Edge detection using evolutionary algorithms new

 Introduction
 Background
 Evolutionary Algorithms
 Bacteria Foraging Algorithm
 Particle Swarm Optimization
 Results and Conclusion
 References

 Edges are significant local
changes of intensity in an image.
A Tulips image

 Edge Detection is the process
of identifying and locating sharp
discontinuities in an image.

 Abrupt change in pixel intensity
Characterize boundary of a object

Edges of the Tulips image


A tulips Image Part of the image Edge of the part of the image

Matrix generated by the Part of the image

CAUSES OF INTENSITY CHANGES

1. Geometric events
Discontinuity in depth and/or
surface colour and texture

2.Non-geometric events
Edge formation due to
Reflection of light discontinuity of surface
Illumination
shadows

REFLECTANCE ILLUMINATION SHADOWS

IMAGE RECOGNITION

SEGMENTATION

IMAGE FUSION

IMAGE TRACKING

The basic idea behind edge detection is to find places in an
image where the intensity changes rapidly, using one of the
two criterions:

1. Find places where the first derivative of the intensity is greater
in magnitude than a specified threshold. (USING
GRADIENT)
2. Find places where the second derivative of the intensity has a
zero crossing. (USING LAPLACIAN)
 Examples of the gradient based edge detectors are Prewit and
Sobel operators.
 An alternative method is an optimal edge detector like the
Canny operator, for two dimensional images.

The IITR image Sobel

Roberts Prewitt

Marr Canny

INPUT
IMAGE ENHANCEME
FILTERING DETECTION
NT

EDGES OF
THE IMAGE LOCALISATI
LINK
ON

 The quality of Edge Detection depends upon a lot of
factors such as lighting conditions, the presence of
objects of similar intensity,density of edges in the
scene and noise.
 There is no good method for automatically setting
these values, so they are manually changed by an
operator each time the detector is run with a different
set of data.
 In the presence of noise, detection of edges becomes
very difficult because both edges and noise are
characterized by high frequency.

1.Corners are often missed.

2.Here we have to choose
Threshold values and width
of the mask. Changing the size of the image
complicates the setting of these values.

3.For different features we need a different operator.

 The name “EVOLUTIONARY ALGORITHM”
suggests, evolution as it is observed in nature is
imitated.
 These algorithms are increasingly sought for
finding optimum solutions for the engineering
problems.
 Well suited to solve complex computational
problems such as optimization of objective
functions , pattern recognition ,image processing,
filter modelling,etc.

The word „„heuristic” is Greek and means „„to know”, „„to find”, „„to discover”
or „„to guide an investigation”, Specifically, „„Heuristics are techniques which
seek good (near-optimal) solutions at a reasonable computational cost
without being able to guarantee either feasibility or optimality, or even in
many cases to state how close to optimality a particular feasible solution
is.” Heuristic algorithms mimic physical or biological processes.
Some of most famous of these algorithms are

ANT COLONY • MIMICS THE BEHAVIOUR OF ANTS
OPTIMIZATION FORAGING FOR FOOD

BACTERIA FORAGING • COMES FROM SEARCH AND THE
ALGORITHM OPTIMAL FORAGING OF BACTERIA

PARTICLE SWARM • SIMULATES THE BEHAVIOUR OF
OPTIMIZATION FLOCK OF BIRDS

GENETIC ALGORITHM • INSPIRED FROM DARWINIAN THEORY

 Given by Kelvin M. Passino (2002)
 Exploits the foraging behaviour of Bacteria
 Foraging can be modeled as an optimization process where bacteria
seek to maximize the energy obtained per unit time spent during
foraging.
 An objective function is posed as the cost incurred by the bacteria in
search of food.
 A set of bacteria tries to reach an optimum cost.
Four Stages in the life cycle of Bacteria
1. Chemo taxis
2. Swarming
3. Reproduction and
4. Elimination and Dispersal
These stages in the search space generate an optimal solution to the
problem of optimization.

In Chemo taxis stage, the bacteria
either resort or tumble followed by
a tumble or make a tumble followed
by a run or swim.
Movement stage of Bacteria

In Swarming, each E. coli
bacterium signals another
bacterium via attractants to
swarm together.
Cell to cell signalling stage.

In the Reproduction the least healthy
bacteria die and of the healthiest each
bacterium splits into two bacteria,
which are placed at the same location

In the Elimination and Dispersal
stage, any bacterium from the total set
can be either eliminated or dispersed
to a random location during the
optimization.
This stage prevents the Bacterium Reproduction stage
Of Bacteria
from attaining local optimum.

Start
Initialization  p: Dimension
Evaluation  S: Population Size
Moving  Nc: Chemotactic steps
Tumble / Swim
 NS: Swim Length Limitation
No
End of Nc?  Nre: Reproduction Steps
Yes
 Ned: Elimination-Dispersal Steps
Reproduction
 Ped: Elimination Rate
No
End of Rep.?  dlt(i): random number on [-1,1].
Yes
where i from 1 to p.
Elimination
 c(i): Step Size for the dimension.
No
End of Eli.?
Yes
19
End

i
J (i , j , k , l )
 J (i , j , k , l ) J cc j, k , l , P j, k , l (1)

i i dlt i
j 1, k , l j, k , l C i
T
dlt i dlt i (2)

i
J (i, j 1, k , l ) J (i, j 1, k , l ) J cc j 1, k , l , P j 1, k , l (3)

Nc 1
i
J health
J i, j, k , l (4)
j 1

The original bacterial foraging (BF) Technique
modified to make it suitable for edge detection.
The nutrient concentration at each position is
calculated using a derivative approach.
Modifications
Search Space
2-dimension search space of bacteria consists of
the x and y coordinates of a pixel in an image.

