Rank-order and morphological enhancement of

Rank-order and morphological enhancement of
Rank-order and morphological enhancement
of image details with an optoelectronic processor
Tomasz Szoplik, Javier Garcia, and Carlos Ferreira
In all-optical processors, enhancement of image details is the result of high-pass filtering. We describe
an optoelectronic processor in which detail enhancement results from the digitally calculated difference
between an original input image and its low-pass filtered version. The low-pass filtering is realized
through the rank-order median and the morphological opening and closing operations calculated by use of
the optical convolver. It is shown that the normalized difference between the morphological white and
black top hats enhances bright and dark image details analogously to the rank-order unsharp masking.
Key words: Optoelectronic image processing, optoelectronic image enhancement, rank-order filters,
morphological filters.
1.
Introduction
Two important methods of nonlinear image processing are rank-order1–4 and morphological5–7 filtering.
Though different from the point of view of mathematical approach, they may lead to similar image modifications. It was proven that rank-order filters are
equivalent to those morphological filters that commute with thresholding.8,9 This condition is met for
the cases of set- and function-processing 1i.e., binary
and gray-scale image-processing2 morphological filters that involve a binary structuring element 1that
is, a flat kernel of local convolution2. Thus rankorder and morphological filtering can be performed in
linear optical systems complemented with electronics, which adds nonlinear thresholding to the optical
convolution. In both methods, processing of a grayscale image slice by slice is based on the threshold
decomposition concept,1 which led to the definition of
the stacking property2 of Boolean functions 1operators2. Nonlinear image processing based on the
thresholded local convolution approach permits operations on image details of the size smaller than or
equal to that of the convolution kernel. The processing results in modifications of local histograms calcuWhen this research was performed, the authors were with the
Departamento Interuniversitario de Optica, Universitat de Valencia, Burjassot 46100, Spain. T. Szoplik’s permanent address is
the Instytut Geofizyki, Universytet Warszawski, Pasteura 7,
Warszawa 02-093, Poland.
Received 7 December 1993; revised manuscript received 25 July
1994.
[email protected]@[email protected]
r 1995 Optical Society of America.
lated for neighborhoods contained within the kernel
windows. The purpose of local histogram modifications can be various, examples of which are noise
removal, image detail enhancement, skeletonization,
and segmentation. In both rank-order and morphological processing the mechanism of detail enhancement is quite similar. The details are extracted as
the difference 1residue2 between the original image
and its nonlinearly processed versions, which are
low-pass filtered. In rank-order processing the usual
low-pass filter is the median one, which neglects
extreme image pixel values contained within the local
convolution window. In morphological processing
the opening and closing transformations have selective low-pass filter properties. In binary images the
opening filters out small sets and small convex details
of objects. Thus the gray-scale images are smoothed
by the opening owing to removal of convex details
that on each grade of gray are thinner than the
structuring element. The morphological closing operation is dual to the opening. Therefore in binary
images the closing fills in small dark holes within
objects and connects closely disjointed parts of objects
into one. The gray-scale images are smoothed by the
closing owing to removal of concave details that are
smaller than the kernel. In terms of intensity the
opening removes bright details of an image, while the
closing removes dark details. Low-pass filtering is
easily performed in an optical system because of its
limited modulation transfer function. Thus the efficiency of optical systems in low-pass filtering results
in good performance of hybrid high-pass filtering
processors. In both methods the size and the shape
10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS
267
of preserved details depend on the neighborhoods
within which the operations are realized.
