Extended Visual Cryptography for Photograph Images - Visual Cryptography and Secret Image Sharing - page 113

This approach adjusts the tones of given images to make the dynamic
ranges as large as possible while every triplet fulfills the constraints given by
Equation (4.1). Ane transformation or piece-wise linear transformation is
most commonly used for tone adjustment [28, 42, 45, 25, 26]. Wu et al. sug-
gested to calculate optimum parameters [42]. However, [42] does not explain
any details how to obtain optimum parameters. Myodo et al. [25] proposed a
method that can determine optimum parameters at once [26]. They claimed
that their method can enhance relative differences to 0.28 on average without
any violation. Their method can control the relative differences independently
by specifying the weights.
Another approach uses a contrast enhancement technique called histogram
equalization or histogram linearization transformation [11], which is very well-
known for improving the contrast of images. The histogram of an image can be
seen as a function h(i) that returns a frequency or probability density of pixels
having an intensity level i, namely a transparency. Histogram equalization
equalizes or flattens a histogram. This means that frequencies of tone levels
are totally uniform and the resulting image may have a high contrast. Chen
et al. [6] as well as Wu et al. [43] suggested a way to improve image quality
by applying histogram equalization to the input images before encryption.
4.4.8 Continuous-Tone Subpixel
Image quality can be improved by increasing tone levels as discussed in Section
4.3.2. There have been some studies improving image quality by introducing
continuous-tone subpixels into encrypted shadow images [29, 45].
Yang and Chen [45] introduced continuous tone into the resulting shadow
images. They extended usual EVCS explained in Section 4.3.3 by substitut-
ing a black subpixel by a gray subpixel having the same gray value as the
original shadow pixel. This approach can be applied to EVCS with an access
structure. The drawback of this approach is the trace of shadow images. The
reconstructed secret image can be observed in superimposed shadow images.
Thus, a secret image should be a logo or text image. One can recognize a
logo as well as shadow images at the same time when shadow images are
overlapped.
Nakajima and Yamaguchi [29] proposed a very unique approach for im-
proving image quality by introducing continuous-tone subpixels. Their method
also deals with a misalignment problem caused by pixel expansion. We will
discuss this method in the next section.