One Way PVD
Wu & Tsai (2003) discovered a new paradigm, i.e. “edge regions of an image can hide a greater number of bits as compared to smooth regions”. They came up with a steganographic algorithm known as PVD. The embedding algorithm in PVD is as described below.
The pixels of the image are raster scanned and a pair of adjacent pixels (
, 
) are termed as a block. For such a block the difference value 
= (
- 
) is found. A range table like Table 1 is considered. This d value belongs to one of the ranges 
whose width is 
= (
. Here, 
and 
are the lower and upper bounds of the range 
. The number of bits that can be hidden in this block is 
. Now 
bits of data are taken from the binary data stream and converted to decimal value b. The new difference value is calculated by hiding b in this block as in Eq. (1).
=
(1)Now 
= 
- d is calculated. If d is an odd number the stego block is 
. If d is an even number the stego block is 
.
The extraction algorithm is as below. The pixels of the stego-image are raster scanned and a pair of adjacent pixels (
, 
) are termed as a block. For such a block the difference value 
= (
-
). The same range table i.e. Table 1 is considered. This d value belongs to one of the ranges 
whose width is 
= (
. Here, 
and 
are the lower and upper bounds of the range 
.The number of bits that can be extracted from this block is 
. An example of embedding is as shown in Figure 1. The block is (50, 65). The difference value is 15; it lies in the range {8, 23}. So lower bound is 8 and n value is 4. Suppose the four bits of data to be hidden is 1010, its decimal value is 10. As d ≥ 0, the new value of difference, 
=8+10 =18. Now m=
-d=3. As d is odd the new value for the block is 
= (48, 66).
Table 1. | Range | Width | No. of Bits |
 Є {0, 7} |  = 8 |  =3 |
 Є {8, 15} |  = 8 |  =3 |
 Є {16, 31} |  = 16 |  =4 |
 Є {32, 63} |  = 32 |  =5 |
 Є {64, 127} |  = 64 |  =6 |
 Є {128, 255} |  = 128 |  =7 |
As per the observation by Zhang and Wang (Zhang & Wang, 2004) this PVD technique is detected by PDH analysis. In PDH of stego-images the zig-zg nature is observed.
Chang et al. (2008) and Lee et al. (2012) extended this PVD idea into 2×2 pixel blocks to improve upon the performance. But they did not prove that their techniques qualify through PDH analysis. Balasubramanian et al. (2014) proposed octonary PVD to improve the performance further and to qualify from PDH analysis.