There are several optoelectronic implementations
of morphological and rank-order nonlinear processors.10–19 In all of them, because of optical convolution, the digital computations are reduced to calculating the maximum, minimum, and other rank-order
values and depend less on the neighborhood shape
and size. In the first demonstration of the optoelectronic rank-order processor a binary spatial light
modulator 1SLM2 was employed to introduce simultaneously into an optical convolver all of the binary
slices of an input image.10 A computer-generated
hologram played a double role of an image beam
deflector for slices and a structuring element. In this
experiment a gray-scale image of 48 3 48 pixels with
16 gray levels was processed in real time. In another
hybrid morphological processor the real-time programmable processing of limited-size images was presented.12 A binary input image and a structuring
element were introduced into an optical system by
means of two SLM’s. The use of a lenslet array
illuminator yielded a convolution due to angular
projection. The convolution with angular projection
was also employed in the morphological processor
with a laser beam scanner.14 In the morphological
processor based on a coherent 4-f type correlator the
impulse response of the Fourier-plane holographic
filter played the role of a structuring element.15,16
In other realizations of rank-order and morphological
processors, noncoherent convolvers by use of either a
plane of misfocus or shadow casting were applied.11,17–19 The slices of the gray-scale input images were introduced into the convolvers by means of
photographic transparencies, a TV monitor, or an
SLM. In all of the above-mentioned systems, looping
and sequential regime of work were necessary as a
consequence of the sequential structure of rank-order
and morphological filters on the one hand and the
threshold decomposition concept and stacking property on the other.
Recently Tasto and Rhodes showed that both rankorder and morphological filtering of threshold decomposed images realized in optoelectronic processors
exhibits a high degree of noise immunity and permits
high-accuracy processing.20 Their assessment as well
as the progress in real-time processing techniques
encourages continuation of research on hybrid optoelectronic systems for both rank-order and morphological processing.
Our aim here is to demonstrate the feasibility and
quality of optoelectronic experimental results of three
algorithms for enhancement of image details: rankorder unsharp masking and morphological black and
white top hats. To establish a link between unsharp
masking and morphological top hats, we define the
normalized difference between white and black top
hats. The difference algorithm enhances both bright
and dark details. The experiment is done on a
realistic-size image with rich texture.
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APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995
2. Rank-Order and Morphological Algorithms for
Enhancement of Image Details
Rank-order and morphological methods of image improvement can be divided into two broad groups of
algorithms, which aim at either image smoothing or
enhancement of image details.3–7,18,21 Image-smoothing algorithms are used for removal of noise that has
one of several possible properties or that is a mixture
of different types of noise. At the same time, information about fine image details is preserved. The noisesuppression algorithms are used for preprocessing of
images that afterward are subjects of enhancement
operations such as, for instance, histogram modifications or edge extraction. A sequence of proper operations may lead to a considerable image improvement
appreciated by a human observer. Application of
smoothing and enhancing algorithms may also precede pattern-recognition tasks.
A. Rank-Order Algorithms for Enhancement of
Image Details
Let 5V1k26 be a discrete input image with Q gray-scale
levels of intensity quantization: k 5 1k1, k22 is a
vector coordinate of an input image element; k1 5 1,
. . . , N1 and k2 5 1, . . . , N2; N1 3 N2 5 N is the image
matrix size. According to the threshold decomposition concept,1 the kth element V1k2 of an input image
is represented as a sum of kth elements of all binary
slices as
Q21
V1k2 5
o X 1k2,
112
q
q51
where Xq1k2 is the kth element of a binary slice of an
input image obtained through decomposition with a
threshold q; that is,
Xq1k2 5
1
50
if V1k2 $ q
otherwise
.
For each slice 5Xq1k26, where braces denote the whole
set of q-level elements, local operations are performed
within a spatial neighborhood S of arbitrary size and
shape that is similar for each kth input-image element.
The spatial neighborhood S is cast by a scanning
binary 1flat2 structuring element that characterizes
the local convolution. The local-convolution operation can be very efficiently performed in a computer
unless the structuring elements do not become too
large. Alternatively, local convolutions can be accomplished in parallel in optical correlators. We believe
that fully programmable correlators for processing of
large images by means of large and arbitrarily shaped
structuring elements should become feasible soon.
The possibility of parallel optical calculation of local
convolutions was the basis of a recently proposed
optical–digital method of local histogram calculation.17
This method results from a theorem proved in Ref. 17,
which says that the local q-level histogram of an
arbitrary neighborhood in an input image is equal to
the pointwise difference of the two convolution pat-
terns obtained by convolving the slices at the levels
q 1 1 and q with a binary mask, thereby defining the
neighborhood. We note that, for each pixel of the
input image, the pixel value in the convolution pattern of the q-level binary slice and the kernel is equal
to the number of pixels in the neighborhood that are
on the q-level and higher values.
