View
225
Download
0
Category
Preview:
Citation preview
8/10/2019 Bhandarkar 1993
1/5
Proceedings o f 1993 International J oint Con ference on Neural Ne twork s
A Genetic Algorithm-based Edge Detection Technique
Suchendra M. Bhandarkar Yiqing Zhang Walter D. Pot ter
Dep artm ent of C omputer Science
University of Georgia
Athens,
GA 30602-7404, USA
Abstract
In this paper we present a genetic algorithm-based cost
minimization technique for edge detection.
Edge de-
tection is formulated
as
a process of choosing a mini-
mum cost edge configuration. The edge configurations
are viewed as two-dimensional chromosomes with fit-
ness values inversely proportional to their costs.
The
design of the crossover and the mutation operators is
described. The knowledge-augmented mutation opera-
tor which exploits knowledge of the local edge structure
is shown to result in rapid convergence. The incorpora-
tion of meta-level operators and strategies in the con-
text of edge detection are discussed and are shown to
improve the convergence rate.
1
Introduction
Edge detection is an impor tant task in computer vision.
It is the front-end processing stage in object recognition
and image understanding systems. The accuracy with
which this task can be performed is a crucial factor in
determining overall system performance.
Most edge detection schemes can be classified as
based on optimal filtering[l,
21,
residual analysis[3], ur-
face fitting[5, 41 and sequential contour tracing
[6,
71. In
spite of the mathematical sophistication of these tech-
niques, the problem of finding true edges that corre-
spond to physical boundaries of an object in an image
is still a very difficult one. Most of the aforementioned
approaches consider the edge detection problem as one
that is based upon the response of the edge detector at
a single pixel location i.e. the nature of the edge struc-
ture around a given pixel in the edge image is largely
ignored. So although the performance of the edge de-
tector in terms of signal-to-noise ratio and localization
accuracy is optimized at each individual pixel location,
the edge image as a whole could still be unsatisfactory
i.e. causing the resulting edges to be thick and frag-
mented and perceptually non-intuitive.
More recently, Tan et al.[8, 91 have cast the problem
of edge detection
as
one of cost minimization. They at-
tempt to overcome the aforementioned shortcomings of
existing edge detection techniques by formulating a defi-
nition
of
an edge that is general enough
to
include most
edge types. Their approach also improves on existing
edge detection techniques by explicitly considering the
local edge structure in the neighborhood of the hypoth-
esized edge pixels. Their approach requires that the
edges detected
as
a result of minimizing the cost func-
tion be thin, continuous, long and most importantly,
occupy an accurately computed location, and partition
dissimilar regions in the image in the best possible man-
ner. Both, hill climbing[8] and simulated annealing[9]
based optimization approaches for edge detection have
been presented.
In this paper, we present a genetic algorithm (GA)
based cost minimization approach to edge detection.
The
G A ,
the conceptual basis of which lies in Darwins
Theory
of
Natural Selection
better known
as the
sur
vival of the f i t tes t , is a heuristic search technique for
obtaining the best possible solution in
a
vast solution
space. Problem-solving methodologies based on GAs
have been acknowledged
as
effective problem solving
tools by many experts in different areas. This moti-
vates us to consider the CA
as
a candidate optimization
technique that could be used to perform edge detection
based on cost minimization.
2 Cost Function for an Edge Im-
age
A
gray scale image is a two dimensional array of pix-
els
G m,n),
1
= {0.25,0.50,0.75}, w j ( S , I )=
{2.00,3.00,4.00}, and w t S ,
= 2 w j ( S , wc S,
Cost Factor
for
Edge Fragmentation
Cost Factor for Number
of
Edge Pixels
C, S,
I = 0.
W d s , W , ( s , I + 0.01.
3
GA-based Edge Detection
GA s are a problem solving methodology based on Dar-
win s theory of evolution. In our GA approach, the
chromosomes in the population are represented by two-
dimensional binary arrays of 1 s or 0 s. A 1 represents
an edge pixel whereas a
0
represents a non-edge pixel.
The chromosomes are an explicit representation of the
edge images. We have chosen a population size of 512
for images of size of 256 x 256 pixels. We remark that
larger population sizes are beneficial for this task be-
cause of the obvious richness in the gene pool and the
large chromosome size.
With each chromosome in the population is associ-
ated a cost
F ( S )
= C lxi wiC i S , . We calculate the
fitness value of each chromosome based on its relative
ranking in the entire population:
fitness[i]
=
(cos t[wors t]- os t[ i] ) ,
4)
where worst denotes the least fit chromosome found in
the present generation. During the earlier phases of
evolution, we set
n =
2. After the solutions converge to
a certain extent, we make n successively larger up to
n = 5.
