# Using Color Difference Compensation Method to Balance and Repair the Image of Art Design

Authors: Hui Ji; Yang Shang
Journal: Complexity
 (2021)

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## Abstract

In the case of complex illumination background, the image has fuzziness and chromatic aberration, which can improve the imaging effect of the image by white balance chromatic aberration compensation. The traditional method uses the contour feature fusion adaptive matching method to compensate the white balance under the complex illumination background, which leads to the good color difference compensation effect when the image pixel is low. A white balance color compensation algorithm for fuzzy chromatic aberration based on wavelet packet decomposition is proposed. The original image was denoised and filtered. The white balance characteristics of the image were analyzed and extracted based on the wavelet packet decomposition method, and the adaptive balance design was carried out to realize the white balance and color difference compensation of the art design chromatic aberration image. By using the known pixel information of the image block to be repaired, the statistical properties of the image block to be repaired are predicted, and the matching cost of the image block to be matched that meets the restriction conditions is calculated. By introducing the objective factor, the matching cost function is improved to balance the restoration process, and the unnatural problem caused by the repeated appearance of some image details in the restoration results is solved. The simulation results show that the method can effectively balance the color difference of the image, improve the aesthetic feeling of the image, and improve the performance of the detail features of the image. The peak signal-to-noise ratio is high.


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## Body

## 1. Introduction

In the field of image processing, it is often faced with some images with complex lighting background for imaging beautification processing, so as to improve the beauty of the image and the ability to recognize the details of such images. However, under the background of multiple concentrating images, affected by the light of various colors, the image appears white balance deviation and imbalance, resulting in color cast. The fuzzy white balance chromatic aberration compensation of color images can smooth and beautify the image, realize the optimization of multi-light background image, and improve the image quality of imaging. The related research will have important application value in the fields of machine vision and video surveillance [1, 2].In the target recognition and real-time tracking system, the color of the same object varies greatly under different illumination, which affects the accuracy of recognition. For example, when an object photographed under incandescent light is placed against a blue sky, the system fails to recognize the object. In the robot football match system, because the lighting at the match site is not a standard light source, the color change caused by illumination will affect the accuracy of tracking and positioning of multiple robots based on color information [3, 4], so it is necessary to make illumination compensation for the collected images. In the target recognition and real-time tracking system, the illumination compensation algorithm should be simple and fast because of the real-time requirement.Aiming at the application of high-precision chromatic aberration measurement, a light compensation method based on a two-color reflection model and a finite-dimensional linear model is designed. The modified method is fast and effective and can restore the image under nonstandard light to the image under standard light D65, which has the characteristics of high accuracy and strong robustness. In this paper, a fuzzy color image based on wavelet packet decomposition of the white balance chromatic aberration compensation algorithm first described the complex illumination under the background of the image acquisition system, . Then the noise in the image acquisition process is filtered out, and the image features are analyzed and extracted based on the wavelet packet decomposition method and the color white balance based on adaptive equalization is designed. The white balance chromatic aberration compensation for fuzzy chromatic aberration image is realized, and the performance is verified by simulation experiments, which shows the effectiveness of the proposed method.