Detail-enhancing algorithms are designed to increase local nonhomogeneities of intensity distribution of an input image. An increase of local contrast
can be accomplished in a variety of ways. A simple
and linear method is to enhance these pixels that
differ from average pixel values calculated within its
spatial neighborhoods S:
Y1k2 5 mean5S3V1k246 1 GAV1k2 2 mean5S3V1k246B,
122
where the output pixel value Y1k2 is given by the sum
of a bias term equal to the average pixel value
calculated within neighborhood S of the input pixel
V1k2 and another term that is a difference between the
input pixel value and the before-mentioned average
enhanced by a gain coefficient G. The above algorithm becomes nonlinear when the mean operation is
replaced with the med operation; that is, the median
value of the neighborhood S is considered as a reference.
The most general nonlinear rank-order unsharp
masking algorithm 1UM2 is defined as follows22:
UM3V1k24 5 A 1 GAV1k2 2 med5S3V1k246B,
132
where S3V1k24 is an arbitrary neighborhood of the kth
element of an input image, A is the offset, G is the
gain coefficient of input-image details that differ from
the median value, and minus denotes a pointwise
subtraction. Taking advantage of the threshold decomposition concept, we process in sequence binary
slices 5Xq1k26 of the input image rather than the
gray-scale input image 5V1k26 itself. For each kth
input slice element a local convolution is made and
the median value med5S3Xq1k246 is calculated within
the kth-element neighborhood, S, defined by the
binary convolution kernel. The pointwise sum of all
processed slices gives the output gray-scale image.
Coefficients A and G are image dependent and are
calculated as follows. Pointwise subtracting the median from the original, we find minimum 12n2 and
maximum 1m2 difference pixel values as well as the
zero level 1as a fraction f of the full range 32n, m42.
Then the gain coefficient is calculated as G 5
[email protected] 1 n2 and the offset A 5 255f.
B. Morphological Algorithms for Enhancement of
Image Details
Morphological filters are composed of two basic operations: erosion and dilation. The erosion is defined
as the locus of the center of the structuring element S
when S is included in the binary slice X, such that in
the extreme case it follows the border tangentially
from inside. The dilation is defined as the locus of
the center of the structuring element when S intersects X, such that in the extreme case it follows the
border tangentially from outside. The simplest morphological filters are the opening and closing. The
morphological opening is defined as follows:
gS5Xq1k26 5 dSeS5Xq1k26,
142
where the erosion eS of the image slice 5Xq1k26 by the
structuring element S is followed by the dilation dS of
the looped eroded slice by the same kernel. The
opening filters out bright details of an input image
and is frequently used to remove salt elements of the
two-sided impulsive noise. The opening of a grayscale image gS5V1k26 is obtained by stacking of the
processed binary slices. The morphological white-tophat algorithm 1WTH2, which enhances bright details,
is defined as the difference 1residue2 between the input
image and its opening23:
WTH5V1k26 5 5V1k26 2 gS5V1k26,
152
where minus denotes pointwise subtraction, which
results in a positive representation of high-intensity
details.
In the black-top-hat algorithm 1BTH2 the morphological closing is employed. This operation, dual to
opening, is defined as
wS5X1k26 5 eSdS5X1k26,
162
where dilation and erosion are made in reverse order
to that of the opening. The closing filters out dark
details of an input image and is frequently used to
remove pepper elements of the two-sided impulsive
noise. Here also the closing of a gray-scale image
wS5V1k26 results from summing up the processed binary slices. The morphological black-top-hat algorithm, which enhances dark features, is defined23 as
BTH5V1k26 5 wB5V1k26 2 5V1k26,
172
where minus denotes pointwise subtraction of an
original from its closing, which results in a negative
representation of low-intensity details.
