# Reversible Image Processing for Color Images with Flexible Control
## 5 Conclusions  
We proposed a novel image processing method for color images to reversibly control multiple functions. In particular, the proposed method attained not only CE but also sharpening and smoothing, brightness increase and decrease, and saturation improvements. This method has three main advantages. First, we verified that one or two types of functions can be used from among five brightness controls: sharpening and smoothing, brightness increase and decrease, and CE. Second, the regulations for the brightness and saturation can be executed independently. Specifically, the regulations never interfere with one another. Finally, full reversibility is ensured by embedding the recovery information so the raw images can be retrieved from the output images.  
The experimental results demonstrated the availability of the proposed method from the standpoints of image quality and reversibility. We first confirmed the effect of each function visually and quantitatively. The proposed method flexibly controlled the brightness and improved the saturation without hue distortion. Next, we explored the maximum limit of each function. It was verified that this method has a wide range of control for each function. With respect to reversibility, the proposed method perfectly reconstructed the raw images in any case. For the embedding process, we compared the amount of recovery information with the hiding capacity. It was proven that the proposed method perfectly  
Figure 10: Raw image and output images under proposed method with two types of brightness controls and saturation improvement (kodim1, \(I_{S}=20\)). (**a**) Raw image. (**b**) Sharpening and brightness increase (\(I_{VSH}=2\) and \(I_{VI}=30\)). (**c**) Sharpening and brightness decrease (\(I_{VSH}=2\) and \(I_{VD}=30\)). (**d**) Sharpening and CE (\(I_{VSH}=2\) and \(I_{VC}=30\)). (**e**) Smoothing and brightness increase (\(I_{VSM}=2\) and \(I_{VI}=30\)). (**f**) Smoothing and brightness decrease (\(I_{VSM}=2\) and \(I_{VD}=30\)). (**g**) Smoothing and CE (\(I_{VSM}=2\) and \(I_{VC}=30\)). (**h**) Brightness increase and CE (\(I_{VI}=30\) and \(I_{VC}=30\)). (**i**) Brightness decrease and CE (\(I_{VD}=30\) and \(I_{VC}=30\)).  
embedded all of the recovery information. We finally verified the performance of coregulation. Our method could effectively apply three functions, namely two types of brightness controls and saturation improvement, to a single image. Through our experiments, it is clear that the proposed method achieved multiple functions for brightness and saturation with full reversibility.  
As described above, our new method has unique advantages over the previous methods. However, there still exists a constraint: the proposed method ensures reversibility for specific functions only. As one solution to tackle this matter, we will investigate flexible control for the hue component. Additionally, we aim to make the combination of multiple functions for a single image free so as to achieve more flexible processing.  
Conceptualization, Y.S. and S.I.; methodology, Y.S.; validation, Y.S. and S.I.; formal analysis, Y.S.; investigation, Y.S.; writing--original draft preparation, Y.S.; writing--review and editing, S.I.; supervision, S.I.; project administration, S.I. All authors have read and agreed to the published version of the manuscript.  
This research received Grant-in-Aid for Scientific Research(C), No. 21K12580, from the Japan Society for the Promotion Science.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
The authors declare no conflict of interest.