Encrypted Image Display based on Individual Visual Characteristics
Ryota Niwa, Fumihiko Sakaue and Jun Sato
Nagoya Institute of Technology, Gokiso Showa, Nagoya, Japan
Keywords:
Multiplex Image Projection, Visual Characteristics, Multispectrum-image Projection, Light-field Display.
Abstract:
In this paper, we propose an encoded image displaying system based on light field decoding by human visual
systems. We focus on the difference of individual characteristics of the human visual systems, and we indicate
that the difference of the characteristics makes a significant difference in the observation results. Based on the
observation difference, we achieve image encoding to a light-field which can be decoded by the human who has
a particular visual characteristic. To achieve the image encoding system, we construct a 5D light field display
system. This 5D LF display controls the spectral distribution of the light rays as well as position and directions.
By using the 5D LF display, we utilize the characteristics of the spectral sensitivity and opticalcharacteristics
of the human visual system. Several experimental results show that our proposed method can disturb the
observation of the general audience and provide appropriate information to a target person.
1 INTRODUCTION
In modern society, confirmation of secure communi-
cation using computers is one of the most critical is-
sues to protect privacy, critical information, etc. In
general, data servers and computer networks have al-
ready had a secure communication system using data
encryption, and encryption techniques are studied
widely and extensively. For example, critical data on
the server are transferred to client computers through
the protected networks by data encryption. The trans-
ferred data is decrypted on the client computer and
the decoded data, i.e. raw data, is displayed to users
through the data displaying devices such as video dis-
play. This fact indicates that displayed data is eas-
ily stolen when malicious persons peek computer dis-
play. This peeping cannot be disturbed even if the
most secure data servers and networks are utilized.
To protect the direct attack on the displaying data,
we need to encrypt the data not only on the computers
but also on the displays. However, if the encrypted
data is presented on the displays, the users need to
decrypt the data by themselves. This decryption is
very hard and requires lots of computation, and thus,
the convenience of the system becomes extremely de-
creased. Therefore, if we want to prevent the decreas-
ing of the convenience of the system, the encrypted
data on display should be naturally and involuntarily
decrypted by only a particular target user.
In our system, we propose an image encryption
system using light field displays. In our system, we
(a)
(b)
(c)
Figure 1: Difference between (a) standard displays, (b)
light-field displays and (c) 5D light-field displays.
focus on the individuality of the human visual sys-
tems. It is known that human visual systems have
a lot of characteristics such as color sensitivity, re-
sponse speed, etc (Hori et al., 2017; Muramatsu et al.,
2016). The characteristics have a difference in a per-
son by person. The fact indicates that all people ob-
serve different images even if they observe the same
scene. We focus on the difference of the observation
results and propose an image encoding system which
can be decoded by only a particular person who has a
target visual characteristic.
For this objective, we construct a 5-dimensional
light field display that can control not only directions
of light rays but also spectral distribution. In gen-
eral light-field displays can emit different light rays
to each direction, as shown in Fig.1(b). By using
this property, various systems are proposed(Wetzstein
et al., 2011; Hirsch et al., 2014; Hung et al., 2015;
Huang et al., 2014), such as 3D display without
glasses, vision-correcting displays, and so on. In our
system, we also control the spectral distribution of
386
Niwa, R., Sakaue, F. and Sato, J.
Encrypted Image Display based on Individual Visual Characteristics.
DOI: 10.5220/0008967003860394
In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 5: VISAPP, pages
386-394
ISBN: 978-989-758-402-2; ISSN: 2184-4321
Copyright
c
2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
each light rays to utilize spectral sensitivities of hu-
man visual systems. This display can control the
4-dimensional light field and 1-dimensional spectral
distribution, and then we call the display 5D light field
display.
By using the display, we propose an image dis-
playing system with encryption by a particular visual
characteristic of the human. In this system, special
encoded light-field are emitted from the display, and
the field is decoded only by a target user. If the other
human observes or peeps the display, their visual sys-
tem cannot decrypt the light field to the original im-
age. Therefore, a secure and involuntary image en-
coding system can be achieved.