For the purpose of comparison of results of rankorder and morphological methods for image detail
enhancement we propose to combine white and black
top hats. The aim is to unite bright and dark details
obtained with top hats, as in the case of unsharp
masking. The difference D5V1k26 between white and
black top hats, which retrieves the original contrast of
details, is defined as follows:
D5V1k26 5 A 1 G3WTH5V1k26 2 BTH5V1k264, 182
where A is a normalization constant and G is the gain
coefficient of extracted details, both of which are
calculated similarly as in the case of Eq. 132. Analogy
between the unsharp masking and the difference of
top-hats algorithms is straightforward. In the first
one, bright and dark details that outlie from the local
median values are properly increased by a factor of G
10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS
269
and displayed on a bias level A calculated for the
whole image. In the second one, bright and dark
details are obtained from calculated differences between the input image and its morphological opening
and closing, then are multiplied by the gain coefficient
G, which depends on the dynamic range of the difference of top hats, and the details are displayed on a
bias level A calculated for the whole image. Both
algorithms are very good contrast detectors suitable
for enhancement of bright and dark details that are
smaller than or equal in size and shape to the
structuring element used to modify the input image.
3.
Experiment and Results
A. Characteristic of an Optoelectronic Experiment Using
Thresholded Convolution
Let us discuss a few sources of noise usually present
in optoelectronic processors composed of one or two
SLM’s, which introduce an input image and a structuring element into the system, a CCD camera, and a
frame grabber. Frequently, an input image is introduced into the optical convolver by means of an SLM
in the form of a liquid-crystal display 1LCD2. Because
of nonuniform thickness of the liquid-crystal sandwich and nonuniform illumination, the intensity values corresponding to logic ones and zeros vary from
one element to another at random for both. For LCD
pixels the contrast ratio C is defined as
C 5 [email protected],
192
where Imax and Imin are the intensities transmitted by
LCD pixels that are on and off. According to Ref. 24
the minimum contrast ratio for each pixel of the
Epson VP-100PS-type LCD used in our experiment is
40. According to Laude et al.,25 the corresponding
maximum contrast ratio for the white-light illumination reaches 60. We want to have an image input
device with as a high contrast ratio as possible. If it
is equal to k, then for a slice that has k times more
pixels in the zero level than in the one level, the
background contains the same amount of energy as
the foreground. A limited value of the contrast ratio
results in a high background level; therefore proper
adjustment of offset and gain in the frame grabber is
necessary to optimize the dynamic range of recorded
images.
At present the best low-end LCD that is commercially available does not exceed 480 3 440 pixels in
size and has a contrast ratio on the level of 100:1.
In fully programmable optical convolvers it can be
used for introduction of large structuring elements of
arbitrary shape. The recent development of verticalcavity surface-emitting lasers gives hope that, in the
near future, microlaser arrays can be used as image
input devices in optical convolvers. Nowadays vertical-cavity surface-emitting laser arrays are easily
switched from the fully on to the fully off state with
frequencies lower than 100 MHz.26
If a structuring element is introduced into the
system by means of an SLM, the threshold level
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APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995
depends also on the number of pixels in the kernel.
The bigger the structuring element, the higher the
threshold.12 Recent analysis of noise effects in optoelectronic order-statistics filtering concludes that operations using higher thresholds have higher probabilities of error.20 Consequently, instead of erosion,
it is advisable to make a binary logic inversion of a
slice, calculate dilation, and again make a complement.
In principle, the idea is correct. However, in the case
of realistic-size images with full gray scale and rich
texture it should be used cautiously. In such images
the first slice is mostly composed of ones and the last
one of zeros. Thus routine use of the above method of
complement processing with respect to all of the slices
makes no sense. With the same method one cannot
improve the results of processing the first and the last
slices. There is a possibility of using the method in
an image-dependent way, in which case the contrast
ratio of the SLM’s used should be taken into account.
In our experiment, dilations, medians, and erosions
are calculated directly.
For the past 20 years LCD’s have been produced in
thin-film-transistor technology.27 In this technology
each pixel of a LCD array has a thin-film transistor
that permits active addressing. The transistor gate
is attached to a horizontal row electrode, the drain is
attached to a vertical column electrode, and the
source is attached to the liquid-crystal electrode.
