This paper introduces the concept of QR images, an automatic method to embed QR codes into color images with bounded probability of detection error. These embeddings are compatible with standard decoding applications and can be applied to any color image with full area coverage. The QR information bits are encoded into the luminance values of the image, taking advantage of the immunity of QR readers against local luminance disturbances. To mitigate the visual distortion of the QR image, the algorithm utilizes halftoning masks for the selection of modified pixels and nonlinear programming techniques to locally optimize luminance levels. A tractable model for the probability of error is developed and models of the human visual system are considered in the quality metric used to optimize the luminance levels of the QR image. To minimize the processing time, the optimization techniques proposed to consider the mechanics of a common binarization method and are designed to be amenable for parallel implementations. Experimental results show the graceful degradation of the decoding rate and the perceptual quality as a function the embedding parameters. A visual comparison between the proposed and existing methods is presented.

A new algorithm to build blue noise masks using centroidal Voronoi tessellations (CVT) and a variant of Lloyd's Algorithm is presented. The algorithm takes advantage of the optimality properties of CVTs and through a modified version of Lloyd's algorithm, achieves optimization of the stacked binary patterns that build the mask. A new ordering for binary pattern design is presented, as well as a new metric that allows the creation of quality profiles of the masks. The masks generated by this method are used to halftone sample images, and quality profiles are created. It is shown that CVT masks outperform masks created by DBS and VaC according to the new metric defined and thorough visual inspection of halftoned images.