Optical image processing using an optoelectronic feedback system with electronic distortion correction

Abstract

Spontaneous pattern formation in an optoelectronic system with an optical diffractive feedback loop exhibits a contrast enhancement effect, a spatial filtering effect, and filling-up of vacant space while maintaining surrounding structures. These effects allow image processing with defect tolerance. Aberrations and slight misalignments that inevitably exist in optical systems distort the spatial structures of the formed patterns. Distortion also increases due to a small aspect ratio difference between a display device and an image sensor. We experimentally demonstrate that the spatial distortion of the optoelectronic feedback system is reduced by electronic distortion correction and the initial structure of a seed optical pattern is preserved for a long time. We also demonstrate image processing of a fingerprint pattern based on seeded spontaneous optical pattern formation with electronic distortion correction.

Full text

Optical image processing using an optoelectronic
feedback system with electronic distortion
correction
Yoshio Hayasaki, Ei-ichiro Hikosaka, Hirotsugu Yamamoto, Nobuo Nishida
Department of Optical Science and Technology, Faculty of Engineering, The University of Tokushima,
2-1 Minamijosanjima-cho, Tokushima 770-8506, Japan
hayasaki@opt.tokushima-u.ac.jp
Abstract: Spontaneous pattern formation in an optoelectronic system with an
optical diffractive feedback loop exhibits a contrast enhancement effect, a spatial
filtering effect, and filling-up of vacant space while maintaining surrounding
structures. These effects allow image processing with defect tolerance.
Aberrations and slight misalignments that inevitably exist in optical systems
distort the spatial structures of the formed patterns. Distortion also increases due
to a small aspect ratio difference between a display device and an image sensor.
We experimentally demonstrate that the spatial distortion of the optoelectronic
feedback system is reduced by electronic distortion correction and the initial
structure of a seed optical pattern is preserved for a long time. We also
demonstrate image processing of a fingerprint pattern based on seeded
spontaneous optical pattern formation with electronic distortion correction.
©2005 Optical Society of America
OCIS codes: 190.4420 Nonlinear optics, transverse effects in, 200.3050 Information processing
References and Links
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1. Introduction
Spontaneous optical pattern formation in nonlinear systems with either an optical or optoelectronic
diffractive feedback loop has recently become an important area of research in nonlinear optics [1-
11]. An optical feedback system (OFS) is typically composed of an optically addressable spatial light
modulator (OASLM) in a two-dimensional diffractive feedback loop. OASLMs exhibit a large
space-bandwidth product, low light intensity operation, and highly tunable nonlinearity, which make
them attractive for studying novel phenomena and applications [12-18]. An investigation of the
temporal evolution of spontaneously formed optical patterns from an initial seed pattern is also
interesting in the context of optical parallel image processing, but only a few studies have been
reported. Recently, the formation of such patterns from seed optical patterns, which are continuously
supplied by an external source, has been investigated in some nonlinear optical systems, and a spatial
frequency filtering effect, spatial locking, and spatial synchronization were observed [19, 20].
Optoelectronic feedback systems (OEFSs), composed of an image sensor and display device, for
example, also spontaneously form interesting patterns, typically, fringes (rolls) and hexagons [21-23],
like OFSs. The advantages of OEFSs include the ease of supplying an initial pattern, the wide
controllability of the nonlinearity, fewer constraints on the optical system, operation under low light
levels due to the high sensitivity of the image sensor, the suitability of recently developed electronic
hardware resources, and the availability of image processing software resources. OEFSs are typically
composed of a liquid crystal display (LCD) and a charge coupled device (CCD) image sensor, which
are readily available and fairly low cost.
