Uniform contrast enhancement (UCE) is a method proposed by Kim et al. [29]. First, the proposed method separates a color image into three channels, red, green, and blue (RGB), and assigns an equivalent number of histogram shifting iterations on each channel. The potential maximum number of repetitions of all the channels is first calculated, and the minimum between the number of repetitions of all channels is used for histogram shifting, data embedding, and contrast enhancement.

(1)pi″={pi′+bk,pi′=Pspi′+1,Ps<pi′<Pcpi′,otherwisewhere pi′ is the ith pixel value in the image, pi" is the pixel value after histogram shifting of pi′. PS is the bin that needs to be embedded, PC is the bin that needs to be combined, and bk is the secret information that needs to be embedded in the kth bit, and its value is 0 or 1. RHS is applied if PS≺PC, LHS otherwise.

Before each histogram shifting, a vector L=(L1,…,Lm,…) to record P_c and the information of the adjacent bins are required. d is used to direct the histogram shifting either RHS if d=1, or LHS if d=−1. When pi′=PC, Lm=0; when pi′=PC−d, Lm=1.

Different from other RDH algorithms, this algorithm requires that the difference between the brightness of the enhanced image and the brightness of the original image is not greater than 1, and the brightness of the defined image is the mean value of all pixels in the image. When the brightness of the original image is greater than the brightness of the enhanced image, RHS is applied, In addition to apply LHS. PS is selected as the pixel value with the largest number of pixel value ranges in JPS, and JPS is dynamically selected according to the brightness difference between the original image and the enhanced image. PC is defined as the number of pixels contained in a pixel value within a certain range and its adjacent pixel values the number sums the minimum pixel value.

Wu et al. [22] proposed an HSP technique based on finding the maximum, median, and minimum values among the RGB image’s three channels. Then, the histograms of the three are combined. The original image is next converted to HSV. How the conversion is done is demonstrated in the following equations.

(2)H={60x(G−BX−Z),X=R60x(B−RX−Z+2),X=G60x(R−GX−Z+4),X=undefined,X=0

(3)S={X−ZX,X≠00,X=0

(4)V=Xwhere X and Z represent the maximum and minimum of each pixel in the RGB model and Y the median.

HSP applies pre-processing to avoid histogram overflow during data embedding. First, move all empty histogram bins of the X channel mentioned in Eq. (2) to the far left of the histogram, and the modified X channel, Y channel and the Z channel are combined to obtain a total histogram, and the merging operation is to merge the bin with the lowest height in the histogram to the adjacent bin. After the merging is completed, the total histogram can be disassembled to obtain the histogram of the three channels after pre-processing. The bookkeeping information records the extra information generated by all previous operations.

During embedding, two bins fL and fR are first found, secret information is embedded into X channel by splitting the 2 highest bins and achieving histogram equalization. To ensure the image quality, Y channel and Z channel are modified based on exploiting Eqs. (5)–(6).

(5)Y'=X'−(X−Y)

(6)Z'=X'−(X−Z)where X' represents the modified X channel, Y' and Z' represent respectively the modified Y channel and Z channel. Y' and Z' are stored using information bookkeeping for recovery purposes.

Three cases are defined with sub-cases by exploiting the Max Channel to determine the number of repetitions applied for each channel while embedding secret bits.

Case 1: If R is max, we maintain all possible repetition numbers for R and Min channels to embed data. Then a comparison is made between the other two channels to find the Med and Min. The ratio between the Max and Med Channels is first calculated, then the number of iterations for the Med channel. Eqs. (7) and (8) demonstrate how to calculate the ratio, and the number of repetitions in case G is the Med channel, and B is the Min channel:

(7)Gratio=GsumRsum

(8)Grep=⌈(1−Gratio)×Gmax−rep⌉where ⌈.⌉ denotes the round operation, Gsum and Rsum are the summation of pixels values respectively of the G channel and R channel, and Gmax−rep the maximum obtained a number of iterations for the G channel. Suppose B channel appears to be the Med. In that case, we maintain the potential number of iterations found for the G channel while calculating the number of iterations applied for the B channel by using its ratio between B and R, i.e., Med and Max channels as shown in Eqs. (9) and (10)

(9)Bratio=BsumRsum

(10)Brep=⌈(1−Bratio)×Bmax−rep⌉where ⌈.⌉ denotes the round operation, Bsum and Rsum are the summation of pixels values respectively of B channel and R channel, and Bmax−rep the maximum obtained number of iterations for the B channel.

