Graphic Quick-Response Codes Without Finder Patterns ^†

Abstract

Quick-response (QR) codes are widely used for information transmission. However, their black-and-white dot structure often lacks visual appeal. Therefore, we developed novel graphic QR codes that remove traditional corner finder patterns and conceal data within redesigned modules. These codes can be scanned, positioned, and decoded directly in software, while paper-based versions can be instantly decoded by overlaying a transparency with printed finder patterns. Experimental results across varying grayscale levels and devices confirmed reliable readability. The proposed QR codes provide enhanced esthetics and security, offering a new direction for future QR code applications.

1. Introduction

The quick-response (QR) code is a two-dimensional barcode consisting of black and white modules arranged in a matrix. Compared to barcodes, QR codes have higher information capacity and are quickly decoded by mobile phones [1]. QR codes utilize Reed-Solomon codes to provide a margin of error in the barcode, which allows them to efficiently correct partial damage or distortion during the scanning process. Since barcodes are inexpensive and fast to produce, they are commonly used for advertising and data transmission [2,3,4]. However, the black-and-white structure is not esthetically pleasing in layout display, and it is difficult to show the corporate and image links. Therefore, the color and structure have been changed to enhance the appearance of 2D barcodes. Wu et al. [5] developed a colorful art barcode by combining barcodes and images and integrating the cover image. The barcode maintains the structure of the barcode and improves the esthetics at the same time. Lin et al. [6] used an error correction mechanism of the QR code to beautify the barcode by clearing out the information points in some areas to give room for the image to display. Although these patterns provide information in a small space, the positioning points in the structure still occupy a lot of barcode space and even distract people’s attention from the image. In this regard, Chen et al. [7] proposed a new barcode method, which eliminates the presence of traditional finder patterns and integrates barcodes into the cover image, but it cannot be decoded directly by a mobile phone, which makes it unpopular for commercial use. Huang and Wang [8] made the barcode transparent using the structure of traditional QR codes and integrated it into the background texture of the document. Their barcode was not affected by the layout of the picture, hence increasing the function of information concealment. In internet streaming, users pay more attention to the security of personal data privacy and authenticity. Therefore, 2D barcodes need to be esthetically pleasing with enhanced security.

The halftone technique was proposed by Frederic E. Ives in 1881. Since photographic images could not be printed on paper, they had to be drawn by artists and engraved on printing plates for reproduction. With the emergence of halftoning technology, the photographic images are split into small dots of different sizes or spacing through the mesh grid to present the detailed structure, indirectly simulating a continuous tone level. The distribution of these dots simulates the transition effect of continuous tone levels. At a certain observation distance, the low-pass filter of the human visual system is utilized to make the halftone images presented with a similar consequence to continuous tone [9]. This has led to the advancement of photo printing technology.

Nowadays, due to computerization, the way of halftone generation and composition is more diversified. Continuous-tone images are converted into a binary numerical arrangement, with “0” as the darkest image and “1” as the brightest. The halftone image is constructed through the arrangement of inking and non-inking. Among them, amplitude modulation (AM) and frequency modulation (FM) dots are widely used in printing applications [10]. In AM, the distance of each inked dot is fixed, and the size of the dots simulates the light and dark changes in the image details. The AM method is widely used due to its simplicity in calculation and its ability to stabilize the image during the printing process [11]. However, its regular arrangement is easily affected by the same frequency, which leads to the occurrence of mesh moiré. In contrast, in FM, each inked dot is of the same size, and the image gradation is presented through the spacing of the dots, resulting in a more detailed texture structure. Since the FM method does not rely on a fixed frequency, it presents the texture structure of the image in greater detail and minimizes the occurrence of moiré. Error diffusion, which is the main method of FM dot generation, is superior to other halftone methods in terms of image quality. It effectively minimizes particulate sensation during the printing process and improves the smoothness and definition of the image [12]. Since the black and white information dots appear during the process of calculating the information dots hidden in the image, Fu and Au [13] used data hiding error diffusion (DHED) to spread the interference evenly to neighboring dots to minimize the visual noise caused by the information dots. Wang et al. [14] proposed an information hiding method in the QR code and added another set of QR codes to enhance the security.