We perform simple roulette wheel selection to se-
lect mates for reproduction based on the relative fit-
ness value of each chromosome. During the crossover
process, we randomly select two sites along the
X
di-
mension, two sites along the Y dimension, and perform
crossover. The mutation operator flips the labeling at a
pixel location, from
0
-
1 or 1
with a prespecified
mutation probability. We set the initial crossover rate
to 0.6 and the initial mutation rate to
0.008.
If after
15 generations, no better chromosome can be fou.nd, we
assume that the present population contains the best
edge image i.e. the edge image corresponding t o the
lowest cost.
3.1
Meta-level
GA
Operators
In addition to the components of a simple GA, we
also apply to our optimization scheme (a) the elitasm
strategy[lO], (b) the Engzneered Condztioning (EC)
operator
[ll]
and (c) the Intelligent or Knowledge-
augmented Mutation operator. We show that these
meta-level operators help to accelerate the convergence
of the population of solutions to the desired optimum.
We also adapt the basic GA parameters during the
course of evolution via dynamic assessment of the per-
formance of the GA.
3.1.1
Elitism Strategy in a Genetic Algorithm
An elitism strategy ensures that the best chromosome(s)
in one generation survive(s) into the following genera-
tion, thus preventing a possible inadvertent loss of high
quality chromosome(s). Although the elitism strategy
may increase the rate by which a population may be
dominated by a highly fit chromosome
or
a set of chro-
mosomes, it appears to improve the overall performance
of the GA[10]. In order to prevent the inadvertent loss
of the best chromosomes due to stochastic roulette se-
lection, we employ a meta-level elitism strategy which
ensures that the best chromosome in the current gener-
ation always survives into the succeeding generation.
3.1.2 Intelligent Mutation
In a traditional GA, the mutation operator just flips a
bit randomly without the knowledge of the chromosome
structure in the neighborhood of the bit being flipped.
In our approach mutations are performed more intel-
ligently by exploiting the local edge structure so that
they will help solutions converge faster . Our mutat ion
2997
8/10/2019 Bhandarkar 1993
4/5
some from the population and modify a small portion
of it. This small portion is a
3
x
3
window centered
around a pixel location chosen at random. The modifi-
cation is performed stochastically based on the knowl-
edge of the edge structure in a local neighborhood. We
compare the modified chromosome with the original one
and if the conditioned chromosome is found to be better
than the original chromosome, we substitute the origi-
nal chromosome with the conditioned one, otherwise we
put the original chromosome back into the population.
~ ~ 1
{ y ]
~ ~ 1e condition five percent of the pixel locations chosen
randomly in the best chromosome (edge image).
El
Figure 2: Examples of Mutation Strategies
3 1 4
Adaptat ion of Basic GA Operators
strategies are selected and performed based on the ex-
amination of the local neighborhood in a
3
x
3
window
centered at a randomly chosen pixel location. Several
heuristic guidelines are followed in order to determine
the probability distribution of the possible mutations:
i) Mutations that result in straight local edge struc-
tures are assigned a higher probability. (ii) Mutations
that result in local edge structures that turn by 45 are
assigned a higher probability than those that turn by
more than 45O. (iii) Resulting valid local edge structures
are more favored than invalid local edge structures. (iv)
For resulting valid two-neighbor local edge structures,
those with higher mutation complexity are assigned a
lower probability, and vice versa. (v) A certain non-
zero probability is assigned to a mutation that would
cause the resulting local edge structure to be an empty
3
x
3
window. (vi) A certain non-zero probability is
assigned to a random mutation in a 3
x 3
window.
In guidelines
(v)
and (vi), probabilities are deter-
mined based on the validity of the existing local edge
structures. If the existing local edge structure is valid,
we assign a lower probability to guidelines (v) and (vi)
otherwise, the probability is higher. Figure 2 shows
some of the mutation strategies employed.
3 1 3 The Engineered Conditioning Operator
We also employ an
Engineered Conditioning
( E C )meta-
level operator that works in combination with the ba-
sic GA operators. The EC operator is an operator
that can be used for local improvement in the search
space[ll]. With the application
of
the EC operator, the
best chromosomes in the population are conditioned
so
that they may acquire the strength and the character-
istics of stronger neighbors. The
EC
operator works
in a hill climbing fashion. We take the best chromo-
Finally, we employ
a
mechanism that adjusts the
crossover and the mutation rates based on dynamic as-
sessment of the performance of the GA. During the ini-
tial stages of evolution, we assign a high probability
value to the crossover operator and a very low probabil-
ity value to the mutation operator. After 5 generations
when the chromosomes in the population converge to-
wards a highly fit chromosome and there is no better
chromosome to be found, we lower the crossover rate
(by 10 percent of the original value) and raise the mu-
tation rate ( to fivefold of the original value). In this
case, mutation is the major source of introduction of
new genetic material to the population. After 10 gen-
erations when no better chromosome can be found, we
lower the crossover rate ( by 10 percent of the original
value) and raise the mutation rate once again (to fivefold
of the original value). After 15 consecutive generations
if there is still no better chromosome to be found,
we
assume that the best chromosome in the present popu-
lation corresponds to a global optimum.
