# Enhanced Steganography for High Dynamic Range Images with Improved Security and Capacity
## 2 Preliminary
### Embedding in [PERSON] et al.'s Scheme
### Embedding in [PERSON] et al. 's Scheme  
The RGBE format, also known as the Radiance format, was introduced by [PERSON] [7] in 1991 as the first efficient HDR image format. This format utilizes 32 bits to represent each pixel in an HDR image, which is more efficient compared to the uncompressed HDR image format that requires 96 bits. In the raw HDR image format, each pixel comprises three color channels: red, green, and blue, and each channel is represented by a 32-bit floating-point value. However, in RGBE images, each pixel consists of four channels to capture the red, green, blue, and exponent values. These channels are represented by 8-bit integers, and their values range from 0 to 255. In the context of HDR image processing, we denote a pixel of raw HDR images as \(P(r,g,b)\), whereas a pixel that has been encoded with the RGBE format is represented as \(P(R,G,B,E)\). The transformation of pixel values from the raw HDR format to the RGBE format can be achieved using the methods described in Equations (1) and (2). \[E=\lceil\log_{2}[\max(r,g,b)]+128\rceil \tag{1}\]\[r=\left\lfloor(256\times R)/\left(2^{E-128}\right)\right\rfloor,\ g=\left\lfloor(256 \times G)/\left(2^{E-128}\right)\right\rfloor,\ b=\left\lfloor(256\times B)/ \left(2^{E-128}\right)\right\rfloor \tag{2}\]  
Due to the exponent channel in the RGBE format, multiple representations exist to express the color of a pixel. Specifically, a pixel \(P(R,G,B,E)\) can also be represented as \(P^{\prime}(2R,2G,2B,E-1)\) (or \(P^{\prime\prime}(\frac{R}{2},\frac{G}{2},\frac{B}{2},E+1)\)) by multiplying (or dividing) each color channel by 2 and subtracting (or adding) 1 in the exponent channel. This feature is referred to as the homogeneity of RGBE, as defined by [PERSON] et al. [13]. To facilitate comprehension, an illustrative example is presented to explicate the embedding operations described below. **Example 1**. : _Table 1 presents the homogeneous representation group (\(HR_{p}\)) elements of a pixel \(P(48,80,44,127)\), which includes \(P(48,80,44,127)\), \(P^{\prime}(24,40,22,128)\), and \(P^{\prime\prime}(12,20,11,129)\) sorted in ascending order of homogeneity, as determined by the exponent channel values. The number of elements in \(HR_{p}\) is equivalent to the homogeneity value (\(HV_{p}\)), while each element is assigned a homogeneity index (\(HI_{p}\)). It should be noted that the element \((12,20,11,129)\) exhibits an odd value of 11 in the blue channel, rendering the division operation inapplicable and thus classifying it as the dominant channel for \(P\)._  
To illustrate the embedding operations in [PERSON] et al. 's scheme in a generalized manner, we present the following example. Specifically, Table 2 is employed to embed the corresponding secret bits into a cover pixel with varying homogeneity values. Building upon the example provided in Table 1, we first compute the \(HV_{p}\) and \(HI_{p}\) values of cover pixel \(P(48,80,44,127)\). Since the HV value of pixel \(P\) is 3, Table 2 is consulted to determine that one bit can be conveyed. Assuming a secret bit of 0 is to be embedded, Table 2 indicates an HI value of 1, resulting in the modification of \(P(48,80,44,127)\) to \(P^{\prime}(24,40,22,128)\), as depicted in Table 1. Conversely, if the embedding secret bit is 1, the corresponding HI value is 0, and \(P(48,80,44,127)\) remains unchanged. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pixel \(P\)** & \(HV_{p}\) & \(HR_{p}\) & \(HI_{p}\) \\ \hline \multirow{3}{*}{\(P(48,80,44,127)\)} & \multirow{3}{*}{3} & (48,80,44,127) & 0 \\  & & & (24,40,22,128) & 1 \\  & & & (12,20,11,129) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Homogeneity of RGBE: an example of pixel \(P(48,80,44,127)\).