Cryptography Reference
In-Depth Information
11.4.2 Large Subpixels Have Better Misalignment Tolerance
In this subsection, we investigate the misalignment tolerance of the large and
small subpixels. And show that shares with large subpixels have better mis-
alignment tolerance when recovering the secret image by its original color than
that with small subpixels. Denote the size of the large and small subpixels as
s 2 s 2 and s 1 s 1 respectively, where s 2 > s 1 . According to Figure 11.5,
the recovered secret image using the small subpixels (Figure 11.5(a)) has a
higher resolution than that using the large subpixels (Figure 11.5(c)). It is ob-
served that Figure 11.5(a) indeed has the refined resolution in detail of Lena
image. We can clearly view the hair in Figure 11.5(a) but the area of hair is
all black in Figure 11.5(c). The image quality using the medium-sized sub-
pixel (Figure 11.5(b)) is between Figure 11.5(a) and Figure 11.5(c). Although
using large subpixels in share has poorer resolution, it will be more robust
to the misalignment error. Next, the misalignment tolerance of different-sized
subpixels is formally analyzed.
FIGURE 11.5
Recovered Lena images for (2,2)-VCS using the different sized subpixels: (a)
the small-sized subpixel, (b) the medium-sized subpixel and (c) the large-sized
subpixel.
Consider a misalignment deviation (d x ;d y ) in the (2; 2)-VCS. All the pos-
sible cases of stacked shares of a white secret pixel (1B1W) and a black secret
pixel (2B0W) with a deviation (d x ;d y ) are shown in Figure 11.3. For the small
subpixel (s 1 s 1 ), we define the whiteness R W;a1 (resp. R W;a2 ) as the ratio
of black area in a stacked two-subpixel area for the case a1 (resp. a2) in Fig-
ure 11.3, and the darkness R B;b1 (resp. R B;b2 ) as the ratio of the black area
in a stacked two-subpixel area for the case b1 (resp. b2) in Figure 11.3. For
the large subpixel (s 2 s 2 ), the corresponding denotations are R 0 W;a1 , R 0 W;a2 ,
R 0 B;b1 and R 0 B;b2 .
To simplify the discussion, we only consider the one dimension deviation,
i.e., (d x ; 0) or (0;d y ). Then we have the following one-dimensional deviation
lemma.
 
 
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