The pixel array is activated a row at a time by
activating the gate lines. In principle this technology ensures accurate switching on and off of individual pixels. Because of cross talk, however, some
of the pixels may switch to another state. Let us
consider possible consequences on the example of the
image of a wedge with uniform distribution of shade,
composed of 256 3 256 pixels, and having 256 grayscale levels. For such an image the difference in the
population of ones between two subsequent slices is
256, that is, 0.004 of the total number of pixels. For
an arbitrary image, such a difference can be even
smaller. The cross talk may disturb this small difference considerably. We conclude that, for our purpose, low-pass filtering in an optoelectronic convolver,
the limitation of the number of gray-scale levels is
justified and advisable. The use of 16 gray-scale
levels of the original picture instead of all 256 ensures
that the number of zeros in subsequent slices does not
decrease when threshold q increases. In this way,
cross talk increases the level of noise, but it does not
cause inversion of the population of ones in a sequence of slices.
In an optoelectronic system composed of a liquidcrystal SLM, a CCD camera, and a frame grabber,
there are two more sources of noise, which enter the
information channel. First, the analog signals are
resampled three times with different resolutions on
their loop between the frame grabber, the SLM, and
the CCD camera. Second, the random noise of the
CCD camera and the SLM reduces the dynamic range
of convolution patterns.
The morphological opening and closing given with
Eqs. 132 and 152 employ thresholds on minimum 1dilation2 and maximum 1erosion2 levels, which in digital
processing correspond to 0 and 255 levels, respectively.
In optoelectronic implementations the minimum and
maximum threshold levels are located just above and
below the levels of noise, which comes from the
above-mentioned sources. For each pixel of the input image the pixel value in the convolution pattern of
the q-level binary slice and the kernel is equal to the
number of pixels in the neighborhood that are at the q
level value and higher. To find the threshold levels,
we use the theorem on local histogram calculation,17
which was recalled in Section 2. In principle, both
local and global histograms, which are functions of
the q argument, should be nondecreasing for zeros
and nonincreasing for ones. The existence of noise,
however, may cause small discrepancies between
theory and practice, especially for extreme q levels.
B.
Experimental System
In our experiment an optoelectronic morphological
image processor with feedback was used, which was a
modified version of that described in a previous
paper.19 Figure 1 shows a block diagram of the
processor. An input gray-scale image is digitally
threshold decomposed into a stack of binary slices.
The next operation is performed in the optical whitelight convolver with a plane of misfocus. Binary
slices are displayed in time sequence on the Epson
VP-100PS-type LCD and imaged with a camera lens
onto the Pulnix TM-765 CCD camera. The system
point-spread function is controlled by misfocusing
and the use of a diaphragm. The point-spread function plays the role of a structuring element. In this
manner every binary slice is optically convolved with
a binary convolution kernel, which results in a stack
of gray-scale convolution patterns. Convolution patterns recorded by the CCD camera are sent to the
Matrox PIP-1024B video digitizer board. After proper
thresholding in the frame grabber, the following
pointwise operations on the binary convolution patterns and further processing are made on a microcomputer. In the case of morphological filters, results of
intermediate operations are reintroduced into the
LCD as looped inputs. The processor is equipped
with TV monitors for observation of input slices,
recorded convolution patterns, thresholded convolution patterns, and final results.
The white-light convolver with a plane of misfocus
is one of the few possible convolver configurations.
The others are angular projection convolvers and
shadow-casting correlators.28 Frequent use of whitelight convolvers in morphological processors and optical parallel logic processors with shadowgrams has
triggered recent interest in their performance.29,30
C. Comparison of Experimental Optical Results and
Digital Results
Performance of detail-enhancement algorithms is demonstrated on the input image of 256 3 256 pixels and
16 gray levels, which is shown in Fig. 21a2. Figure
21b2 presents the results of a digital median filter with
a binary kernel of 5 3 5 pixels. Figure 21c2 shows an
example of the output of an optical median filter with
a flat structuring element of the same size. Visual
examination of both results confirms good performance of the optoelectronic processor. For the purpose of quantitative comparison we use the mean
absolute error 1MAE2 as a measure of similarity. The
MAE, which is frequently used in filter optimization
problems,31 is defined as follows:
MAE 5
Fig. 1. Block diagram of the morphological optoelectronic image
processor. Operations are shown in circles, and data arrays are
shown in squares.