## 2. Related Works

Due to the poor natural conditions of imaging under multiple illumination background, the image obtained by imaging equipment is usually blurred and produces color aberration, which is sensitive to the difference between the external environment and the surrounding color, resulting in errors and distortions in the imaging equipment’s view-taking and intelligent analysis, and reduces the imaging quality. In the traditional method, the fuzzy image color white balance of chromatic aberration compensation technology mainly uses the compensation method based on multi-scale weighted [5], Harri, corner detection based white balance chromatic aberration compensation method [6], and white balance chromatism compensation method based on edge contour integration, and so on [7]. This method is based on the noise reduction processing of blurred images. The feature of the bright spot is extracted, and then the white balance chromatic aberration compensation is realized by the scale step fusion method. The common disadvantage is that the restoration effect is not good when the chromatic aberration pixel-level is reduced. Li et al. [8] proposed a fuzzy color image based on multi-scale spectrum separation deviation algorithm, the white balance in the process of image feature extraction cascade classifier design spectrum characteristics of the image recognition, as a pheromone realization of white balance and compensation pixel level fusion, but the disadvantage of the method of computing cost is larger, The real-time performance is not good, and its application value in the fields of real-time video monitoring and image tracking processing is not high [9].Lighting color compensation methods can be divided into two categories: mapping and nonmapping. The mapping theories mainly include von Kries color coefficient law [10], gamut mapping theory, lookup table method, and spectral sharpening theory [11]. Nonmapping theories [12] mainly include retinal cortex theory, neural network model, supervised color constant algorithm, color space-based method, and light compensation method based on a finite-dimensional linear model. Based on the study of color adaptation, the coefficient theory [13] was put forward, and it was believed that a diagonal matrix could be used to describe the relationship between the color of the same object surface under two illumination conditions. Von Kries’ theory is the basis of many correction methods. Two-color gamut mapping algorithms, Mvext and Crule, are proposed [2] to map the image color stimulus value under unknown lighting to the canonical gamut. The color gamut mapping method proposed by Forsyth is improved to map the 3-D color vector to the 2-dimensional color perspective space [14]. However, this method is applicable to all kinds of synthetic images or real images containing a few colors. The lookup table method [15] is to build a table with the help of chromaticity measurement data. For this purpose, a certain number of true colors that are sufficient to represent the image must be selected and listed in the table. If the reproduced color is not in the color table, it can be obtained by interpolation or approximation. The lookup table method needs a large number of standard chromatographic and color block data. The more the number of color blocks, the higher the precision of illumination compensation. Spectral sharpening theory [16] is mainly used to improve the DMT color constant algorithm. The illumination compensation method based on mapping realizes the color space conversion by determining the mapping relationship between the source color space and the target color space. This method is often used in digital cameras, scanners, monitors, printers, and other image input and output equipment for color correction processing.The Retinex theory [17] proposed that the color change caused by illumination is generally gentle, usually manifested as a smooth illumination gradient, while the color change effect caused by surface change is usually manifested as a mutation. By distinguishing the two kinds of changes, people can distinguish the light source change and the surface change of the image, so as to know the color change caused by the light source change and maintain the constancy of color perception. The theory of the retinal cortex can be applied to the trichromatic and opposing color systems. A light compensation method based on a neural network was proposed [18], which estimated the color of the light source through neural