2842 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 23, NO. 7, JULY 2014 QR Images: Optimized Image Embedding in QR Codes Gonzalo J. Garateguy, Student Member, IEEE, Gonzalo R. Arce, Fellow, IEEE , Daniel L. Lau, Senior Member, IEEE, and Ofelia P. Villarreal, Member, IEEE Abstract—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. Index Terms—QR codes, image embedding, halftoning. I. I NTRODUCTION Q UICK response (QR) codes [1], [2] have rapidly emerged as a widely used inventory tracking and identi- fication method in transport, manufacturing, and retail indus- tries [3]. Their popularity is due to the proliferation of smart phones, capable of decoding and accessing on line resources as well as its high storage capacity and speed of decoding. QR codes are used in a variety of applications, such as accessing websites, download personal card information, post information to social networks, initiate phone calls, reproduce videos or open text documents. This versatility makes them a valuable tool in any industry that seeks to engage mobile users from printed materials. Not surprisingly QR codes have been widely adopted in the marketing and publicity industry thanks Manuscript received September 6, 2013; revised December 31, 2013 and April 14, 2014; accepted April 16, 2014. Date of publication May 2, 2014; date of current version May 20, 2014. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Karsten Mueller. G. J. Garateguy is with Mathworks, Natick, MA 01760 USA (e-mail: ggarateg@udel.edu). G. R. Arce and O. P. Villarreal are with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19711 USA (e-mail: ggarateg@udel.edu; ofeliap.villarreal@gmail.com). D. L. Lau is with the Department of Electrical and Computer Engi- neering, University of Kentucky, Lexington, KY 40506 USA (e-mail: dllau@engr.uky.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIP.2014.2321501 to the advantage they provide in tracking the performance of publicity campaigns. An important problem of QR codes is its impact on the aesthetics of publicity designs. The square shapes and limited color tolerance, severely impairs their integration into billboard designs or printed materials. This challenge has generated great interest for algorithms capable of embedding QR codes into images without loosing decoding robustness. There have been several efforts to improve the appearance of such embed- dings [4]–[15] which can be classified in two categories, methods that modify the luminance or color of image pixels and methods that replace QR modules. The methods presented in [6] and [7] base the strategy on finding the best group of QR modules to substitute by the image or logo in the QR code. Other methods take advantage of unused modules in the padding regions [8]–[10] to introduce the image without affecting the decoding robustness. In [7] the impact of replacing code modules with image pixels was studied. The authors concluded that to retain high rate of decodability, the ratio between image and code area should be approximately proportional to the correction capacity of the code. It was also found that superimposing images over finder or alignment patterns severely decrease the probability of correct decoding. As a consequence it is common for logos or images to be located at the center of the code for these methods as depicted in Fig. 1(a). In general these approaches do not take advantage of the codeword generation process and this imposes restrictions in the location of modified modules. This problem was addressed by recently developed techniques [4], [11], [12] which manipulate the Reed Solomon encoding procedure to maximize the area coverage without reducing the correction capacity. The second category of embedding algorithms is based on the modification of the pixel’s luminance. The approach in [5] chooses central pixels of each module to modify its luminance since this is the area usually sampled by the decoder. This approach provides an adequate trade off between robustness and visual distortion but the number of center pixels modified is in general a large proportion of the module area and creates undesirable low pass artifacts [see Fig. 1(c)]. A method which implements a similar idea is LogoQ [13]. In [16] a method to introduce colors into QR codes was proposed with the goal of increasing its data capacity and a detailed study of the interference between different color layers was presented. Two embedding methods which are related to the method presented here are [14] and [15]. In [14] the author chooses the modified pixels in the code based on the average luminance of 1057-7149 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.