1
N
o 0med 5S3V1k246 2 med
d
op5S3V1k2460,
1102
k
where subscripts d and op indicate digitally and
optically calculated medians. The absolute value of
the difference 1i.e., error2 between optical and digital
results is summed over the whole image matrix,
normalized to the 256 gray-levels score, and divided
by the total number of pixels. Analogously, MAE can
be defined for morphological operations and filters
used in our experiment. Table 1 details values of
such experimental parameters as MAE, minimum
error, maximum error, and threshold value. In the
first row, experimental parameters of optoelectronic
calculation of the median are presented. The MAE
equals 2.4 6 0.1 gray-scale levels of the 0–255 range,
which means that the optical median filtration is
made within 1% accuracy with respect to the digital
calculations. For some pixels the maximum difference between optical and digital results reaches almost half of the gray-scale range, however. In principle the threshold value for obtaining the median
should be on the level of 0.5. Nevertheless, the
10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS
271
Fig. 2. Experimental results of digital and optoelectronic calculations: 1a2 input image of 256 3 256 pixels with 16 gray levels, 1b2 digital
median filtration with a square binary kernel of 5 3 5 pixels 31c2–1h2 are also obtained with a square binary kernel of 5 3 5 pixels4 1c2 optical
median filtration, 1d2 digital unsharp masking, 1e2 optical unsharp masking, 1f 2 optical morphological black top hat, 1g2 optical morphological
white top hat, 1h2 normalized difference of optical white and black top hats.
above-discussed sources of noise can produce a shifting of the experimental local histograms. Therefore
the experimental threshold value is 0.55 6 0.05.
With this threshold value the MAE is minimized.
According to Eq. 122, the results of digital and optical
median filtering are used to calculate unsharp
masking. Pointwise subtracting the median from
the original, we find minimum 12n2 and maximum
1m2 difference pixel values as well as the zero level 1as
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APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995
a fraction f of the full range 32n, m42. The gain
coefficient is calculated as G 5 [email protected] 1 n2. The
offset equals A 5 255f. In Figs. 21d2 and 21e2 the
results of digital and optical unsharp masking are
presented, respectively. Obviously they preserve the
similarity of digital and optical results of median
filtration.
Intermediate optoelectronic operations necessary
to obtain morphological white and black top hats are
Fig. 2.
continued.
summarized in Table 1. The second and the third
rows contain experimental parameters of the calculated erosion and dilation. In contrast to theoretical
predictions the difference between digital and optical
dilations is greater than in the case of the median
filter. The accuracy of optical calculation decreases
to ,1.6%. For erosion we obtain, in accordance with
expectations, the worst result. The accuracy of optical calculation in comparison with the digital one
decreases to ,3.2%. The last two rows of Table 1
present parameters of optical calculating of opening
and closing, which simultaneously correspond with
Table 1.
Values of Experimental Parametersa
Filter Type
MAE
min er
max er
th
Median
Erosion
Dilation
Opening
Closing
2.4 6 0.1
7.9 6 0.7
4.0 6 0.2
8.0 6 0.3
6.9 6 0.1
0
0
0
0
0
104 6 8
160 6 16
144 6 16
128 6 16
144 6 16
0.55 6 0.05
0.975 6 0.005
0.025 6 0.005
0.12 6 0.03
0.955 6 0.005
a Mean absolute error (MAE), minimum error (min er), maximum
error (max er), and threshold value (th) are listed for optoelectronic
calculation of the following filters: median, erosion, dilation, opening, and closing.
10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS
273
calculating white and black top hats, respectively.
In the case of opening we list parameters of the second
operation, that is, of dilation made on the eroded
image. The MAE and the minimum and maximum
errors have values similar to the case of regular
erosion. Thus errors made in two subsequent steps
do not accumulate in a direct way. The threshold
level of dilation made on the eroded image is 5 times
higher than in the case of regular dilation. Finally,
for closing, that is, erosion made on the dilated image,
we find the experimental parameters comparable to
those obtained for the case of regular erosion.