network training. The training samples of the neural network light compensation algorithm usually adopted synthetic images and required that the surface reflectance of the composite image and the color of the light source were known. The neural network can also use the real image, but for the real image, it is necessary not only to know the real light source color of the real image sample but also to consider artificial noise, mirror reflection, camera nonlinearity, flash, and other interference. This model can only be used to distinguish the chromaticity coordinate value of image illumination, but not to identify the spectral energy distribution of image illumination, so it could not obtain the reflection characteristics of the object surface in the image. A supervised illumination compensation algorithm [19] was proposed to calculate and eliminate the effect of illumination by placing a color plate for correction in the environment. It is difficult to obtain the reflectivity of the color slice and the channel response characteristics of the color imaging system. Based on affine invariant theory and central matrix analysis of color histogram, a supervised color constancy algorithm [20] was obtained. Compared with Novak’s algorithm, although the reflectivity of the color slice and the channel response characteristics of the imaging system are not required to be known, the zero coordinates of the imaging system are still required to be known in the actual calculation. A light compensation method based on supervised color swatch is proposed [21]. Compared with previous methods, it does not need to know the surface reflectance of the supervised color swatch, nor the channel response characteristics and zero-point coordinates of the color imaging system. However, the selection of supervised color swatches is not representative, and it is difficult to obtain enough training samples with reasonable distribution, so this method cannot be widely used. The image chromaticity compensation method is used to achieve image chromaticity compensation by adjusting and correcting the dispersion distance of each channel in the image captured by the image capturing device. The method includes the following steps: capturing a reference point image, obtaining the dispersion distance between the two reference points and the predetermined channel in the reference point image, calculating a dispersion correction ratio, and storing the dispersion correction ratio.The light color compensation method based on the finite-dimensional linear model was proposed. Starting from the system imaging model, the spectral reflectance of the object was restored by the acquired color value, and then the standard color value was obtained by combining the spectral power distribution of the standard light source [22]. It is believed that if the surface reflectivity of an object can be determined, the color presented by the surface under various lighting can be obtained by calculation [23]. It is pointed out that the spectrum of natural light can be accurately expressed by the basis function. Principle component analysis (PCA) is used to analyze the surface reflectance of Munsell color blocks. It is pointed out that the spectral reflectance expressed by the first three feature vectors is 99% consistent with the actual measured reflectance [24–26], which proves that the spectral reflectance function of most objects is bandwidth-limited, and the spectral reflectance can be represented by three feature vectors [27–30]. The method based on the finite-dimensional linear model simplifies the spectral power distribution of the light source and the representation of object reflectivity, which is a big step forward in solving the problem of the insufficient constraint of color vision. It is one of the hot spots of illumination color compensation algorithms at present [31, 32].The existing light color compensation methods have their own limitations, and many problems are yet to be solved. In this paper, a color compensation method based on color space conversion is proposed for target recognition and real-time tracking color qualitative analysis occasions. The method is simple, fast, and easy to implement. Aiming at the application of quantitative color analysis such as art design quality inspection, a light color compensation method based on a two-color reflection model and a finite-dimensional linear model is designed, which can restore the image under nonstandard light to the image under standard light D65.