We have demonstrated that the temporal evolution of the optical patterns in OEFS exhibits a
contrast enhancement effect, a spatial filtering effect, and filling-up of vacant space while
maintaining surrounding structures [23]. The existence of these effects was confirmed under the
condition that a seed pattern was provided for just the first frame; that is, its operation was not
continuously forced by a pattern. We have also demonstrated that these effects can perform optical
image processing with defect tolerance, in particular, optical image processing for fingerprint patterns
[23]. Fingerprint patterns are being widely applied for identification and security purposes. The
verification of fingerprint patterns generally requires time-consuming preprocessing, including
contrast adjustment and noise elimination, before extracting feature points (minutia), such as ridge
endings, ridge divergences, bifurcations, dots, islands, and enclosures. However, the outcome of the
feature extraction is strongly influenced by the fingerprint conditions, such as the existence of dry
skin, sweat, and damage or injuries. Nevertheless, the OEFS in the above-mentioned study could
transform the seed fingerprint pattern to the pattern without defects while maintaining surrounding
structures.
In a practical OEFS, aberrations of the optical system and slight misalignments are inevitable.
They distort the isotropic spontaneous pattern formation. Furthermore, the distortion of the patterns
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formed increases as a result of a small difference in aspect ratio between the LCD and the CCD
image sensor. Consequently, the resulting distortions prevent preservation of features in the pattern
evolution process, and reduce the performance of the OEFS for the optical image processing.
In this paper, we experimentally demonstrate that such distortions in optical pattern evolutions
from an initial seed optical pattern, including fingerprint patterns, can be reduced with electronic
distortion correction. In Section 2, the experimental setup of the OEFS is described. In Section 3, the
principle of the electronic distortion correction for stabilization of patterns formed in the OEFS, that
is, for long-term preservation of initial structures of the seed pattern, is described. In Section 4, it is
experimentally demonstrated that the initial structures of the seed pattern is preserved with the
electronic distortion correction, and the optical pattern evolutions with the long-term preservation
property of the initial structures performs an optical image processing with defect tolerance for a
fingerprint pattern. The defect tolerance is originated from filling-up effect of vacant space while
maintaining surrounding structures. This is the most important characteristic in the use of the optical
pattern evolutions in the OEFS for optical image processing. In Section 5, we conclude our study.
2. Optoelectronic feedback system
Figure 1 shows a schematic representation of the OEFS used in our experiments. Using a simple
exponential relaxation response of an internal state u(x, y, t) of the LCD at a position (x, y) and time t
to a control signal p(x, y, t), the space-time evolution of the internal state is
τ
∂
u(x,y,t)
∂
t
= - u(x, y, t) + l2
∇⊥
2u(x, y, t) + p(x, y, t), (1)
where
τ
is the time constant of the LCD and
∇⊥
2 is the Laplacian in the x and y directions that
describes transverse diffusion with a diffusion length l [21]. The LCD performs intensity modulation
with a modulation characteristic F on the internal state u, and the output light wave A and its intensity
I is
I (x, y, t) = |A(x, y, t)|2 = F[u(x, y, t)]. (2)
The intensity modulation characteristic F is approximated as F(u) = I0[1 − cos(u)]/2, where I0 is the
incident light intensity. The control signal p(x, y, t) for a diffractive feedback light intensity Id (x, y, t)
on the CCD image sensor is described as
p(x, y, t) = G[Id(x, y, Z, t)], (3)
where G includes the input/output characteristic of the CCD image sensor, the electric conversion
performed by a computer, which in this experiment is an inversion characteristic, and the conversion
from an electric signal given to the LCD to the internal state u. The characteristic between the light
intensities I1 and I2 as described by I2 = G[F(I1)] is a sigmoid function. The characteristic is presented
in Ref. 22, when the CCD image sensor and the LCD are directly connected without the electric
conversion by a computer. The feedback light is formulated by considering free-space propagation
over a length Z. By use of the stationary, scalar, paraxial wave equation, the amplitude of the
diffracted feedback wave Ad(x, y, Z, t) satisfies
∇⊥
2Ad(x, y, Z, t) - 2ik
∂
Ad
∂
z
= 0, (4)
where k = 2π/
λ
is the wave number and Ad(x, y, 0, t) = A(x, y, t). The model equations from (1) to (4)
are equivalent to those for an OFS [10], because the time difference, given by a scanning mechanism
of the LCD and the CCD image sensor, in the area interacting laterally with diffractive feedback is
smaller than the response time of the LCD, and it is regard as the state of the LCD changes about the
same time in the local area.