2 RELATED WORKS
Light field display is studied extensively(Wetzstein
et al., 2011; Hirsch et al., 2014; Hung et al., 2015;
Huang et al., 2014) and utilized for various kinds of
image representation. The most representative light
field display is an autostereoscopic display. The au-
tostereoscopic display presents different images in
the right and left directions. Thus, different images
to be observed in the right and left eyes, and it re-
alizes stereoscopic viewing. The light field display
has been utilized for visual correcting display with-
out glasses(Huang et al., 2014). In this display, vi-
sual characteristics such as myopia and hyperopia are
corrected by controlling the light field without using
glasses. Furthermore, a method measuring the de-
tailed optical characteristics of human eyes has been
proposed(Hori et al., 2017). In this system, observers
observe different images according to their character-
istics. In this case, the observation results indicate the
characteristics of the observer, and thus, we can mea-
sure detail characteristics without individual measur-
ing devices.
On the other hand, many methods that focus on the
spectral sensitivity of the human visual system have
been proposed(Nonoyama et al., 2013; Muramatsu
et al., 2016). Nonoyama et al. proposed a technique
that presents different images for each observer who
has different sensitivities(Nonoyama et al., 2013). In
this method, a multiband display which can control
spectral distribution pixel by pixel is utilized. Also, a
method to measure human spectral sensitivity based
on observation results has been proposed(Muramatsu
et al., 2016).
Although both of these methods are based on hu-
man visual characteristics, both require special im-
age presentation devices and have been independently
studied. However, since these multiple factors are in-
cluded in a human visual system, more various ap-
plications can be expected if these characteristics can
be used simultaneously. In this paper, we propose
an encrypted image presentation system based on op-
tical characteristics as well as spectral sensitivities.
Furthermore, we construct a 5D light field display to
achieve the abovementioned displaying system. The
5D light field display built for this purpose can be ex-
pected to be applied to a broader range of information
presentation technologies in addition to the encrypted
image presentation proposed in this paper.
3 HUMAN VISUAL SYSTEMS
In this section, we describe the characteristics of hu-
man visual systems that are utilized in our system.
As described in 1, human visual systems have sev-
eral kinds of characteristics, such as color sensitivity,
response time, and so on. Besides, these character-
istics have individuality, and then, the characteristics
are different in person by person. In our system, we
focus on the differences of the characteristics. Based
on the differences of the characteristics, we propose
an image encryption method to a light-field which can
be decoded by only a particular user who has a tar-
get visual characteristics. Especially, we utilize the
individuality of spectral sensitivity and optical aber-
ration of human eyes, and we describe the details of
the characteristics in this section.
3.1 Spectral Sensitivities
We first describe the spectral sensitivity of the human
visual system. In our eyes, light-rays from the tar-
get objects pass through the pupil, and light-sensitive
cells, which are called cone cells, receive the light
rays. The cells emit stimulus depending on the input
light rays.
There are three kinds of cone cells, which are L,
M, and S cells. Each cell have different spectral sen-
sitivity x(λ), and the cells emit a stimulus which de-
pends on their sensitivity and spectral distribution of
the received light as follows:
S
a
= K
Z
E(λ)x
a
(λ)dλ, (1)
where a indicates a kind of cell, λ is a wavelength of
the light, E(λ) is the spectral distribution of the input
light, and K is a coefficient for the normalization. In
this case, the observed color is determined by a com-
bination of these stimulus S
a
. Therefore, the observer
observes the same color when the combination of S
a
is the same even if the light spectral E is different.
Encrypted Image Display based on Individual Visual Characteristics
387
Inversely, even if the light rays which have the
same spectral distribution E are provided to the ob-
servers, they observe different colors if the combina-
tion of S
a
is different. These observation differences
often occur because spectral sensitivity x is different
in person by person. Based on these differences of
sensitivity, we encrypt the image to the light field.
3.2 Optical Characteristics
We next, consider the optical characteristics of the
eyes. We have lenses in our eyes, and these lenses
converge the light ray to our retina. If the lens has an
ideal shape to converge the light rays, perfect images
can be projected to the retina. However, the lenses
have various forms. That is, the lens has individual-
ity, and thus, the conversion result of the light rays
becomes a different person by person.