## 3. Preprocessing of Color Difference Compensation Method for Art Design Image Equalization Restoration Process

In order to compensate the white balance color difference of the image under the complex illumination background, it is necessary to collect and process the image first. In the process of image acquisition and imaging, the color of the image output by the image acquisition system based on high-resolution pixel digital devices is blurred due to the background sensitivity caused by the sensor's coke, jitter, optical system error, imaging output, and other complex light. This paper studies the image acquisition under the complex background of illumination model, which is shown in Figure1.Figure 1
Collection model of art design image equalization processing.As shown in Figure1, the left part is the collection part of artistic chromatic aberration, including lighting, features, and filtering; the middle part is the modeling and image mapping part; and the right part is for the establishment of chromatic aberration feature library, standardization, and modeling scoring. In the abovementioned image acquisition and imaging model design, we construct an image information model. Under the action of complex lighting, the output image is obtained through the mathematical model. g represents the color of the blurred image, which contains the complex background light of the noisy image, such as the details of the edges and textures. The state equation is described as follows:(1)gx=Jx1−yx+B1+yx,where A is the environmental light effect component, y (x) is the light transmission of the imaging environment, J (x) and y (x) are the noise coefficient of the original image, and J (x) is the noise in the first step of feature selection, which is optimized and extracted as y (x). According to the above equation, suppose that A represents the pixel complexity of the image, J (x) is the scene albedo at x in the geodetic coordinate system, B (x) is the chromatic aberration deviation degree of illumination, and C (X > Y) is the illuminance chromatic aberration contrast parameter, u is the noise factor, v is the extracted noise factor, C+ is the parameters of chromatic aberration contrast of illumination C (X > Y). Otherwise, the relationship between C2, structural features, and s (x > Y) is defined as follows:(2)CX,Y=2u,2V+3C12Ux+Uy−C2.In the complex illumination background, the image structure similarity is(3)K=Cv,e−∑v2e2.The initial pixel of the initial wavelet packet is fixed at 15 × 15. The image processing template is determined by the similarity of the sub-band wavelet of the image,m ∗ n. The texture mesh of the fuzzy chromatic difference image is divided into 3 × 3 template, and the similarity of the wavelet structure of the image is solved. Through the above analysis, the objective optimization function of image imaging can be expressed as follows:(4)Kv,e=vTv+e−1e+1∑e−1.In order to solve the problems of determining the sequence of image restoration and searching the sample image blocks, a new art image equalization restoration algorithm based on color difference compensation is proposed. It determines the position of the image block to be repaired by the new priority calculation function. Then, based on the known pixel information, the average value of the restored image blocks in each color component is estimated, and all the unmatched image blocks in the known image region are screened accordingly, and then the image block with the least matching cost with the current image blocks is found. Finally, by copying the corresponding information in the best matching image block to the unknown pixel part of the current image block, the repair of the current image block is completed. Similarly, the restoration of the entire designated image area is completed step by step in the unit of image blocks. The specific algorithm flow is shown in Figure2.Figure 2
Flow chart of art image equalization restoration algorithm for color difference compensation.In graphic art design, the description of the objective process is mainly to extract physical art design parameters through instruments and tools. With reference to related mathematical formulas and evaluation systems, the subjective evaluation parameters were extracted and analyzed, such as image resolution, number of dots, image density, spectral reflectance density, and color. Among them, the following evaluation mathematical formula is used:(5)T=1−t0−tit0+ti⋅γ2.In general, the smaller the registration errort0 is, the higher the evaluation accuracy of the product will be. When calculating the registration error t1, the value range of TA is shown in Table 1.Table 1
Evaluation criteria of set alignment error.
TAFine productOrdinary goodsWeight distributionFour openFolioFully openFour openFolioFully openMain body<0.10<0.15<0.20<0.20<0.30<0.500.6General<0.15<0.20<0.30<0.30<0.40<0.600.4According to subjective test standards, combined with the company’s requirements for printing quality, we first measured the ink layer density, ink stack printing rate K value, and art design dots in the field of art design, and checked the transfer printing quality of ink dots and the level of art design image reproduction curve. In addition, the optical index measurement is based on the color image, for example, the consistency of spectral distribution, the stability of different spectrum and same color effect, the range of chromatic aberration, and so on. Table2 describes the range properties of chromatic aberration, from which we can understand the color aberration (NBS and the degree of visual discrimination).Table 2
Color difference and color difference.
Color difference (NBS)Feel the color difference0.0–0.5Slight off-color0.5–1.5Little off-color5–3.0Small color difference3.0–6.0Large color difference6.0Big color differenceIn the subjective evaluation, the most important evaluation of image sharpness is the evaluation of the contour compactness of image levels, the brightness comparison evaluation of adjacent image levels, and the texture evaluation of image details. These three parameters interact with each other and affect the evaluation of sharpness that is computed as shown in Table3. Table 3 below is the weight setting relationship of the above parameters.Table 3
Weight setting of definition reappearance evaluation parameters.
Measurement evaluation parameterTagWeightStep density errorTE1.6Dot shape factorSF1.75Additional dot densitySD1.65Dot enlargementDG1.54Three colorsLE1.1Effective density ratio in dotDP0.64Field densityDP0.53SaturationA0.46GrayG0.48Hue errorLS0.32