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Fig. 1. Schematic representation of a model of an OEFS. CCD: charge-coupled device image sensor,
LCD: liquid crystal display.
As shown in Fig. 2, the OEFS is mainly composed of an LCD and a CCD image sensor, which
respectively perform conversion from a serial electrical signal to a parallel optical signal and vice
versa. The components from the CCD image sensor to the LCD play a similar role to an OASLM,
except for their spatially discrete pixels and scanning mechanism. Spontaneous pattern formation
occurs when the intensity conversion characteristic from the CCD image sensor to the LCD is an
inversion characteristic [22]. In our previous study, the inversion characteristic was achieved by the
parallel Nicol arrangement of a polarizer and analyzer; this is different from conventional LCDs,
where the crossed Nicol arrangement is used. The input/output characteristic that was determined
experimentally is described in Ref. 22. In the present OEFS, the crossed Nicol arrangement, which
gives the best performance of the LCD, is used, and the inversion characteristic is calculated in a
personal computer. The computational load is very small compared with the calculation required for
electronic distortion correction described later. The LCD is controlled by a frame grabber with a
resolution of 640 × 480 pixels. The frame rate of the OEFS is less than or approximately equal to 30
Hz. The frame rate cannot be determined exactly, because the CCD image sensor and the LCD are
operating asynchronously in the present OEFS.
The light from a He-Ne laser with wavelength λ=633 nm is spatially modulated by the LCD, and
the modulated light is fed to the CCD image sensor through an optical system. The optical system
performs a ~1/4 reduction of the image size on the LCD to match the image size on the CCD image
sensor. The optical system can perform the linear image transformations of rotation, diffraction, and
spatial frequency filtering for controlling the transverse interactions, in addition to expansion and
reduction of the patterns. In the system, a low-pass spatial frequency filter (SFF) eliminates diffracted
light originating from the pixel structure of the LCD. The CCD image sensor and a lens, which are
enclosed within the dashed rectangle in Fig. 2, are axially moved as a single unit to adjust the free
propagation length Z. Thus, Z is the distance from the image plane of the LCD to the plane P, which
is imaged onto the plane of the CCD image sensor.
In practice, the OEFS has spatial distortions, including aberrations of the optical system, slight
misalignments, and a small difference in aspect ratio between the LCD and CCD image sensor;
therefore, the feedback intensity distribution Id(x, y, Z, t) is distorted. A personal computer and frame-
grabber are used not only to give an initial seed pattern, to capture the image sequences, and to
analyze the temporal evolution of the patterns, but also to calculate the correction of these distortions.
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Fig. 2. Experimental setup. See text the description.
3. Electronic distortion correction
In order to reduce the distortion, electronic distortion correction is introduced in the OEFS. In this
electronic distortion correction, the transformation from the LCD to the CCD image sensor is
approximated with geometrical optics, and the image detected with the CCD image sensor is returned
to the LCD with an inverse geometrical transformation. Let the coordinates on the plane of the LCD
and the CCD image sensor be (x, y) and (u, v), respectively. The geometrical transformation from the
LCD plane to the CCD image sensor plane involves a lateral shift between the devices, lateral
magnifications, including the aspect ratio mismatch between the devices, device rotation, and
nonlinear distortions. The output point (x1, y1) is transformed by lateral deviation and lateral
magnification from the input point (x, y) as:
x1 = A0 + A1x (5a)
y1 = B0 + B1y. (5b)
The point (x1, y1) is transformed to the point (x2, y2) by a rotation of the CCD image sensor by an
angle
Θ
, and is denoted as:
x2 = x1cos
Θ
+ y1sin
Θ
,
y2 = -x1sin
Θ
+ y1cos
Θ
. (6)
When (x2, y2) is converted to polar coordinates (r2,
θ
2), the nonlinear distortion is approximated with a
3rd order polynomial as:
r = r2(1 + Cr22), (7)
Where C is a coefficient, and r2 = (x22 + y22)1/2. Then, (r2,
θ
2) is converted back to the rectangular
coordinates (u, v) on the CCD image sensor by:
u = r2cos
θ
2,
v = r2sin
θ
2, (8)
where
θ
2 = arctan(y2/x2). Therefore, the transformation from (x, y) to (u, v) that represents the
geometry of the OEFS is described by Eqs. (5-8).