Case 2: The same steps are exploited as in Case 1 if G is Max. As a result, the G channel and B channel will maintain the potential number of iterations if the B channel is Min, and only the one of R will change by using the Eqs. (11) and (12)

(11)Rratio=RsumGsum

(12)Rrep=⌈(1−Rratio)×Rmax−rep⌉where ⌈.⌉ denotes the round operation, Rsum and Gsum are the summation of pixels values respectively, of the R channel and G channel, and Rmax−rep the maximum obtained number of iterations for the R channel. If B is Med Channel and R is Min Channel, G and R will keep the potential number of iterations, and only one of B will change by applying Eqs. (13) and (14)

(13)Bratio=BsumGsum

(14)Brep=⌈(1−Bratio)×Bmax−rep⌉

Case 3: If B is Max, the same process is applied as in case 1. Hence, if R is the Med channel and G is the Min channel, the B channel and G channel will keep the previously obtained number of repetitions, and only one of R will change by applying the Eqs. (15) and (16)

(15)Rratio=RsumBsum

(16)Rrep=⌈(1−Rratio)×Rmax−rep⌉where ⌈.⌉ denotes the round operation, Rsum and Bsum are the summation of pixels values respectively of R channel and B channel, and Rmax−rep the maximum obtained number of iterations for the R channel. If the G channel is Med and R channel, the Min, B channel, and R channel will keep their potential max number of iterations, and only the one of B will change by applying the Eqs. (17) and (18)

(17)Gratio=GsumBsum

(18)Grep=⌈(1−Gratio)×Gmax−rep⌉

With the exception of utilizing a different number of repetitions for the Median Channel, we apply the strategy in [31] employed to embed secret bits. The following algorithm reveals the description of the embedding process.

When hidden data is processed, bits are embedded in all channels, and most pixel values appear to be either extremely low or extremely high, which causes distortions in the image. The proposed method gives out a solution by adjusting the image with no loss of data embedded. The first step to adjusting an image consists of extracting channels of the original image. Secondly, each pixel of the original channel is added to the corresponding pixel of the enhanced channel, then we round the result divided by 2 to have a coefficient used to obtain the adjusted pixel. Let’s consider Pi,j a pixel from the original channel before enhancement, Pi,j′ a pixel from the enhanced channel, and Pi,j″ a pixel of the adjusted channel. Pi,j″ is obtained by applying Eq. (19):

(19)Pi,j″=Pi,j′−Ci,jwhere Ci,j denotes the coefficient of adjustment of the pixel Pi,j′. Ci,j is obtained using the following equation:

(20)Ci,j=⌈Pu,j′−(Pi,j+Ci,j)/2⌉where ⌈.⌉ denotes the round operation.

The proposed method, as aforementioned, carries out data embedding, contrast enhancement, and the opposite process, which entails data extraction and image recovery. The original image is an additional tool in the proposed method’s data extraction and image recovery processes. The adjusted enhanced image is first divided into three channels. To acquire the coefficient taken from the LSB of the adjusted pixels, each channel’s composing pixel is compared to the original channel pixel. The improved pixel with embedded data is then obtained. The original image is restored following data extraction using the methods described in [31]. To illustrate the data extraction and image recovery workflow, an illustration is proposed. Let’s consider Pi,j=99, Pi,j′=90, using Eq. (20), Ci,j=−5. Hence, by exploiting Eq. (19), we obtain Pi,j"=95. When Pi,j" is compared to Pi,j, we get 9 to be close to the double 5. Hence, we extract five from Pi,j" to obtain Pi,j′. Then from Pi,j′ we perform data extraction and image recovery following the steps in [31].