In this study, we developed a technique that removes the finder pattern and redesigns the finder pattern mechanism to reduce the visual interference of finder pattern points and combines them with corporate images. In terms of information security, the graphic QR code without a finder pattern is more visually meaningful and secure than the traditional barcode, as the module disassembles and hides the information (Figure 1). We redesigned the structure of the positioning point and combined it with the corporate image for better image display through microstructure adjustment. The results of different printing outputs were tested and compared in terms of recognition rate and readability. The output of barcode images can be decoded directly, while the printed codes can be decoded in real time by superimposing the positioning points.

2. Methods

2.1. Module Design

In this study, we used the barcode hiding technique [15], where the cover image and barcode information are mixed together. The barcode used was the sixth version of QR code, with a structure of 41 × 41 modules and an error tolerance level of H (30% error tolerance). The sixth version (41 × 41) was used as the outward structure, resulting in a total of 123 × 123 sub-modules. Subsequently, to increase the barcode size, the two axes were shifted outward by 21 units each, resulting in a structure with 165 × 165 submodules, and the size of each submodule was set to 4 pixels, which ultimately resulted in a real output size of 660 × 660 pixels (Figure 2). In addition, we adopted the FM algorithm in the halftone technique to combine the image with the graphic QR code and integrate the enterprise image. The FM algorithm presents the gradation of the image by clustering black and white dots, which is easily combined with the black and white modules in the QR code. In the algorithm, when the position is used as a QR code’s information point, it matches the black and white information points at that position, while the rest is used as a representation of the image’s tone.

The developed QR code conveys two-dimensional information in a matrix arrangement of black and white modules, and each module is split into 3 × 3 submodules, where the information point of the barcode information QR code (41 × 41) is hidden in the center of each submodule of the barcode. Structurally, to minimize the possible expansion of the mesh caused by the black squares, each module is appropriately modified. The module is composed of 4 × 4 pixels, so it is shrunk by 1 pixel at each corner of the module (Figure 3). The barcode can be seen from a distance to reduce the intensity of the black presence of the barcode, and at the same time, it increases the stability of the barcode. The graphic QR codes without finder patterns match three characteristics of anti-counterfeiting raised by van Renesse: hidden features, variable information, and machine readability [16].

2.2. Finder Pattern Removal in QR Code

To remove finder patterns, the information points with the binary image are encoded in the graphic QR code, and then mask is used to retouch the clutter around the image and remove the original finder pattern symbols. Since the graphic QR code needs to be localized, a set of black boxes is defined and added around the output so that the four corners of the boxes can be used to decode the barcode message, as shown in Figure 4.

2.3. Graphic QR Code in Different Grayscale Levels

To test the practical application, the graphic QR code was printed and scanned into electronic scripts with 10 different grayscale scales (Figure 5). A Matlab Equation (1) was used to divide the grayscale Y between 0 and 1 into 10 equal parts, with the darkest being “0.0” and the brightest being “0.9”, k1 being the input image and k2 being the processed image. After the paper output, the number of errors and the decoding performance of each set of grayscales are scanned and analyzed to find out the best output parameters.

k2 = imadjust(k1,[0  1],[Y   1]);

(1)

2.4. Decoding Methods and Data Restoration

The graphic QR codes developed in this study are decoded by using a standalone program or a mobile phone with the finder patterns of the QR code. The printed and scanned barcode was sampled and then input to the MATLAB R2023b program for location grabbing. The 660 × 660 pixel graphic QR code was sampled at every four intervals, resulting in a 165 × 165 pixel barcode structure, which was cropped to 123 × 123 pixels after the boundary cuts (Figure 6). Then, the original barcode structure was restored at the second interval. Using the function of real-time scanning and decoding, the structure can be restored and decoded by a mobile phone through the overlapping of the paper with the finder pattern when the output barcode is used in advertisement and paper output (Figure 7). To test the output results of different grades, two output machines were used in this study, namely Fujifilm Apeosprint C5240 (low resolution) and Fujifilm Apeos C3570 (high resolution) Tokyo, Japan.

3. Results and Discussion

In this study, each set of barcodes in an external size of 660 × 660 pixels was printed on paper at 600 dpi, so the actual size of a single barcode was 2.8 × 2.8 cm. The paper was scanned at 1200 dpi and analyzed. Since the dark areas of the image are susceptible to problems such as dot gain of the mesh dots and diffusion of the mesh dots, the following two scenarios were considered when testing the barcodes (

Table 1. Definitions of “False Black” and “False White”.