Figures 21f 2 and 21g2 show black and white top hats
calculated optically according to Eqs. 162 and 142,
respectively. We note that both results of morphological processing are satisfactory. The wide presence of
a black background confirms the good quality of
optically calculated opening and closing.
Figure 21h2 presents the result of the difference
between optical white and black top hats calculated
according to Eq. 172. The normalization constant A
and the gain coefficient G are calculated in exactly the
same way as in the case of the unsharp masking
algorithm. We note that the experimental morphological result that combines bright and dark details of
the image is easier to examine visually than the
results of a rank-order unsharp masking algorithm
calculated either digitally or optically. It is a consequence of the opening, closing, and median filter
definitions that the combination of white and black
top hats has a broader histogram than unsharp
masking. Thus in the case of the morphological
difference of top hats the dynamic range of the output
image is more evenly employed than in the unsharp
masking case.
4.
Concluding Remarks
Optoelectronic implementation of the rank-order and
morphological algorithms for image detail enhancement has been presented and compared with digitally
calculated results. High-pass morphological and
rank-order filtering based on calculation of a residue
of an input image and its processed version does not
depend strongly on the quality of optically realized
low-pass filtering. The optical part of the system is a
white-light convolver using the plane of misfocus.
The input image is introduced into the system by
means of the Epson VP-100PS-type LCD, which is
built in thin-film-transistor technology. Owing to
cross talk, error in row- and column-wise addressing
of pixels may result in that a kth pixel value in the
upper slice 5Xq111k26 being bigger than the same kth
pixel value in the lower qth slice. Therefore for the
purpose of optical low-pass filtering it is advisable to
use a limited number of slices, which in consequence
are more sparse. In this way the benefits of using an
optical convolver are twofold: first, convolutions are
made in parallel, and calculation time does not depend on the structuring-element size and shape;
second, processing of a fraction of the whole set of 255
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APPLIED OPTICS @ Vol. 34, No. 2 @ 10 January 1995
slices is sufficient. From the point of view of a
human interpreter, however, the quality of results
remains good.
The experimental optical results of the median
filtering and the morphological erosion, dilation, opening, and closing are compared with the digitally
calculated correspondents. The mean absolute error
defined by Eq. 192 describes the average per image
pixel distance between digitally and optically calculated results. An optical median is calculated within
1% accuracy with respect to the digital calculations.
For optical dilation the accuracy decreases to 1.6%.
For optically calculated closing, accuracy decreases to
2.7%. The lowest accuracy is found for the cases of
optical erosion and opening, only 3.1%.
In this paper we have defined the normalized
difference between morphological white and black top
hats, which enhances bright and dark details of an
input image simultaneously. The experimental result of the difference algorithm is favorably compared
with that of the rank-order unsharp masking algorithm, the reason being the better use of the dynamic
range of the output image. Both algorithms give
image-dependent results; however, probably in most
of the cases, the top-hats difference algorithm gives
an output image with a bigger number of wellpopulated gray-scale levels in the histogram than the
unsharp masking algorithm. This results from the
fact that the top-hat difference algorithm is defined by
combination of erosions and dilations, that is, through
maximum and minimum thresholds. Consequently,
visual inspection of the top-hats difference algorithm
output is easier than in the other case, as the overall
contrast is higher.
The optoelectronic processor performance depends
on the level of noise present in the system. Several
sources of noise have been discussed. One of the
most important is the limited contrast ratio of the
LCD used. Nevertheless, we believe that improvement of the accuracy of optical calculations of rankorder and morphological filters will take place in the
near future.
This work was supported by the Spanish project of
the Comisión Interministerial de Ciencia y Tecnologı́a
1project TAP93-0667-C03-032. T. Szoplik acknowledges a GO WEST grant from the Commission of the
European Communities, Cooperation in Science and
Technology with Central and Eastern European Countries 1grant CIPA3511CT9206482. C. Ferreira acknowledges a GO EAST grant from the Commission
of the European Communities, Cooperation in Science and Technology with Central and Eastern European Countries 1grant ERB-CIPA-CT-93-16712.
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10 January 1995 @ Vol. 34, No. 2 @ APPLIED OPTICS
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