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In 2013, workers at a German construction company noticed something odd about their Xerox photocopier: When they made a copy of the floor plan of a house, the copy differed from the original in a subtle but significant way. In the original floor plan, each of the house's three rooms was accompanied by a rectangle specifying its area: the rooms were 14.13, 21.11 and 17.42 square metres, respectively. However, in the photocopy, all three rooms were labelled as being 14.13 square metres in size. The company contacted the computer scientist David Kriesel to investigate this seemingly inconceivable result. They needed a computer scientist because a modern Xerox photocopier doesn't use the physical xerographic process popularized in the nineteen-sixties. Instead, it scans the document digitally, and then prints the resulting image file. Combine that with the fact that virtually every digital image file is compressed to save space, and a solution to the mystery begins to suggest itself.
Compressing a file requires two steps: first, the encoding, during which the file is converted into a more compact format, and then the decoding, whereby the process is reversed. If the restored file is identical to the original, then the compression process is described as lossless: No information has been discarded. By contrast, if the restored file is only an approximation of the original, the compression is described as lossy: some information has been discarded and is now unrecoverable. Lossless compression is what’s typically used for text files and computer programs, because those are domains in which even a single incorrect character has the potential to be disastrous. Lossy compression is often used for photos, audio, and video in situations in which absolute accuracy isn't essential. Most of the time, we don't notice if a picture, song or movie isn't perfectly reproduced. The loss in fidelity becomes more perceptible only as files are squeezed very tightly. In those cases, we notice what are known as compression artifacts: the fuzziness of the smallest jpeg and mpeg images, or the tinny sound of low-bit-rate MP3s.
Xerox photocopiers use a lossy compression format known as jbig2, designed for use with black-and-white images. To save space, the copier identifies similar-looking regions in the image and stores a single copy for all of them; when the file is decompressed, it uses that copy repeatedly to reconstruct the image. It turned out that the photocopier had judged the labels specifying the area of the rooms to be similar enough that it needed to store only one of them—14.13—and it reused that one for all three rooms when printing the floor plan.
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