Can blurred text be read

A Gaussian blur replaces every pixel with a weighted average of its neighbours. That is a linear operation with a known shape, and linear operations with known shapes can be approximately inverted. This is not a flaw in any particular implementation; it is what a convolution is. Undoing one is a standard problem with a standard name — deconvolution — and it has been studied for decades because telescopes and microscopes need it.

What stops a recovery attempt in practice is never the mathematics. It is the noise, the quantisation, the compression, and above all how much of the original signal the blur threw away. Those are the four things worth reasoning about.

The useful question is not “is a blur reversible”. It is “how many different originals could have produced this blurred result, and can somebody enumerate them?”

A known typeface

If the attacker can render the same characters in the same font at the same size, they do not need to invert anything. They can blur every candidate and compare. Screen type, official documents and number plates are all rendered from a small set of well-known faces at predictable sizes, which is why they are the easy cases.

A short string from a small alphabet

Six digits is a million possibilities, which a laptop enumerates in seconds. Six characters of free English text is far more, and a sentence is hopeless. The length and the alphabet set the size of the search, and most of the things people cover — a plate, a postcode, a date of birth, the last four digits of an account — are short strings from small alphabets. Many of them also have formats and checksums, which cut the search further before it starts.

A small radius relative to the characters

This is the one people misjudge. A blur radius of eight pixels sounds substantial and is almost nothing against type that is sixty pixels tall. What matters is the ratio of the radius to the size of the features being hidden, and a stroke is a feature: if the radius is smaller than a stroke width, the stroke positions survive almost intact.

Plenty of pixels

Recovery needs measurements, and every pixel is a measurement. A large, high-resolution picture of a document is a better target than a small one, which is the opposite of what intuition suggests — people assume a big clear picture is more obviously risky and then blur it more gently because it looks worse when blurred hard.

The tool sets its default blur radius as a fraction of the region’s short side rather than as a fixed number of pixels, for the reason above. The fraction it uses ranges from about two per cent at the lowest setting to about eighteen per cent at the highest.

Even the bottom row is qualified, and deliberately. A strong blur over a long sentence is genuinely hard to recover. A strong blur over a six-digit number, in a known font, in a large picture, is a search problem with a small answer set. The covering being strong does not change the size of the answer set.

A mosaic is not a blur run harder. It is a different operation: the region is divided into blocks and each block becomes its own average. That genuinely destroys more information than a blur of comparable visual strength, because within a block there is nothing left at all.

What survives is the arrangement of the block averages, and that arrangement is not random. Published work has recovered text and matched faces from mosaics precisely by treating the block averages as a fingerprint and searching a candidate set for whatever produces the same fingerprint. The defence against that is to make the blocks large enough that there are too few of them to fingerprint — which is why this tool sizes blocks as a fraction of the region rather than in pixels, and why a mosaic over a plate is still a bad idea at any block size that leaves the plate looking like a plate.

• If the content would cause real trouble in the wrong hands, use the solid fill. There is no scenario in which it is the wrong answer, and it is one press away.
• If you are covering something to be polite rather than to protect — a stranger's face in a landscape, a logo you would rather not advertise — a blur is fine and looks better.
• If you must use a blur or a mosaic on something that matters, make the region larger than the thing in it and turn the strength up until the region is one tone. Then look at it and ask whether you can still tell how many characters were there.
• Check the saved file, not the preview. It is the only step in this whole subject that catches your own mistakes rather than a stranger's cleverness.

The companion page, blur, mosaic or solid, turns this into a table by subject.