# Reversible Image Processing for Color Images with Flexible Control
## 1 Introduction  
Recently, we widely use image processing applications to obtain desired images. These techniques, however, do not ensure reversibility. If we aim to recover a raw image, then the raw image itself or editing information is required in addition to the processed image (hereafter the output image). This problem notably affects devices with a limited storage capacity, such as smartphones and laptops. Furthermore, in fields for particular types of images such as medical, military, and satellite images, it is essential to perfectly restore raw images. Thus, reversible image processing techniques have been actively researched to recover raw images without increasing the image's data amount. Specifically, reversible contrast enhancement (CE) [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13] methods have been proposed. They have been commonly researched for images with uncompressed formats such as tiff, bmp, and pgm or ppm. These methods guarantee reversibility by using reversible data hiding (RDH) techniques.  
Data hiding techniques have been studied to detect malicious alterations in images and prevent unauthorized use of images [14; 15]. They are classified as two types: irreversible and reversible. The former has accomplished high resistance against attacks and a high hiding capacity. However, it can never restore raw images, even after data extraction. On the other hand, the latter is generally vulnerable against attacks and has a relatively low hiding capacity, while raw images can be perfectly recovered after data extraction. The above reversible CE methods are based on the latter technique and can reconstruct raw images by embedding recovery information into the images.  
Most of the reversible CE methods [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] have been investigated for eight-bit grayscale images. Multiple methods [1; 2; 3; 4; 5] were proposed for natural images to refine the CE effect, while some other methods [6; 7; 8] focused on medical images. On another front, the methods developed by the authors of [9; 10] had an automatic CE function without manuallycontrolling complex parameters. When these methods are directly applied to color images, perceptible hue distortion arises. Additionally, there are few methods specifically for color images. Nevertheless, two previous methods [11; 12] have been proposed to tackle this problem. These methods execute the CE function for color images but still cause hue distortion or cannot ensure reversibility. Furthermore, they perform only the CE function, and other functions have not been considered. Note that the bit depth of their target color images is 24 bits.  
To attain an extra function, we previously proposed a reversible image processing method for color images [13] that is based on the method in [12]. It achieves CE and saturation improvement independently. To ensure reversibility, it embeds the recovery information by using an RDH method.  
In this paper, we propose a novel image processing method for color images with perfect reversibility. The proposed method enables flexible control for brightness (i.e., sharpening, smoothing, increasing, decreasing, and CE). Additionally, the saturation can be selectively improved. This method is an extension of our previous method [13] and preserves its advantages. Through our experiments, we verify the availability of the proposed method from the standpoints of image quality and reversibility.  
The rest of this paper is organized as follows. In Section 2, we describe the related works and background information to facilitate understanding of the proposed method. In Section 3, we propose a new reversible image processing method. The experimental results demonstrate the performance of the proposed method in Section 4. Finally, we conclude this paper in Section 5.