A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths, spacings and sizes of parallel lines. These barcodes, now commonly referred to as linear or one-dimensional (1D), can be scanned by special optical scanners, called barcode readers, of which there are several types. Later, two-dimensional (2D) variants were developed, using rectangles, dots, hexagons and other patterns, called matrix codes or 2D barcodes, although they do not use bars as such. 2D barcodes can be read using purpose-built 2D optical scanners, which exist in a few different forms. 2D barcodes can also be read by a digital camera connected to a microcomputer running software that takes a photographic image of the barcode and analyzes the image to deconstruct and decode the 2D barcode. A mobile device with a built-in camera, such as smartphone, can function as the latter type of 2D barcode reader using specialized application software (The same sort of mobile device could also read 1D barcodes, depending on the application software).
The barcode was invented by Norman Joseph Woodland and Bernard Silver and patented in the US in 1952. The invention was based on Morse code that was extended to thin and thick bars. However, it took over twenty years before this invention became commercially successful. UK magazine Modern Railways December 1962 pages 387–389 record how British Railways had already perfected a barcode-reading system capable of correctly reading rolling stock travelling at with no mistakes. An early use of one type of barcode in an industrial context was sponsored by the Association of American Railroads in the late 1960s. Developed by General Telephone and Electronics (GTE) and called KarTrak ACI (Automatic Car Identification), this scheme involved placing colored stripes in various combinations on steel plates which were affixed to the sides of railroad rolling stock.
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EPFL2023
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We consider three-dimensional cubic barcodes, consisting of smaller cubes, each built from one of two possible materials and carry one bit of information. To retrieve the information stored in the barcode, we measure a 2-D projection of the barcode using a ...