The most critical parameter of the lens is the fo-
cal length. By using the focal length f , the refractive
power D of a lens is represented as follows:
D =
1
f
(2)
Although the D represents an essential character-
istic of the lens, other several parameters are required
to describe the whole characteristics such as optical
aberration. As mentioned above, a general lens shape
includes distortion, and the distortion causes the op-
tical aberration. The aberration producesinaccurate
converging of light rays. The aberration is also in-
cluded in the lens of eyes. We use the parameters
of the aberration as the individuality of the lens. We
utilize Zernike polynomials(von F. Zernike, 1934) to
represent the aberrations by a few parameters.
Let W (x, y) denote optical aberration at point (x, y)
on the lens. The aberration W (x, y) is represented by
Zernike bases Z
m
n
(ρ, θ) as follows:
W (x, y) =
k
∑
n=0
n
∑
m=−n
C
m
n
Z
m
n
(ρ, θ) (3)
where C
m
n
denote Zernike coefficients, and they repre-
sent the optical aberration of the lens. The parameters
(ρ, θ) satisfy x = ρ cos θ, y = ρ sin(θ). The Zernike
bases are computed as follows:
Z
m
n
(ρ, θ) =
∑
n−m
2
s=0
(−1)
s
(n−s)!ρ
n−2s
s!(
n+m
2
−s)!(
n−m
2
−s)!
·
cos|m|θ (m ≥ 0)
sin|m|θ (m < 0)
(4)
The bases are shown in Fig.2. By using the Zernike
bases, the individuality of the lens is described by
Zernike coefficients C
m
n
. In this paper, we describe
the set of these coefficients by W.
Figure 2: Zernike bases: numbers below each images indi-
cates n and m.
4 OBSERVATION OF THE LIGHT
FIELD
4.1 Light Field
We consider the observation of the light field. We first
describe a summary of the light field. In the real 3D
scene, many and various light rays are flying. The
light field represents the status of the light rays in the
scene. The 4D light field is a partial representation
of the plenoptic function(Adelson and Bergen, 1991),
which represents the complete status of the light rays
in the scene.
In the light field representation, we attent to a
plane in the scene to describe light rays because light
rays fly straightforward in the scene. When the light
ray passes through the point (x, y) and it directs to
(u, v), this light ray is regarded as a point (x, y, u, v)
in the 4D light field. Let L(x, y, u, v) denote intensity
of a light ray at point (x, y, u, v) in the 4D light field.
Cameras converge the light rays by lens and
project to a 2D image. This light ray converging can
be regarded as partial integration of the 4D light field.
The 4D light field display emits the light field to the
scene from displaying a plane.In this section, we con-
sider the observation of the light field.
4.2 Light Field Observation based on
Ray Tracing
We consider light field observation based on ray trac-
ing. In this discussion, we consider not 4D light field
consisted by (x , y, u, v), but 2D light field consisted by
(x, u) to simplify the description.
Let us consider the case when a light ray is emitted
from a point x
1
on display direct to u
1
as shown in
Fig.3. In this case, the light ray reaches a point x
2
by
the transformation of the light field as follows:
x
2
u
2
=
1 a
0 1
x
1
u
1
(5)
VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications
388
Figure 3: Ray tracing from light field display to observer.
Furthermore, the light ray is refracted by a lens as fol-
lows:
x
2
u
0
2
=
1 0
−
1
f
1
x
2
u
2
(6)
where f denotes a focal length of the lens. The light
ray finally reaches to a point x
3
on a retina as follows:
x
3
u
3
=
1 b
0 1
x
2
u
0
2
(7)
This transformation is integrated as follows:
x
3
u
3
=
1 b
0 1
1 0
−
1
f
1
1 a
0 1
x
1
u
1
(8)
By using the transformation of the light field, obser-
vation of the light field can be described in an ideal
case. However, the general lens shape is distorted
from the ideal shape, and thus, we need to consider
optical aberration caused by the distortion.
