A Study on Parameters of Image Encryption Based on Moiré Pattern
Zhe-Ming Weng
a
, Dao-Shun Wang
a)
, Shun-Dong Li
b)
,Xiang-Yang Luo
c)
a)
Department of Computer Science and Technology,Tsinghua University,Beijing, China
b)
School of Computer Science, Shanxi Normal University, Shanxi, China
c)
Information Science and Technology Institute, Zhengzhou, China
Abstract—In image encryption based on moiré pattern, a secret
image is hidden to an encrypted image by a reference fringe
pattern. When the reference fringe pattern and the encrypted
image are superimposed or by simple computation, the secret
can be reconstructed. Generating reference fringe pattern and
encrypted image depends on selection of different parameters.
Although some experimental results demonstrate validness of
their algorithms based on moiré pattern, related parameters
are not given. In this paper, we first discuss two
superimposition models for grey-scale image and analyze
reconstructed images with different parameters, and then
obtain relationship among reconstruction quality and
parameters of generating equations. Experimental results show
the validness of the obtained relationship among
reconstruction quality and different parameters.
Keywords-image hiding; moiré pattern; reconstruction
quality
I. INTRODUCTION
When two images are superimposed, a new different
pattern appears. This kind of pattern is called ‘moiré pattern’.
Based on this phenomenon, Muñoz-Rodrı
guez and
Rodrı
guez-Vera [1] proposed a novel image encryption
based on moiré pattern performed by computational
algorithms. A certain reference fringe pattern is used to
encrypt a secret image. The secret image can be
reconstructed by simple computation with the same
parameters. Ragulskis and Aleksa [2, 3] improved this
algorithm and proposed an image hiding algorithm based on
time-averaging moiré. The secret image can be reconstructed
by naked eye when a time-averaging moiré pattern is
harmonically oscillated in a predefined direction. Based on
their algorithm, Ragulskis and Aleksa [4] proposed an image
hiding algorithm based on time-averaged fringes produced
by non-harmonic oscillations. Ragulskis et al. [5] proposed
an image hiding algorithm based on circular moiré fringes.
Sakyte et al. [6] proposed an image hiding algorithm based
on near-optimal moiré gratings. Palivonaite et al. [7]
proposed an image hiding algorithm in time-averaged
deformable moiré gratings. Petrauskiene et al. [8] proposed a
dynamic visual cryptography based on chaotic oscillations.
In these improved algorithms [2-8], the basic generating
equations and parameters are almost the same as those in [1].
Experimental results of [1-8] did not give related parameters,
nevertheless, we know that the reconstruction quality may be
different when we use the same algorithm with different
parameters (about this point, see Fig. 1 of section 2). So, it is
worthwhile to study the relationship among reconstruction
quality and parameters of generating equations.
This paper is organized as follows. Section 2 reviews the
algorithm proposed by Muñoz-Rodrı
guez and Rodrı
guez-
Vera and discusses two superimposition models for grey-
scale image. In Section 3, we propose a method to calculate
the reconstruction quality and give its relationship with
parameters of generating equations. Then in Section 4, we
use the proposed method to compare and discuss the
reconstruction quality in another image hiding algorithm
based on moiré pattern. Section 5 concludes the paper.
II. PREVIOUS WORKS
Muñoz-Rodrı
guez and Rodrı
guez-Vera [1] proposed an
image encryption based on moiré pattern performed by
computational algorithms. It is one of the most typical image
hiding algorithms based on moiré pattern. A certain
reference fringe pattern is used to encrypt a secret image.
The secret image can be reconstructed by simple
computation with the same parameters.
This algorithm is reviewed as follows.
TABLE I. ALGORITHM PROPOSED BY MUÑOZ-RODRGUEZ AND
RODRGUEZ-VERA
, ,
, and the secret image
for every pixel in
compute
according to (2)
for every pixel in
compute
according to (1)
compute
according to (3)
In this algorithm,
denotes the reference fringe
pattern and it can be obtained as
, (1)
where and are the background intensity and contrast
of the fringe pattern, respectively, and
is the fundamental
frequency.
denotes the encrypted image and it is described
as
, (2)
where the intensity function stands for the secret
image.
denotes the moiré pattern and it is described by
(3)
According to (1) and (2), the value of the pixel is
between and . So we can let . In image