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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

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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.

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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.

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