## 4. Image Feature Extraction and White Balance Color Difference Compensation Improvement

On the basis of image acquisition system design and noise reduction processing, the white balance color difference compensation of fuzzy color difference image is carried out to improve the imaging level and ability of the image under complex illumination background. The traditional method uses the contour feature fusion adaptive matching method to compensate the white balance under the complex illumination background, which leads to the poor color compensation effect when the image pixel is low. In order to overcome the disadvantages of traditional methods, this paper proposes a white balance color compensation algorithm based on wavelet packet decomposition for fuzzy color aberration images. The wavelet packet decomposition method is used to decompose the details and extract the features of the fuzzy chromatic aberration image. The wavelet analysis method has spatial and temporal resolution, and the calculation is simple. In this paper, the wavelet analysis method is used to construct the image’s Harris wavelet packet function as follows:(6)fx,y=γx1−x1+N−σy1+N.On the basis of wavelet decomposition feature analysis and extraction of the above images, three-level wavelet decompositiony is used to improve the design of the white balance color difference x compensation algorithm. The key technologies of algorithm improvement are described as follows. The sensitivity coefficient of white balance of fuzzy chromatic aberration image under wavelet decomposition is H, and the adaptive equalization of chromatic aberration after wavelet decomposition for three layers is as follows:(7)Eu=∑cjuH.According to the dimension of the pixel, the image is divided into three categories: color image, gray image, and binary image. For color art design products, its defects are mainly shape defects and color defects. Shape defects focus on the changes of image shape features, such as linear defects, dot defects, and planar defects, which are represented by the difference of gray values between two images at corresponding points. The color defect focuses on the color difference of the whole or part of the image, such as color aberration, color deviation, and so on. The defect types of grayscale images without considering color information can be classified as follows: (1) point defects with the small area but large pixel value difference, such as missing printing, ink splashing, local or large-scale character missing printing, and so on; (2) linear defects with small width and wide distribution area, such as scratch, streak, and so on; (3) each direction of the image alone or at the same time in the offset, such as overprinting that is not allowed, dislocation, and so on; and (4) image defects exist in a large range, such as paste version, dirty version, and so on. Binary image, that is, black and white images, has only two discrete gray levels: 0 and 1. There is little difference between the types of defects and those of gray-scale images, but the types of defects are quite different. For different defects, the number and position of black and white pixels that we can use are different.From the viewpoint of art and design technology, art and design image itself should have the appearance of the computer for data collection features, and from the perspective of art design in industrial production, print quality is mainly composed of art and design image aesthetic factors, technical factors of the art design technology, and art and design product consistency factor control. Aesthetic factors mainly refer to that trademark designers conceive and design the structure, color, graphics, text, and other visual features of trademarks according to the aesthetic point of view, so as to achieve the direct reference factors that are beautiful, are attractive to consumers, and can reflect the corporate culture concept. Technical factors refer to the technical indicators that truly reflect the characteristics of various shape parameters of printing products in the process of artistic design, such as image accuracy, gray scale, color value, color difference, text position, shape, and so on. The consistency factor is an objective factor considering the stability of production, which describes the degree of difference of technical factors between printing sheets. Because it is a continuous production in time and space, it will bring more or fewer differences between the sheets. In addition to the production process problems, such as replacement of materials and stop inspection, these uncertainties will also bring a certain difference between the sheets. The consistency factor is a measure of how a series of successive products differ based on the same shape in different parts of a sheet.In this paper, a linear interpolation method is proposed to measure the light color. Under the CIE standard observation condition, the images of the standard whiteboard are taken repeatedly from different angles and distances. The mean values ofR, G, and B channels obtained by each measurement were calculated, namely, different points in the RGB space. The line segment representing illumination in the space was obtained by linear minimum variance fitting, namely, the illumination axis L. The specific steps are as follows:(1)
Fix the digital camera at the place away from the white plane SOCM(2)
Take two pictures from different observation angles (0° and 45°)(3)
Change the position of the white plane (20 positions at different distances from the light source) and repeat steps 1 and 2(4)
From the 40 images obtained, take a square region of 100 × 100 pixels from each image and calculate the mean value and variance ofR, G, and B of each region(5)
The curve represented by the mean value in theRGB space is drawn by linear minimum variance fitting, which is the illumination color vector. Illumination color estimation results obtained using a linear interpolation method are shown in Table 4.Table 4
Illumination color estimation.
Light sourceRGB spatial light axisXYZ spatial light axisAxis of rotation inXYZ spaceAR = 0.7558X = 0.2754u = 0.6434G=0.5915Y = 0.2317v=−0.7652B = 0.7553Z = 0.9345w=0.2D65R = 0.5972X = 0.0256u = 0.6835G=0.5832Y = 0.0239v=−0.7303B = 0.5503Z = 0.0983w=0.4According to the finite-dimensional linear model, if the light source is known, the photosensitive characteristic of the acquisition system is known, and the output tristimulus value of the acquisition system is known, the spectral reflectance can be reconstructed to obtain the color value under a specific light source. The specific algorithm steps are as follows:(1)
Estimate power distribution of ambient light spectrum(2)
Determine the surface reflectivity basis function(3)
Obtain the weight coefficientJ′ of the surface reflectivity basis function(4)
Obtain the tristimulus value under the standard light source D65The first three feature vectors were obtained using principal component analysis as spectral reflectivity basis functions, as shown in Table5.Table 5
Basis function of surface reflectivity.
Wavelength (nm)Basis functionR1 (t)R2 (t)R3 (t)4000.1672−0.04760.24334050.1473−0.08620.22664100.1362−0.09730.17414150.1293−0.10340.16454200.1262−0.10670.17014250.1243−0.11860.16634300.1232−0.11820.15544350.1234−0.12320.1494