The six parameters A0, A1, B0, B1, C, and
Θ
are set based on the following calculation. At first, a
27×19 array of N small bright points is displayed on the LCD as sampling points at the same time,
and the image is detected by the CCD image sensor through the optical system. Next, the coordinates
of n-th detected point, [u0(n), v0(n)] (n = 1, 2, ..., N), are obtained by the threshold operation of the
image and the centroid detection of each bright area. From the relation between a point at (x, y) on the
LCD and the corresponding point at (u, v) on the CCD image sensor, the coefficients in Eqs. (5-8) are
determined by the downhill simplex method [24] for the estimation function
[u−u0(n)]2
n
=
1
N
∑
+[v−v0(n)]2. Finally, the coordinates (u, v) on the CCD image sensor corresponding to
all pixels on the LCD are calculated. The coefficients calculated with the method described above
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were A0 =0.977, A1 =1.00, B0 =-0.267, B1 = -0.537, C = 0.000176, and
Θ
=0.00125. In this case, since
the optical system was set such that the deviation at its center was small, the distortion became bigger
at the periphery of the operation region. The system has not only linear distortions, such as a lateral
displacement, magnification mismatch, rotation, and aspect ratio difference, but also the nonlinear
distortion caused by aberrations of the optical system.
In general, the coordinates (u, v) calculated from a point (x, y) by Eqs. (5-8) do not match the
pixel position of the CCD image sensor. Therefore, I(u, v) is calculated using linear interpolation of
the four pixel values on the CCD image sensor, I(i, j), I(i, j+1), I (i+1, j), I (i+1, j+1), where i and j are
integer, that are neared to (u, v) as follows:
I(u, v) = (1-q){(1-p)I(i, j) + pI(i+1, j)} + q{(1-p)I(i, j+1) + pI(i+1, j+1)}, (9)
where p = u/W - i and q = v/W - j, and W is the defined size of a pixel; in our experiments, W = 1.
4. Experimental results
Fringes formed in the OEFS have a main spatial wave number Kz = 2
π
(λ|Z|)-0.5 on the plane P, for the
free-propagation length Z [8, 16, 17]. Therefore, when circular fringes with the wave number Kz are
initially supplied, the circular fringes should be maintained for a long time. In a practical OEFS,
however, the initially-given circular fringes with Kz became distorted gradually, as shown in Fig. 3,
because the OEFS has aberrations, slight misalignments, and an aspect ratio difference, as mentioned
above. Figure 3(a) shows the temporal evolution of patterns whose center coincides with the optical
axis of the system (on-axis region). The size of the images is 100 × 100 pixels on the LCD. Figure
3(b) shows patterns whose center is shifted from the optical axis (off-axis region) by 100 pixels in the
x-axis and 100 pixels in the y-axis on the LCD. These patterns were observed at 1/30 s, 5/30 s, 10/30
s, 15/30 s, and 20/30 s, respectively. The distortion of the formed patterns becomes larger at the
periphery. The patterns in Figs. 3(a) and 3(b) were obtained without electronic distortion correction.
