Visually Significant QR Codes

While QR codes have recently become popular as a method of rapidly bringing information to consumer, they have the drawback that they contain no human readable content. This project concerns combining image data with QR codes while maintaining the machine readability of the code. We break each module down into pixels and halftone it to correspond to the image data while preserving the overall shade necessary for QR readability. One method dynamically creates a library of common module types and then finds the library module which best approximates the image while respecting the QR constraint. These templates provide a good starting point for a modified DBS algorithm, which further improves the image quality. Another approach uses convex optimization on an input grayscale image, followed by a halftoning algorithm, to produce a black and white result which combines the image and QR code. A third method involved intelligantly halftoning the modules using thresholds based on the qualities of the input data and QR code. Finally, we consider data loss and use entropy calculations to investigate how the algorithms affect the amount of data encoded. ∗Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan. [email protected] †Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois. [email protected] ‡Department of Mathematics, University of Kansas, Lawrence, Kansas. [email protected] §Department of Mathematics, Simon Fraser University, Vancouver, British Columbia. [email protected] ¶Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois. [email protected] ‖Department of Mathematics, Iowa State University, Ames, Iowa. [email protected]