3 2
Experimental Results
The GA-based edge detection technique which incorpo-
rates intelligent mutation, elitism, the EC operator and
adaptation of basic GA operators was implemented and
tested on several images. Figure 3 shows one such gray
scale image and Figure 4 the resulting edge image. The
GA-based edge detection technique was experimentally
compared with the hill climbing[8] and the simulated
annealing[9] based techniques. The GA was found to
perform better than the hill climbing algorithm and as
well
as
the simulated annealing algorithm in terms of
the quality of the final edge image. Although the hill
climbing algorithm was faster, it tended to get trapped
in
a
local optimum. Between the GA and simulated an-
nealing, the solutions were found to approach the global
minimummuch faster in the integrated GA as compared
to the simulated annealing algorithm.
2998
8/10/2019 Bhandarkar 1993
5/5
Figure 3: Gray Scale Test Image
Figure 4: Edge Image using GA-based Optimization
4 Conclusions and Suggestions
for Future Work
In this paper, we implemented a GA-based cost mini-
mization approach to edge detection and compared it
with hill climbing- and simulated annealing-based ap-
praoches. The simulated annealing algorithm and the
GA-based approach were seen to produce the best re
sults. We intend to extend our work described in this
paper in the following areas: (i) parallelization of the
GA-based approach to edge detection, (ii) design of
more effective meta-level genetic algorithm operators
and (iii) investigation of alternative (and hopefully bet-
ter) chromosomal representation schemes for represent-
ing edge images. In conclusion, we feel that genetic
algorithm-based optimization techniques have a major
role to play in image processing and computer vision.
With the use of suitable parallel hardware, genetic al-
gorithms can be used to design robust processing tech-
niques for most vision applications.
References
tion, IEEE Transactions on Pattern Analysis and
Machine Intelligence, Vol. PAMI-8, No. 6, pp. 679-
698, November 1986.
P. Perona and J. Malik, Detecting and localizing
edges composed of steps, peaks and roofs,
Intl.
Conf. Computer Vision,
Osaka, Japan, Dec. 1990,
pp. 52-57.
M.H. Chen, D. Lee and
T.
Pavlidis, Residual Anal-
ysis for Feature Detection, IEEE Transactions on
Pattern Analysis and Machine Intellagence, Vol.
PAMI-13, No. 1, January 1991, pp. 30
-
40.
R.M.
Haralick, Digital step edges from zero cross-
ing of second directional derivatives, IEEE Trans-
actions on Pattern Analysis and Machine Intelli-
gence, Vol. PAMI-6, No. 1, pp. 58-68, January,
1984.
V. Nalwa and T. Binford, On detecting edges,
IEEE Dansactions on Pattern Analysis and Ma-
chine Intelligence,
Vol PAMI-8, No. 6, pp. 699-714,
November 1986.
G.P. Ashkar and J.W. Modestino, The contour
extraction problem with biomedical applications,
Computer Graphics and Image Processing, Vol. 7,
pp. 331-355, 1978.
[7]
A .
Martelli,
An
application of heuristic search to
edge and contour detection, Communications of
A C M , Vol. 19, No. 2, pp. 73-83, February, 1976.
[8]
H.L.
Tan,
S.B.
Gelfand, and E.J. Delp, A com-
parative cost function approach to edge detection,
IEEE Bansaction on Systems, Man, and Cyber-
netics, Vol. 19,
No.
6, pp. 1337-1349, Novem-
ber/December, 1989.
191 H.L. Tan, S.B. Gelfand, and E. J. Delp, A cost min-
imization approach
to
edge detection using sim-
ulated annealing,
IEEE Transactions on Pattern
Analysis and Machine Intelligence,
Vol. 14, No.
1,
pp. 3-18, January, 1991.
[lo]
D.E. Goldberg, Genetic Algorithms in Search,
Optimization, and Machane Learning, Addison-
Wesley Publishing Co.: Reading, MA, 1989.
[ll] W.D. Potter, J.A.Miller, B.E. Tonn, R.V. Gand-
ham, C.N. Lapena, Improving the reliability of
heuristic multiple fault diagnosis via the EC-based
genetic algorithm,
Journal of Applied Intelligence,
Vol. 2. pp. 5-19, 1992.
[l]J . Canny, A computational approach to edge detec-
999
Recommended