A universal algorithm for discretizing bichromatic two-dimensional graphic codes

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Abstract

Mathematical foundations and algorithms for recognizing bichromatic two-dimensional graphic codes, regardless of their type (QR codes, DataMatrix, GridMatrix, etc.) are presented. The stages of achieving the result include detecting the code, localizing it within an arbitrary quadrilateral, transforming the quadrilateral to a canonical square, constructing a grid of elements (modules) of the square code, and filling it with a sequence of bits. It is shown that perspective transformation formulas make it possible to transform localized quadrangular regions to canonical squares with an acceptable error level for further processing. A flat grid of square code elements is formed based on the search for extrema of the derivatives of the pixel intensity distribution of the square image along the axes x and y. The algorithm for filling grid cells (code modules) with a sequence of zeros and ones uses information about the average intensity of each such cell. At the end of the paper, the algorithms are tested on a variety of real images of two-dimensional codes, and the limitations of the proposed algorithms are examined.

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About the authors

A. A. Trubitsyn

Ryazan State Radio Engineering University named after V.F. Utkina; Kvantron Group LLC

Author for correspondence.
Email: assur@bk.ru
Russian Federation, 59/1 st. Gagarina, Ryazan, 390005; 28a st. Engelsa, room. H2, Ryazan, 390010

M. V. Shadrin

Kvantron Group LLC

Email: m.shadrin@kvantron.com
Russian Federation, 28a st. Engelsa, room. H2, Ryazan, 390010

S. I. Holkin

LLC “Operator-CRPT”

Email: assur@bk.ru
Russian Federation, 15 Rochdelskaya st., building 16A, premises I, Moscow, 123376

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Supplementary files

Supplementary Files
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2. Fig. 1. Transformation of a quadrilateral (1ʹ2ʹ3ʹʹ) into a square (1234): (a) diagram of the inverse transformation, (b) diagram of pixel intensity calculation.

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3. Fig. 2. Transformation of a QR code (a), previously localized by a quadrangle (1234) on the upper face of a cube according to the formulas: (b) – (2), (c) – (3).

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4. Fig. 3. Transformation and discretization of DataMatrix: (a) – original localized code for processing, (b) – result of transformation of quadrangle (1234) into canonical square, (c) – average modulus of derivative with respect to y of intensity of square code and piecewise linear background, (d) – average modulus of derivative after subtracting piecewise linear background, (d) – overlay of grid with n × n = 24 × 24 cells, (e) – code with binary modules.

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5. Fig. 4. Processing of two-dimensional codes: (a) – Aztec, (b) – GridMatrix. Top row 1 – original images, middle row 2 – result of detection, localization, transformation into a canonical square and discretization into modules of two-dimensional code, bottom row 3 – result of binarization of code modules (two-dimensional sequence of 0 and 1).

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6. Fig. 5. Results of a full cycle of low-quality DataMatrix recognition: (a) – original image of the code on a tin can, (b) – code after detection and localization, transformation and discretization, (c) – binarized canonically oriented code.

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7. Fig. 6. Effect of QR code defocusing: (a) – ideal code and intensity profile of the selected line (σ = 0.49), (b) – defocused code and intensity profile of the selected line (σ = 0.20).

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