3.1. Food Image EnhancementExperiments were conducted to illustrate the performance of the proposed method using digital food images. Parameters α, β, MIN, and MAX are set as to 3, 0.1, 0.2, and 0.8, respectively. θ is 72, which is the average value of h, using the top 100 ranking photos posted as of April 2021 on the SNS site “SnapDish”, which specializes in cooking [21]. The problem in this calculation is that the values of h differ greatly between −180 and 180, even though they have almost the same hue. Therefore, θ is determined using the following equation: where <·> is the average operator for all the images. a*¯ and b*¯ are the average values of a* and b* in each image.Figure 6 shows the experimental results of seven digital images. These are 24-bit color images (1) 1015 × 501 pixels, (2) 1920 × 1080 pixels, (3) 1919 × 1080 pixels, (4) 1706 × 960 pixels, (5) 1280 × 1280 pixels, (6) 1478 × 1108 pixels, and (7) 1280 × 664 pixels in size, respectively. The first column shows the original images, the second column shows the resulting images using the proposed method, and the third, fourth, and fifth columns show the resulting images using the methods in Ref. [2], in Ref. [6], and in Refs. [12,13]. In (b1), the unnatural coloring of whitish colors is improved compared with (b) in Figure 3. In (b2) and (b3), the chroma of the sweets is appropriately enhanced, whereas the blue and gray dishes remain nearly identical. In (b4) and (b5), the cake and crab are vivid, whereas the brown and white tables are largely unaffected. In (b6) and (b7), the yellow areas are effectively brightened. In addition, we can see that the proposed method provides sufficient color enhancement compared to the comparison methods. However, the resulting image of (e4) is vivid compared with (b4), which was obtained by the proposed method. In the experiments, the same parameters were used for all images. This was done to demonstrate the versatility of the proposed method. However, to further improve the performance of the proposed method, it is necessary to consider a scheme by changing the parameters based on the statistics of the input image.The difference in hue between the resulting and original images is calculated as follows [22].

||Δh*||=2Ce*Co*sin|he−ho|2,

(9)

where he and ho are the hues of pixels paired with the resulting and the original images, respectively. Similarly, Ce* and Co* represent chromas. · denotes the absolute value. Furthermore, the difference ΔC*=Ce*−Co* is calculated to verify the degree of image enhancement. Table 1 lists the averages and standard deviations of ||Δh*|| and ΔC*. We can see that the averages of ||Δh*|| in all resulting images by the proposed method are smaller than those of the comparison methods, and the hue is almost preserved. Furthermore, the averages of ΔC* indicate that the proposed method can improve the chroma compared to the comparison methods.SSIM [23] is measured as the image quality metric for objectively evaluating the performance of the proposed method. When SSIM is closer to 1, the enhanced image is structurally similar to the original image. Table 2 shows SSIMs between the original images and the resulting images with respect to Figure 6. This value is the average of SSIM calculated for each RGB component. From Table 2, we see that the proposed method gives better results compared to the comparison methods.Figure 7 shows the scatter plots of the hue and chroma corresponding to Figure 6. The chroma is enhanced within a limited range of hues by the proposed method. However, due to the relationship between the RGB color space and the CIELAB color space, the range of possible values for C* varies depending on L*. Therefore, there are areas where C* does not increase uniformly.Furthermore, Scheffe’s paired comparison test [24,25] was conducted as a subjective evaluation of the resulting images in Figure 6. Randomly selected images were placed left and right, and the two images were evaluated by six examinees (average age: 20.5 years, 4 females and 2 males) about which image is preferable as a food image. The examinees evaluated the two images by selecting one of [−2,−1,0,1,2], where the higher values indicate that the right image is preferable to the left image. The yardstick method was used to obtain the evaluation value of each image. Table 3 shows the evaluation values by Scheffe’s paired comparison test. A higher value indicates a higher evaluation of the image. From Table 3, we see that the proposed method is superior to the comparison methods except in the case of image 4.