Keywords

1 Introduction

“Why doesn’t the color match?” Anyone who has ever worked in color publishing has probably asked (or been asked) this question. Color management is the proper tool for users who want to match or, more realistically, get an “optimal color reproduction” [1]. Generally, the original can be converted to configuration file through the intentions of perception, saturation, relative colorimetric, and absolute colorimetric, respectively, etc. [2]. However, mappings between color spaces are ubiquitous in image processing problems such as gamut mapping, decolorization, and image optimization for color-blind people, vehicle contour identification, and design of industrial products [3–5]. To be curious, what type of mapping and the error range of the corresponding correction are most suitable in different experiments?

Different people have different views at this question. Si Li-li gets a conclusion: It is suitable for the use of perceptual mapping to pay attention to tone and level of performance of the original type; pay attention to color rendering of the original type is suitable for the saturation mapping; and for accurate reproduction of images is suitable for the absolute colorimetric mapping [6]. Sanmartin et al. think that the appropriate parameters for converting the device-dependent RGB color space into a device-independent color space were established. The color data were then compared using the CIELAB color formula [7]. In addition, Wang Hai-wen et al. think that the color gamut mapping can be divided into one-dimensional mapping, 2-dimensional mapping, and 3-dimensional mapping in the space dimension [8, 9].

This experiment draws the color gamut mapping to search the answer. The original RGB mode is converted to four CMYK modes through four intentions. The above CMYK modes are represented in the Lab space with tolerance range calculated. Furthermore, the most suitable color gamut mapping output printing verified the accuracy of color gamut conversion.

2 Experimental

2.1 Observation of Color Tolerance

In the Lab mode of Ps, the values of the mapping colored block Lab are accurately selected as the center of the coordinates and the 3-dimensional coordinate system of Lab is well established, where a is x axis, b is y axis, and L is z axis. Unfortunately, in the limits of equipment, only Ps software is used to draw three color gamut graphs using a–b, a–L, and b–L to determine the spatial domain of each color tolerance of four CMYK modes. According to the phenomenon of color contrast, however, it fills background with center color to be easily observed by human eye. For example, the Lab date of center is (52, 74, 55), red color tolerance as shown in Fig. 22.1.

Fig. 22.1
figure 1

Red a–b color tolerance

Full size image

In the background color, it just uses the pencil tool to circle tolerance. After the painting, the background layer is hidden, and the coordinates of the 4 points of the ellipse are recorded, for example, Fig. 22.2. It is in the laboratory standard D65 light box to observe the color range. The red color is represented as a domain of tolerance: L = 49 ± 1.235, a = 69 ± 2.854, and b = 50 ± 1.432.

Fig. 22.2
figure 2

Ellipse in red a–b color tolerance

Full size image

2.2 Calculation and Location of Color Tolerance

In Lab space, the color difference equation, the chroma difference, and hue difference equation of CIE 1931 are performed. Rhinoceros 5.0 is used to draw the above formula and observation results in the Lab color space, for example, red color range as shown in Fig. 22.3.

Fig. 22.3
figure 3

Red color range chart

Full size image

2.3 Substitute Measurement Data of Mapping Color

The intention of the document is converted into the configuration file, such as perception, saturation, relative colorimetric, absolute colorimetric. Their color difference and tolerance are located in measurement, as shown in Table 22.1 and Fig. 22.4.

Table 22.1 Color difference between RGB manuscript and four kinds of mapping
Full size table
Fig. 22.4
figure 4

Color tolerances of 4 mapping forms

Full size image

From the Fig. 22.4, overall color tolerance: absolute colorimetric > saturation > relative colorimetric = perceived. So the experiment absolutely chooses absolute ratio color as an example. It is suitable for the accurate reappearance of the image in this study.

2.4 Print Output and Error Analysis

The experiment makes ICC color management on computer and Heidelberg printing machine, doing plate through the CTP equipment, at last using Heidelberg offset printing machine output proofs. In order to ensure the reliability of data, experiment selects different substrates such as powder paper, coated paper, and offset paper. The use of optical density measuring instrument gets color value of CMYK, XYZ, and Lab.

The relationship is analyzed between the measurement points and the tolerance range. Lines go through the area which is the direction of linear change and the error range is the length of point movement. The red color in digital printing 80 g copy paper is selected as an example. Its Lab value was 39.170, 45.120, and 17.310. The original red color in absolute colorimetric value of Lab is 51, 71, and 50. The error range of modified is s = 20.204395 (±2.1e−05) square units.

2.5 Summary

The tolerance of different color conversion modes is calculated from two aspects of subjective and objective. In the subjective aspect, reasonable samples are selected and the ideal results are obtained; in the objective aspect, through the theoretical formula calculation of tolerance range and substituting the data, experiment draws tolerance more intuitively showed. The color gamut is intended to specify the configuration file with an absolute colorimetric based on the subjective feeling of human visual perception and color difference formula. According to the color range, L, a, and b are selected for the calculation of limit value of chromatic difference, hue difference standard.

3 Conclusions

This paper establishes the mathematical conversion model of Lab based on the plane theory and verifies the accuracy of the conversion model achieving the requirements of the faithful copy in printing industry. According to the different printing process, the replication scheme can be used to improve the replication accuracy between color printing and electronic manuscripts. When the color digital images output to paper, eyes cannot feel color difference between paper color and computer display, which avoids printing pale losses. The numerical relationship is fed back to the process of color gamut conversion and image reproduction, such as realization in scanning moiré. Then, color measurement and calculation are carried out again to verify the accuracy of color gamut conversion.