Next, an experiment using the same circular fringes as the initial input was performed in the
OEFS with electronic distortion correction. As shown in Fig. 4, the distortion was reduced
drastically; the difference between the patterns formed in the on-axis and off-axis regions was very
small. Furthermore, the initial structure of the formed patterns was well-maintained in both regions.
Figure 5 shows the changes of the sum of the squared difference (SSD) between each temporally
evolved pattern I1(i, j, t) and the pattern at the 1st frame. The SSD for measuring the difference
between a temporally evolving pattern I1(i, j, t) with a mean
μ
1(t) and a variance
σ
1(t)2 and a
temporally evolving pattern I2(i, j, t) with a mean
μ
2(t) and a variance
σ
2(t)2 is defined as
D(t) =
∑
i
∑
j{[I1(i, j, t) -
μ
1(t) ] /
σ
1(t) - [I2(i, j, t) -
μ
2(t)] /
σ
2(t)}2/N, (10)
where N is the number of pixels. In this experiment, I2(i, j, t) = I1(i, j, 1),
μ
2(t) =
μ
1(1), and
σ
2(t) =
σ
1(1). For example, the SSD between two random patterns is about 0.015. In the on-axis region,
because the distortion of the system is small, the effect of the distortion correction is not noticeable.
On the other hand, in the off-axis region, the reduction of the SSD is remarkable and the distortion
correction worked very well. By introducing the electronic distortion correction, the OEFS became to
preserve the initial structures for long time in the pattern evolution process.
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Fig. 3. Temporal evolution of (a) patterns whose operating center coincides with the optical axis of the
system (on-axis region), and (b) patterns whose operating center is shifted from the optical axis (off-axis
region) by 100 pixels in the x-axis and 100 pixels in the y-axis on the LCD. These patterns are observed
at 1/30 s, 5/30 s, 10/30 s, 15/30 s, and 20/30 s from the left, respectively.
Fig. 4. Temporal evolutions of patterns (a) in the on-axis region, and (b) in the off-axis region in the
OEFS with electronic distortion correction.
Fig. 5. Temporal changes of the SSDs between each temporally evolving pattern and the pattern at the
1st frame (a) in the on-axis region and (b) in the off-axis region in the OEFS with electronic distortion
correction. The dotted and the solid lines indicate the SSDs of the pattern evolutions in the OEFS (a)
without and (b) with the electronic distortion correction, respectively.
We next apply the OEFS with electronic distortion correction to image processing of a fingerprint
pattern. Figures 6(a) and 6(b) show an original fingerprint pattern A with a natural defect and the
same fingerprint pattern A' with an artificial defect, respectively. The fingerprint pattern was obtained
by pushing it against a glass plate, illuminating it with a red light emitting diode, and detecting the
reflected light intensity distribution with a CCD image sensor. When the fingerprint patterns without
and with the artificial defect, A and A', were initially supplied to the OEFS with electronic distortion
correction, the respective temporal evolutions at 1/30 s, 7/30 s, and 22/30 s are shown in Figs. 7(a) to
7(c) and Figs. 7(d) to 7(f), respectively. These patterns were in the off-axis region. Both temporal
evolutions proceed while increasing the contrast and removing both the natural and the artificial
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defects, when the system is configured so that the principal wave number of the fingerprint pattern
matches Kz, because the optical pattern in the vacant space (defect) is formed while maintaining and
connecting surrounding structures with Kz, when the shorter side of the defect has the length shorter
than or approximately equal to the fringe spacing (2
π
/Kz), as the artificial defect given to the
fingerprint pattern shown in Fig. 6(b). The bifurcation, which is a typical minutia, which initially
existed in the fingerprint pattern, was well preserved, and its position was almost fixed. Furthermore,
the pattern transformed from the fingerprint pattern A' with an artificial defect, shown in Fig. 7(c),
almost agreed with the pattern transformed from the original fingerprint pattern according to the
temporal evolution of patterns, as shown in Fig. 7(f). Therefore, the OEFS performs image
conversion while exhibiting defect tolerance. The defect tolerance is originated from filling-up effect
of vacant space while maintaining surrounding structures in spontaneous optical pattern formation.