4.3 Light Ray Distortion by Optical
Aberration
Let us consider the case when the light ray does not
reach to ideal point (x, y), but (x
0
, y
0
) = (x + ∆x, y +
∆y) by optical aberration through the point (X,Y ) on
the lens as shown in Fig.4. In this case, the difference
(∆x, ∆y) is computed as follows:
∆x
∆y
=
"
R
n
·
∂W (X,Y )
∂x
R
n
·
∂W (X,Y )
∂y
#
(9)
where n denotes refractive index and R denotes dis-
tance from a point (X ,Y ) to (x, y). Under the assump-
tion optical aberration W is known, (∆x, ∆y) is com-
puted. Thus, we achieve a light ray tracing by com-
putation of ideal point (x, y) from light field transfor-
mation and (∆x, ∆y) from optical aberration.
4.4 Light Transport Matrix
As described in the previous section, light rays trac-
ing from a display to the observer is achieved. Based
on the ray tracing, we next consider image transfor-
mation from a 4D light field to a 2D observed image.
Let L(x, y, u, v) denote intensity of a light ray from a
Figure 4: Optical aberration by lens distortion.
pixel (x, y) to a direction (u, v). When an observer
who has optical aberration W receives the light ray
at pixel (x
r
, y
r
), we define the light transport matrix
T (x, y, u, v, x
r
, y
r
, W) as follows:
T (x, y, u, v, x
r
, y
r
, W) =
1 if L(x, y, u, v) reaches to (x
r
, y
r
)
0 otherwise
(10)
By using the light transport matrix, observed image I
is computed as follows:
I(x
r
, y
r
) =
∑
x,y,u,v
T (x, y, u, v, x
r
, y
r
, W)L(x, y, u, v) (11)
By this computation, observation of a light field by an
observer can be described linearly.
5 5D LIGHT-FIELD DISPLAY
In order to utilize the visual characteristics mentioned
above, we construct a 5-dimensional light-field dis-
play which can control the spectral distribution of the
light rays. In this section, we show the detail of the
construction of the display.
5.1 Multiband Display
We first show the construction of multiband display,
which can control light spectral distribution on 2D
image pixel by pixel. In this display, we construct a
multiband projector and project the multiband image
from the backside of the screen, as shown in Fig.5.
In this system, several projectors which equip dif-
ferent optical narrow band-pass filter, as shown in
Fig.6, are utilized. By combining each bandwidth
images, we construct a multiband projector. By pro-
jecting the multiband image from the backside of the
screen, the multiband image is scattered by the screen.
Thus, we achieve the construction of a 2D multiband
display.
5.2 5D Light Field Display
We next describe the construction of the 5D light field
display utilizing the multiband display. In standard
4D light field display, lens array or barrier structure is
utilized to emit a light ray in a particular direction. In
Encrypted Image Display based on Individual Visual Characteristics
389
Figure 5: 2D Multiband display by rear projection of a
multiband projector.
Figure 6: Examples of spectral transmittance of narrow
bandpass filters equipped on a multiband projector.
Figure 7: 5D light field display using multiband display and
barrier structure.
our system, we use the barrier including a lot of holes
is set in front of the multiband display, as shown in
Fig.7
In this system, The barrier structure, which has
many holes, is set in front of the multiband display, as
shown in the figure. In this case, only light rays emit-
ted from a particular pixel to a specific direction pass
through the hole, and the other rays are disturbed by
the barrier. As a result, the hole virtually emits differ-
ent light rays in each direction. Besides, the spectral
distribution of the rays is controlled since the multi-
band display emits the rays. Finally, we achieve a 5D
light field display that can emit different spectral light
rays to each direction from each pixel. By using the
constructed 5D light field display, we next consider
image encoding to the light field, which can be de-
coded by only a specific visual characteristic.
6 LIGHT FIELD SYNTHESIS FOR
IMAGE ENCRYPTION
6.1 Observation of 5D Light Field
For considering the image encoding method, we de-
fine a 5D light field observation model based on visual
characteristics.