The relative contrast error (RCE) computed between the original and enhanced image is used to assess the CE effect. RCE = 0.5 means the image contrast is unchanged, whereas RCE > 0.5000 denotes improved image contrast. In Table 1, the RCE resulting from all the methods applied in the Kodak Lossless True Color Image Suite Image set is greater than 0.5000. This means that the proposed method can perform contrast enhancement. In Table 2, the RCE of the images from USC image set are less than 0.5000 when applying methods using HSP based algorithm. However, the proposed method in all images of the USC image set outperformed in contrast enhancement. As a result, Table 4 displaying the average result of RCE and other metrics of performance reveals that the proposed method keeps the RCE greater than 0.5000 showing how it performs better contrast enhancement than some existing methods.

The effectiveness of the image quality is assessed by employing metrics such as Peaked Signal-to-Noise Ratio (PSNR), Structural Similarity index (SSIM) and Relative Mean Brightness Error (RMBE). The PSNR ratio measures the strength of a signal in relation to its noise power. In addition, a higher PSNR indicates less noise added to the original image. SSIM calculates the similarities between the original and enhanced images and gives values from 0 to 1, with 1 indicating that the images are identical. RMBE calculates the difference in average brightness between the original and improved images. Tables 1, 2 and 3 show the numerical results of PSNR, SSIM and RMBE. The proposed method achieves a higher average PSNR and SSIM values in all the images than other methods. Figs. 1 and 2 display the enhanced images using different methods.

The selected area in blue on Figs. 1, and 2 are displayed separately from the enhanced images. This shows the physical difference between the proposed and earlier methods acquired visual quality. In comparison to the clouds from the image enhanced by previous methods, the clouds in the selected area obtained by the enhancement of 4.2.05 by the proposed method are whiter and brighter. Meanwhile, some methods change the color of clouds to a deep gray. The wall on the image of the house, which was enhanced by UCE and bi-histogram shifting, has a somewhat incorrect yellow tint, while the propose method enhances the white on the wall. The black circle around the eyes is darker and looks greener on Kodim04, enhanced in Figs. 1b–1d. While using [32] and the proposed method, there is no visible greener appearance, however, kodim04 is greatly enhanced. When enhancing USC03, more extra distortions are added to the image, giving it a 3D appearance.

The enhanced USC03 in Fig. 2i resembles the original image, demonstrating that no contrast enhancement was performed. The color of the background in the last displayed image was altered during data embedding, but the proposed method makes the tree appear much more realistic. The proposed method successfully produces contrast enhancement for color images of all the image sets. Table 4 summarizes the average result of metrics of performance used to assess the proposed method image quality.

The CIEDE2000 is frequently used to access color preservation and color distortion. The value is anticipated to be as low as possible to prevent color distortion. However, if the CIEDE2000 value is 0, the original image and the enhanced are the same. Table 4 shows the overall CIEDE2000 outcome. The proposed approach fails in maintaining color. But compared to other methods, Tables 1, 2 and 3 reveal that colors of some images have been successfully maintained by the proposed method after enhancement.

UCE as well as the method in [31] used to make a comparative analysis with the proposed method embeds data by repeating the histogram shifting. All the methods are given the same number of repetitions of 40, and then the proposed method applies changes based on its algorithm. To make fair the comparison with the method in [32], the same amount of data is given to all the images to embed and complete the analysis of the embedding rate. The column title embedding rate in different tables reveals the proposed method’s embedding performance and prior ones. The overall results reveal that the method in [31] embeds more data than the other methods. However, the proposed method does not rank last in the embedding rate. Hence the embedding rate of the proposed method can be considered reasonable.