False Black	False White
The white dot is misrecognized as a black dot	The black dot is misrecognized as a white dot

). “False black” was defined as the white module being misinterpreted as a black module, and “False white” as the black module being misinterpreted as a white module. Each set of codewords contains eight modules, and if there were a false black or a false white module, the codeword was determined incorrectly. In the experiment, the default error tolerance level of the barcode was H. Therefore, the number of errors in the output graphic QR code must be controlled within 30% of the total number of codewords (172), and when the number of codeword errors was more than 52, the whole barcode was declared unreadable.

3.1. Low-Resolution Machine Output

The output of the Fujifilm Apeosprint C5240 is shown in

Table 2. Error analysis of QR code printed at low resolution.

Grayscale Levels	Error Module Number	False Black Number	False White Number	Module Error Rate	Codeword Error Number	Codeword Error Rate
0.0	119	68	51	0.07	39	0.22
0.1	146	79	67	0.08	42	0.24
0.2	101	56	45	0.06	35	0.20
0.3	94	53	41	0.05	36	0.21
0.4	102	60	42	0.06	38	0.22
0.5	143	79	64	0.08	63	0.36
0.6	129	72	57	0.07	60	0.35
0.7	96	54	42	0.05	40	0.23
0.8	95	55	40	0.05	49	0.28
0.9	102	63	39	0.06	60	0.35

for low-resolution printing devices, such as office desktop printers and home printers, and the graphic QR codes without finder patterns images in half of the grayscale levels can be read by decoding. However, the five-level barcodes with brighter grayscale are prone to pattern distortion and decoding errors.

3.2. High-Resolution Machine Output

To improve the decoding success rate, we analyzed the output of the Fujifilm Apeos C3570, a higher-resolution printing device, and the results are shown in

Table 3. Error analysis of QR code printed at high resolution.

Grayscale Levels	Error Module Number	False Black Number	False White Number	Module Error Rate	Codeword Error Number	Codeword Error Rate
0.0	95	54	41	0.06	30	0.17
0.1	100	56	44	0.07	35	0.20
0.2	97	54	43	0.06	29	0.16
0.3	97	56	41	0.06	39	0.22
0.4	96	54	42	0.06	41	0.23
0.5	104	62	42	0.06	46	0.26
0.6	94	53	41	0.06	43	0.25
0.7	96	56	40	0.06	47	0.27
0.8	91	52	39	0.05	40	0.23
0.9	108	68	40	0.06	59	0.34

. Most grayscales were decoded without any problem. The smaller the parameter value, the darker the graphic QR code, the lower the error rate, and the better the ability to read the graphic QR code. On the other hand, the larger the parameter value, the brighter the color of the graphic QR code, resulting in a higher error rate, potential decoding failure, and slightly reduced QR code readability.

3.3. Comparison of Grayscale Levels in Different Printing Devices

The error rate of high-resolution printing equipment was lower, while low-resolution gradation was read smoothly. The darker the gray level, the more stable the barcode is and the better the image can be read; while the brighter the gray level, the more prone to errors, which affects the interpretation of the barcode (Figure 8).

3.4. Application with Added Printed Finder Patterns

To use present QR codes with the developed ones in this study, the original positioning points are superimposed to restore the barcode information in the physical barcode application and then decoded by the mobile phone in real time. The QR code needs to be output in about 1.3 times larger size (3.5 cm) for large-scale posters in the future.

4. Conclusions

Removing the QR code finder patterns reduces the problem of the barcode’s visual appearance affecting the layout of advertisements and articles. Through the microstructure design, the information data of the cover image and the hidden QR code are smoothly mixed, and the security of the barcode is enhanced. The developed QR code is vivid on paper output, and the success rate is better for values with lower grayscale values. According to the comparison of different output devices, high-resolution output devices also have a higher chance of successful barcode reading. The QR code with a physical mask is decoded on mobile phones with flexibility and compatibility with the customary decoding method. The graphic QR code without finder patterns developed in this study can be used to beautify the products and advertisements in the future.