This characteristic is most important and novel in the use of the optical pattern evolutions in OEFS
for optical image processing.
Fig. 6. (a) An original fingerprint pattern A and (b) the same pattern A' with an artificial defect.
Fig. 7. Temporal evolutions at 1/30 s, 10/30 s, and 22/30 s when the fingerprint patterns without and
with the artificial defect are initially supplied to the OEFS with the electronic distortion correction.
Figure 8 shows the temporal changes of the SSDs between the temporal evolutions of the original
fingerprint pattern A and those of the fingerprint pattern A' with the defect. The bold dashed curve
and the bold solid curve indicate the SSDs when the OEFS was used without and with the electronic
distortion correction, respectively. The SSDs in the OEFS gradually decayed with oscillation.
Introducing the electronic distortion correction resulted in a smaller SSD. The effect of the correction
was particularly noticeable in the off-axis region. The oscillation is caused by a drop in the frame rate
of the OEFS [22] caused by the increased computational complexity required for the electronic
distortion correction. The temporal pattern evolutions starting from the fingerprint pattern with the
defect gradually approached those from the original fingerprint pattern; that is, the OEFS operated
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properly regardless of the defect. The SSDs, however, started to increase from the 15th frame (0.5s).
The SSDs between two trials starting from same initial pattern in the OEFS without and with the
electronic distortion correction gradually increased, as indicated by the thin dashed curve and the thin
solid curve in Fig. 8. From the experiment, it is thought that slight distortions have not been removed
completely.
Fig. 8. The bold dashed curve and the bold solid curve indicate the temporal changes of the SSDs
between the temporal evolutions of the original fingerprint pattern and those of the fingerprint pattern
with the artificial defect, when the OEFS was used without and with the electronic distortion correction,
respectively. The thin dashed curve and the thin solid curve indicate the temporal changes of the SSDs
between two trials starting from same initial pattern in the OEFS without and with the electronic
distortion correction, respectively.
5. Conclusions
We have experimentally demonstrated spontaneous optical pattern formation from an initial seed
pattern in an optoelectronic feedback system composed of an LCD and a CCD image sensor. The
optoelectronic feedback system, with electronic distortion correction, produces patterns with reduced
distortion, caused by inevitable aberrations and slight misalignments that exist an optoelectronic
system, and a small difference in aspect ratio between the display (LCD) and the camera (CCD).
Therefore, the initial structure of the seed pattern can be maintained for a long time with electronic
distortion correction. A contrast enhancement effect, a spatial filtering effect, and filling-up of vacant
space while maintaining surrounding structures allow image processing with defect tolerance. In
particular, the filling-up of vacant space in spontaneous optical pattern formation is a unique effect
that is unattainable using linear optical processing such as a spatial filtering. Preprocessing, including
contrast adjustment and noise elimination, which is generally carried out before feature extraction
and verification, are important in the image-processing field. The spontaneous optical pattern
formation system we propose performs such processing automatically. Therefore, we expect that
spontaneous optical pattern formation created with a nonlinear system including an optical diffractive
feedback loop will offer various advantages in the image-processing field.
Acknowledgments
This research was partially supported by the Ministry of Education, Culture, Sports, Science and
Technology of Japan, Grant-in-Aid for Scientific Research on Priority Area: molecular
synchronization for design of new materials systems and Grant-in-Aid for Scientific Research (B),
and the Satellite Venture Business Laboratory of The University of Tokushima.
(C) 2005 OSA 13 June 2005 / Vol. 13, No. 12 / OPTICS EXPRESS 4665
#7144 - $15.00 USD Received 13 April 2005; revised 4 June 2005; accepted 4 June 2005