First, we consider the spectral property of the ob-
servation. This observation can be written in linear
equations because the light spectral distribution of the
light rays in our system is a linear combination of the
narrow-band projectors. We consider the case when
the light field displays consist of N projectors, and
E
n
(λ) denotes the spectral distribution of each pro-
jector. In this case, the stimulus S
a
is computed by
the spectral sensitivity x
a
(λ) as follows:
S
a
=
N
∑
n=1
l
n
Z
E
n
(λ)x
a
(λ)dλ
=
N
∑
n=1
l
n
c
na
(12)
where c
na
=
R
E
n
(λ)x
a
(λ)dλ and l
n
is intensity of
the emitted light from projector n. As shown in the
Eq.(12), stimulation values S
a
by multiband display
observation are computed by linear equation using
sensitivity coefficients c
na
. We describe the set of sen-
sitivity coefficients by c in this paper.
Based on the above mentioned linear equation,
we consider the observation of a 5D light field. Let
L(x, y, u, v, n) denote intensity of a light ray from a
pixel (x, y) to a direction (u, v) by a projector n. When
the sensitivity of the observer is c
na
, stimulation val-
ues S
a
(x
r
, y
r
) at (x
r
, y
r
) are computed as follows:
S
a
(x
r
, y
r
) =
∑
x,y,u,v,n
c
na
T (x, y, u, v, x
r
, y
r
, W)L(x, y, u, v, n)
(13)
where T is a light transport matrix. As indicated in
this equation, the observation of the 5D light field
emitted by a 5D light field display is represented by
linear equations.
6.2 Image Encoding to 5D Light Field
by Multiplex Image Displaying
We last consider image encoding to 5D light-field for
encrypted image displaying. For this objective, en-
coded light-field should be satisfied with the follow-
ing conditions.
• The light-field can be observed as an original im-
age by a target person.
VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications
390
• The light-filed should be decoded to a meanless
image when the other audience observes the field.
To satisfy these two conditions, we consider two
kinds of image encoding method. In this section, we
describe image encoding based on the multiplex im-
age displaying.
In this way, a light-field which are decoded to dif-
ferent two images by a target person and by the other
person who has representative visual characteristics
are computed. We consider the case when the optical
aberration W
t
and sensitivity c
t
for a target person is
known, and representative aberration W
r
and sensi-
tivity c
r
is provided. Typically, W
r
represents char-
acteristics of the normal vision and c
r
represents the
CIE color space, and we assume that the characteris-
tics are known as similar as the target characteristics.
Let S
t
denote observation by the target based on
W
t
and c
t
, and S
r
denote a representative observation
based on W
r
and c
r
. In this case, we define evalu-
ation value E
m
for providing objective image S
0
t
and
S
0
r
for the target person and representative audience as
follows:
E
m
= kS
0
t
− S
t
k
2
+ kS
0
r
− S
r
k
2
(14)
where the light the light-field L composing the ob-
served result S
0
is limited depending on the property
of the projector as follows:
0 ≤ L ≤ L
max
(15)
where L
max
is the maximum intensity of the display.
By minimizing the value E
m
in this range, a light-field
which provides images S
0
t
and S
0
r
to the target and au-
dience is computed. Thus, image encryption, which
can be decoded by a target person, is achieved.
In this method, we can easily estimate the light-
field by just solving linear equations. However, as
mentioned in the introduction, visual characteristics
are different in person by person. Therefore, it is
not easy to define representative characteristics for
this encoding. If a person whose characteristics are
far from the defined representative characteristics, ob-
serves the light field, we cannot predict what image is
observed by this person.
6.3 Image Encoding based on
Difference Maximization
We next consider the image encoding method, which
uses only the target characteristics. In this method,
we focus on the change of observed image when the
visual characteristics change. As described in the pre-
vious section, observed image change depends on the
characteristics of the observer, and then, the observed
results change when the characteristics changes. If
Figure 8: 5D Light field display.
we want to hide the original image by changes in the
characteristics, the observed image should be changed
drastically by the small change of those characteris-
tics. That is, the derivative of observed image wrt
the visual characteristics should be maximized for our
image encoding. Therefore, we define an evaluation
value E
m
for image encoding as follows:
E
m
= kS
0
t
− S
t
k
2
− k
dS
t
dW
t
k
2
− k
dS
t
dc
t
k
2
(16)
where c
t
is a set of the coefficients for spectral sensi-
tivity. In this minimization, the range of the light-field
is also limited by Eq.(15). By minimizing the E
m
in
this range, the light-field for our image encoding can
be estimated. When the target person observes the
light-field, the light-field is decoded to the objective
image S
0
t
. In contrast, the result is far from the S
0
t
when
the other audience decodes the light-field.
