darks and big lights, which is exactly what a notan is made of. Art teachers tell students to squint for that reason.
It also borrows the photographer's focusing ring. Turn it a little too far and every point of light spreads into a small disc, and the picture softens evenly everywhere.
The metaphor breaks on what gets changed. A squint changes only what you see; the subject is still sharp. Blur changes the very image that is about to be cut, so its softening goes straight into the outline. And a lens spreads each point into a disc with a rim, where a Gaussian spreads it into a soft hill with no rim at all.
A history
In art
Softness has been a tool for as long as painting has had edges. Leonardo's sfumato, from the Italian for smoke, dissolved outlines into gradual transitions, so that forms seem to emerge from shadow rather than be drawn around. Around 1900 the Pictorialist photographers turned to soft-focus lenses and hand-worked printing processes to make photographs look less like records and more like etchings and charcoal drawings.
In both cases the softness was the point. In a notan it is only a means. The finished work has the hardest edges there are; blur is used so that the hard cut that follows falls in a quieter place.
In printing
Printers have even used deliberate blur to sharpen. In the darkroom technique of unsharp masking, a negative was contact-copied onto low-contrast film through the thickness of its own base, so the positive came out blurred. Laid back on the negative, the blurred positive canceled the broad tones and left the fine detail, and the print looked crisper. Digital editors kept the name.
Blur also cleans up copy for the press. A picture already printed as halftone dots, scanned to be printed again, fights its new screen and throws up moiré patterns, so it is blurred, or descreened, until the old dots dissolve. Tracing a photo from a magazine page is the same problem, with the same cure.
In technology
The bell curve that Gaussian blur is named after belongs to Carl Friedrich Gauss, who used it in 1809, in his work on the orbits of heavenly bodies, as the shape of errors of measurement. Three box blurs imitate it because of the central limit theorem: pile up enough simple averages and the result tends toward Gauss's curve. W. M. Wells made the case in 1986 for building Gaussian filters from cascades of uniform ones, because they are so cheap to compute; and Frank Crow's summed-area tables of 1984 showed how a box average of any size could be had for four look-ups.
Blur also became a theory of seeing. In 1980 David Marr and Ellen Hildreth found edges by blurring an image with a Gaussian and looking where its second derivative crossed zero. In 1983 Andrew Witkin described scale-space filtering, and in 1984 Jan Koenderink, in “The Structure of Images”, showed that blurring by ever larger Gaussians is governed by the heat equation: a blurred image is an image in which heat has been allowed to spread. Detail that disappears as the blur grows is small; detail that survives is large. The “Blur” slider is one step along that scale.
In professional software
Softening a photo before it is traced is standard practice, and the programs share a name for it: Gaussian blur, set as a radius in pixels. Most also offer a median filter, which removes specks while keeping edges crisper than a blur does.
- Adobe Photoshop. ‘Filter › Blur › Gaussian Blur’ asks for a radius in pixels, and ‘Filter › Blur › Box Blur’ is the plain average that Studio Notan runs three times. For grainy or dusty scans, ‘Filter › Noise › Median’ and ‘Filter › Noise › Dust & Scratches’ replace stray pixels with values drawn from their neighbors, and hold edges better than a blur. Run any filter on a Smart Object and it becomes a Smart Filter, which you can reopen and change later.
- Adobe Illustrator. Image Trace works on the image as it was placed, so the usual habit is to blur or clean the photo in Photoshop first and trace it afterwards. Its ‘Noise’ setting removes small areas after the split, which is Studio Notan’s Detail, not Blur.
- Inkscape. In the ‘Multicolor’ mode of ‘Path › Trace Bitmap’, a ‘Smooth’ checkbox applies a Gaussian blur to the image before it is traced.
- GIMP. ‘Filters › Blur › Gaussian Blur’ and ‘Filters › Blur › Median Blur’ do the same two jobs as Photoshop’s Gaussian Blur and Median, and preview the result on the canvas as you adjust them.
What carries over. Use the least blur that stops the edges fraying, and judge it on the two-tone result, not on the soft photo. Radii do not carry across as numbers: Photoshop measures its radius on the full-size photo, while Studio Notan measures on a working copy at most 2048 pixels across, so the same number softens a large photo far less in Photoshop. And a blur made there without a Smart Filter is baked into the pixels; here it is a setting, and 0 gives back the photo as it was.
Try this
- Open a photo of a textured surface, such as paper, fabric or a stone wall, set “Preview” to “Two-tone” and raise “Blur” a step at a time. Stop when the edges stop fraying.
- Trace some lettering at “Blur” 0 and at 4, with “Preview” on “Outlines”. Watch the serifs blunt and the small counters close.
- Try to lose a scatter of specks with Blur, then with “Detail”, and compare what happens to the edges of the big shapes.
Going further
See Levels: black, mid, white and Preview and opacity.
- David Marr, Vision
- Tony Lindeberg, Scale-Space Theory in Computer Vision