A Universal Algorithm for Discretizing Bichromatic Two-Dimensional Graphic Codes

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.