## 5 Experimental Study and Result Analysis
### Embedding Rate  
The embedding rate is one of the key parameters that we need to consider when analyzing an RDH scheme. In a medical image transmission context, this defines the number of bits (from the clinical report) that we can embed in the medical image so that we shall restore the original image during the extraction of hidden bits. Mathematically, the embedding rate is defined as  
\[E^{R}=\frac{N^{E}}{N^{T}} \tag{8}\]  
where \(E^{R}\) is the embedding rate, \(N^{E}\) is the number of bits embedded in the medical image, and \(N^{T}\) is the total number of pixels in the medical image. The embedding rate from the proposed RDH scheme relies on the bit plane compression that we can achieve from the bit planes. The compression ratio obtained from each of the bit planes of the eight images (four natural images and four medical images) is given in Table 1. Table 1 gives an overall idea regarding the compression ratio and its relationship with the bit plane. The RLE and modified Elias gamma encoding cannot always ensure the compression of the data. The compression method will provide compression only when lengthy runs of bits are in the bit plane. The medical images are generally very smooth with smooth textures. Hence, we shall see that several most significant bit planes give high compression (compression ratio greater than 1). In Table 1, the cells are marked with two different colors (_green/red_). The _green_ color indicates that the corresponding bit planes are compressed with a compression ratio greater than 1. This indicates that we shall obtain some free space to embed additional data. The cells colored with _red_ indicate that those planes are compressed with a compression ratio of more than 1 (the size of the compressed data is greater than the size of the actual data). Such planes we cannot use for the data-hiding process. Figure 6 depicts bit planes extracted from the natural images, and Figure 7 depicts bit planes extracted from the medical images. Figure 6: Bit planes extracted from the natural images (Row 1: original images. (**a**) Peppers, (**b**) baboon, (**c**) airplane, (**d**) boat. Row 2: plane 7; row 3: plane 6; row 4: plane 5; row 5: plane 4; row 6: plane 1; row 7: plane 0). Figure 7: Bit planes extracted from the medical images (Row 1: original images; (**a**) medical image-1; (**b**) medical image-2; (**c**) medical image-3; (**d**) medical image-4. Row 2: plane 7; row 3: plane 6; row 4: plane 5; row 5: plane 4; row 6: plane 1; Row 7: Plane 0). The average embedding rate obtained from the four natural image classes is shown in Figure 8. Note that the four natural image classes have their own features. The average embedding rate from _Misc._ and _Sequences_ are high compared to the two other classes since the images in the first two classes are so smooth, which will lead to high compression. The embedding rate obtained from all 100 medical images is graphically represented in Figure 9. Since the medical images in the dataset have entirely different characteristics, the embedding rate varies. The results show that from most of the images, we obtain an embedding rate of more than 1. The proposed approach is also compared with the conventional RLE with the Elias gamma scheme to demonstrate the improvement of the proposed modified Elias gamma encoding approach. In Table 2, the RLE + EG indicates the use of conventional run-length encoding with the Elias gamma encoding approach. Similarly, RLE + MEG indicates the proposed method based on run-length encoding with a newly modified Elias gamma approach.