7 EXPERIMENTAL RESULTS
7.1 Environment
In this section, we show several experimental results
in our proposed method. We first describe an ex-
perimental environment. In this experiment, we con-
structed a 5D light field display using four projectors,
translucent screen, and an optical barrier, as shown in
Fig.8. Each projector equipped a narrow band-pass
filter, and thus, each projector project narrow band
light. Figure 9 shows spectral distribution of each pro-
jector. The projector projected images from the back-
side of the screen, as shown in Fig.7 and the screen
scattered the light in any directions. A transparent
LCD was utilized for the barrier structure, and the dis-
play showed many holes in a black screen. The barrier
set in front of the screen, and it blocked unnecessary
light rays.
As an observer, the camera is set in front of the
display. To control the optical characteristics of the
lens with reproducibility, we observed the light field
by the camera. For obtaining the light field by a single
Encrypted Image Display based on Individual Visual Characteristics
391
Figure 9: Spectral distribution of each projectors.
Figure 10: Camera on a moving stage.
camera, the camera was set on the moving stage, as
shown in Fig.10, and it observes five images at the
center, left, right top and bottom positions.
From the image, two observers who have differ-
ent visual characteristics are simulated. Observed im-
ages by each observer were synthesized by light field
rendering technique(Gortler et al., 1986) according to
their optical characteristics. They have different fo-
cal lengths, and the image synthesis reproduces it. A
color temperature conversion filter represents the dif-
ference in spectral sensitivity. In observation by a tar-
get person (i), the standard image was obtained with-
out the filter. The filter was equipped in a case when
the other audience (ii) observed the display.
7.2 Results
Let us show the experimental results by our proposed
method. Figure 11 shows observation results by us-
ing multiplex image displaying described in 6.2. In
this technique, objective images (a) and (b) are uti-
lized for a target (i) and the other audience (ii). They
observed images (c) and (d), respectively. As shown
in this figure, (i) and (ii) observed different images
that are similar to their objective images. The results
indicate that our proposed method can present differ-
ent images based on their visual characteristics, that
is, image encryption based on the characteristics can
be achieved.
Figure12 shows image observation results when
difference maximization described in 6.3 is utilized.
In this figure, (a) shows an objective image, (b) shows
an observed result by (i), and (c) shows an observed
result by (ii). In this figure, (a) and (b) are similar to
each other, and it indicates that a 5D light field dis-
play presents the appropriate light field. However, (c)
(a) (b)
objective images
(c) (d)
observed images
Figure 11: Image encryption based on multiplex image dis-
playing: (a) and (b) shows objective images for a target and
the other person, and (c) and (d) shows observed results.
(a) (b) (c)
Figure 12: Image encrypting by difference maximization:
(a) shows objective image, (b) shows observed result by a
target and (c) shows observed result by the other person.
was not different from (b), and the fact indicates that
the image encryption is not achieved correctly by dif-
ference maximization in this experiment.
We consider that the reason for the results is the
resolution of the light field display. In order to achieve
image encryption based on difference maximization,
it is necessary to project different light for each fine
direction. However, resolution for the direction com-
ponent is rough in our light field display, and then we
did not maximize the difference in optical character-
istics. In the next section, we show the result using
hight resolution light field display in the synthesized
environment, and the results will indicate the effec-
tiveness of the difference maximization.
7.3 Evaluation in Synthesized
Environment
We next show evaluation results in a synthesized en-
vironment for more detailed analysis. In this experi-
ment, the resolution of the light field display was 100
x 100 x 5 x 5, and the display controls the spectral
distribution of the light by combining four narrow-
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392
(a) (b) (c) (d)
Figure 13: Observation difference by different Zernike co-
efficients: (a) shows displayed image and (b), (c) and (d)
indicates observed result by (i), (ii) and (iii) respectively.
band light. An observed camera set in front of the
display observes the light field display. There are
three observers, (i) a target, (ii) 2nd target who has
representative characteristics and (iii) the other audi-
ence whose characteristics are different from both (i)
and (ii), and they have different visual characteristics
In their optical characteristics, only higher-order four
coefficients for Zernike bases are different because
low-order characteristics such as focal length will be
corrected by using glasses in general. Figure13 shows
the observation results of a standard display by their
characteristics. As shown in this image, observed im-
ages, although the observed images are blurred, the
results are similar to each other. These images show
higher-order coefficients do not have a significant in-
fluence in standard display observation.