## 5. Results Analysis

In order to test the performance of the algorithm in this paper in realizing the white balance color difference compensation and imaging optimization of images under multiple illumination backgrounds, simulation experiments were carried out. The hardware environment of the simulation experiment was Intel (R) 2.3 GHz CPU, 2 GB memory, and a 32 bit Windows 7 PC. Based on MATI_AB 2010 programming platform, mathematical programming is carried out to achieve algorithm code design. In parameter design, the neighborhood window of the wavelet packet is set as 9 × 9. The maximum frame frequency of image acquisition is 60 FPS; the acquisition pixel is 500,000; the aperture is F14; the exposure time is 11 s; and the image size is 600 × 400. On the basis of the above simulation environment and parameter settings, the image processing is carried out, and the simulation experiment of white balance color difference compensation of fuzzy color difference image is carried out. In order to quantitatively analyze the performance of the algorithm, different methods are adopted, and the peak signal-to-noise ratio of image imaging quality is taken as the test index. The simulation results are shown in Figure 3. It can be seen from Figure 3 that the proposed method has a higher peak signal-to-noise ratio of image imaging, indicating better imaging quality.Figure 3
PSNR performance comparison.In order to verify the effectiveness of the improvedRGB color difference formula, 40 pairs of color codes with similar visual perception to human eyes were selected from the standard chromatography. The distribution of color codes in the RGB color space is shown in Figure 4. X-Ritter 528 spectrophotometer was used to measure the corresponding tristimulus value Y and Z, according to the measured tristimulus value to calculate the chromaticity value X and Y of each color standard. Taking L0 nm as an interval, 31 pairs of color codes with the main wavelength of 400–700 nm within visible light wavelength were selected. The variation diagram of the chromatic aberration curve obtained using the above three chromatic aberration calculation formulas is shown in Figure 5. As can be seen from Figure 5, within the whole visible wavelength, the improved RGB chromatic aberration formula is basically consistent with the calculation results of the CIEDE2000 chromatic aberration formula, which is currently recognized as the most accurate calculation. In order to show the consistency of the improved RGB color difference calculation formula and the CIEDE2000 color difference formula more intuitively, the CIEDE2000 color difference formula is used as the standard to calculate the other two color difference calculation formulas and their deviations, including the maximum deviation, the minimum deviation, and the average deviation. The deviation curves of CIELAB and the improved RGB color difference formula and CIEDE2000 are shown in Figure 6.Figure 4
Distribution of color code inRGB space.Figure 5
Variation of chromatic aberration curve.Figure 6
Variation of deviation curve.The method presented in this paper was used for feature extraction, and the error matching points were eliminated by variable scale dynamic shrinkage search. The moving target and beautification part of the image imaging area were automatically divided into imaging space through feature clustering, and the feature clustering results under the color difference compensation color channel were obtained, as shown in Figure7.Figure 7
Feature clustering results of color difference compensation color channel.The gray histogram of a color image mainly represents the range and number of pixels distributed in the gray level of the whole image, while the match chart can more easily mark the number of pixels in a specific gray level. Figure8 shows the grayscale histogram of the standard image and its match legend.Figure 8
Grayscale image and match legend.
(a)(b)It can be seen from Figure8 that the gray histogram of color images is similar to the PS and NK images previously studied on color images. These three kinds of images reflect the distribution of pixels in the image gray space, that is, the number and range of distribution of pixel statistics; there are three forms of representation.


## 6. Conclusion

Due to the poor natural conditions of imaging under multiple illumination background, the image is relatively blurred and produces color aberration, which is sensitive to the difference between the external environment and the surrounding color, resulting in errors and distortions in the imaging equipment’s view-taking and intelligent analysis, and reduces the imaging quality. This paper proposes a white balance chromatic aberration compensation algorithm for fuzzy color images based on wavelet packet decomposition. First, it describes the image acquisition system under the complex lighting background and then performs noise filtering on the acquired image based on wavelet packet. The decomposition method analyzes and extracts image features and designs the color white balance based on adaptive equalization. Through the study of the white balance color difference compensation method of the image, the smooth beautification processing of the night multi-illumination image is realized, and the imaging quality of the image is improved. In this paper, a smoothing algorithm based on white balance chromatic aberration compensation is proposed for night multi-illumination chromatic aberration images. The target space is automatically divided by feature clustering for night multi-illumination chromatic aberration images, and the detail features of night multi-illumination chromatic aberration images are smoothed and beautified to the maximum extent to improve the algorithm. Simulation results show that the proposed algorithm has better image smoothing and beautification performance, higher output (SNR and PSNR), lower computational overhead, and superior performance.



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