We first evaluate the method based on the mul-
tiplex image displaying. Figure 14 shows objective
images and observed results. In this figure, (a) ob-
jective images for a target (i), and (b) image for 2nd
target (ii) were utilized for computing the light field.
For comparison, results based on only spectral sensi-
tivity and results based on only optical characteristics
are shown simultaneously. Three persons observe all
light fields, and the results are shown in each column.
As shown in the result (c), (d), and (f), (g), meth-
ods utilizing the light field provided different images
to the target persons. Besides, the other person ob-
served an entirely different image from both objective
images. The results indicate that image encoding us-
ing light field is very sensitive to changes in visual
characteristics. Therefore, the other audience cannot
observe the original image even if their visual char-
acteristics are different from the representative ones.
The fact indicates that our proposed method can hide
original information when the characteristics of the
audience are different from the target.
Figures (i), (j), and (k) show results based on spec-
tral sensitivities. In these results, changes in observed
images are not so significant. The reason for the re-
sults is the low degree of freedom in controlling spec-
tral distribution. In this experiment, the distribution
was controlled by only four combinations of the light.
Therefore, they are not enough to change the observed
image according to characteristics. The result will
(a)
(b)
objective images
(c) (d) (e)
results based on our proposed method
(f)
(g)
(h)
results based on optical characteristics
(i)
(j)
(k)
results based on spectral sensitivities
Figure 14: Image encoding results based on the multiplex
image displaying: (a), (b) show objective images for a target
and the other, (c), (d) (e) show observed result based on
the proposed method by a target, 2nd target and the other.
Images (f), (g) (h) are based on only optical characteristics,
and (i), (j), (k) shows results on only spectral sensitivity.
become better when more detail controlling can be
achieved in spectral distribution control.
We next show results based on difference maxi-
mization. In this experiment, only a single objective
image was used for a target person (i) to synthesis the
light field. The light field was observed by three per-
sons, the same as the previous experiment.
Figure15 shows observed results based on differ-
ent characteristics. In this figure, all methods provide
appropriate results for the target person (i) as shown
in (c), (f) and (i). However, (ii) and (iii) can read the
original information when only spectral sensitivities
are utilized as shown in (j) and (k). The fact indicates
that the difference of the spectral sensitivities is not
enough for hiding the original information. In con-
Encrypted Image Display based on Individual Visual Characteristics
393
(a)
objective image
(c) (d)
(e)
results based on our proposed method
(f)
(g)
(h)
results based on optical characteristics
(i)
(j)
(k)
results based on spectral sensitivities
Figure 15: Image encoding results based on the difference
maximization: (a) shows objective image for a target, (c),
(d) (e) show observed result based on the proposed method
by a target, representative and the other. Images (f), (g)
(h) are based on only optical characteristics, and (i), (j), (k)
shows results on only spectral sensitivity.
trast, the proposed method and the difference in the
optical characteristics disturb the reading of the origi-
nal information by (ii) and (iii). Notably, the proposed
method hides the information both (ii) and (iii) suffi-
ciently.
These results indicate that our proposed image en-
coding method can hide original information from the
other observers. Notably, the multiplex image dis-
playing method is much useful to protect the original
information.
8 CONCLUSION
In this paper, we propose an image encoding method
to the light field for image encryption. In this method,
we focus on the difference of the visual characteris-
tics in the human visual system and achieve the image
encryption based on the difference. Especially, we fo-
cus on optical characteristics on the lens and spectral
sensitivities of the human visual system. For utiliz-
ing the multiple characteristics effectively, we built a
5D light field display for image encryption. We pro-
pose an image encoding method to the 5D light field
based on the multiplex image displaying and differ-
ence maximization. This image encryption method is
more effective since the method requires only individ-
ual visual characteristics to decrypt the image.
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