Chemo taxis
 Goal of this stage is to let the bacterium search for the edge pixels of the
image.
 Another goal is to keep the bacterium away from the noisy pixels.
 Probabilistic derivative approach is used to find the edge pixels.
Swarming
 A bacterium relies on other bacteria
 The bacterium that has searched an optimum path, signals other bacteria so
that they can reach the desired optimum path swiftly.
 That optimum path is the best edge detected.
 Bacterium releases both attractant and repellant.
 Bactreia congregate in to groups and move in a concentric manner.
Reproduction
 The population is sorted in the ascending order of the accumulated cost
 Half of the least healthy bacteria dies and each of the other healthiest bacteria
splits up into two.
Elimination-Dispersal
 Each bacterium in the population is subjected to elimination-dispersal with
some Probablity.

RESULT OF BACTERIA FORAGING
ALGORITHM

A Cameraman Image Edge Detected using BFOA
With split ratio 4

Edge detected using BFOA
With split ratio 12

 Edges are accurately detected
 The result of this algorithm may show
disconnected edges as shown in Fig
 Thick edges can be seen due to bacteria moving
parallel to an edge.
 Since BFOA has been devised with the aim of
global extremes, this error is expected.

 Proposed by Kenedy and Eberhert (1995)
 Global optimization method
 Population based Evolutionary Algorithm based on social-
psychological principles
 Simulates a social model such as flocking of birds, schooling of
fish etc.
 PSO algorithm attempt to maximize or minimize a given set of
data by generating a random set of particles which move with
randomly changing velocity throughout the search space.
 The Particle with the best position is selected and other particle
will swarm towards it.
 Successfully applied to training neural networks, optimizing
power system,fuzzy control systems, robotics, antenna design
and computer games.

The velocity update equation is given by

The next position of the particle will be

 Best Edge is nothing but a COLLECTION OF
PIXELS WHICH ARE ON CURVES.
 PSO based algorithm can be used to detect those
curves.
 To Apply PSO based algorithm in edge detection
“Each Particle represents a CURVE”

The movement directions from a
pixel to one of eight neighbours

An example for a curve passing through pixel A

5 5 5 4 3 3 4 4 5 0 0 0 0 0 ......

Particle encoding for the curve above

The dimension of the vector representing a particle depends on image size.
Each Curve can be encoded using the direction of movement from a pixel to
the next pixel on the curve.
The Best fitting Curve is selected which passes through a pixel.
All other neighbour curves (Particles) swarm towards the Best fitting Curve.

 Homogeneity and
 Uniformity factors
 The first one measures the homogeneity of the pixels on a curve and the second one
measures the intensity similarity of these pixels.
 The homogeneity operator can be formulated as below:

(5)

Homogeneity factor of a curve: This factor shows the average of homogeneity of the pixels on a
curve where the homogeneity of each pixel on the curve is calculated based on equation (5).
This factor is defined as below:

(6)
Uniformity factor of a curve: The pixels on a curve often have similar values of intensities;
hence we introduce a new concept that we call the uniformity factor of a curve. This factor
can be computed for any curve as below:

(7)

 Objective function is needed to calculate the fitness of the particle at each
point. In case of edge detection the objective function is calculated with
the help of homogeneity factor and uniformity factor. Here, we search the
curves which pass through a pixel. We expect to make the homogeneity
factor bigger, the uniformity factor smaller, and the length of the curves
bigger. So heuristically this function is defined as below:

(8)

Flow chart depicting the General PSO Algorithm:

Start

Initialize particles with random position
and velocity vectors.
particles exhaust

For each particle’s position (p)
Loop until all

evaluate fitness

Loop until max iter
If fitness(p) better than
fitness(pbest) then pbest= p

Set best of pBests as gBest

Update particles velocity (eq. 1) and
position (eq. 3)

Stop: giving gBest, optimal solution.

RESULTS OF PSO

Edge Detected Using Sobel Operator
A Test Image

Edge Detected using PSO

A
A noisy Image Output Using Sobel Operator

Output Using PSO

 Ease of implementation
 High rate of convergence
 Fewer operators
 A limited memory for each particle to save its
previous state
 High capability to optimise noisy functions

 Bacteria Foraging method finds robust edges even in the
complex and noisy images. This work opens a new domain of
research in the field of edge detection using bio-inspired
algorithms. This method performs better than many other
standard methods.
 Particle Swarm Optimization (PSO) is a computational
intelligence method. Here the results of PSO are compared with
the Sobel operator and this algorithm outperforms the Sobel
operator.
 A main advantage of these algorithms is detection of edges
in one step and there is no need for smoothing, enhancement and
localization as pre-processing steps.
 The PSO algorithm used here gives the output only for
predefined shapes (e.g. Circle, Triangle etc). An improvement
can be made so that this algorithm can be applied for the
complex images also.

1. R afael C. Gonzalez, Richard E.Woods and Steven l. Eddins “Digital
Image Processing using MATLAB” Second Edition
2. Om Prakash Verma, Madasu Hanmandlu, Puneet Kumar , Sidharth
Chhabra, and Akhil Jindal, “A Novel Bacterial Foraging Technique
for Edge detection ”, 2011 IEEE
3. Kelvin M. Passino , “Biomimicry of Bacteria Foraging and Control
for Distributed Optimization and Control”, JUNE 2002 IEEE, pp 52-
67
4. Mahdi Setayesh1, Mengjie Zhang1 and Mark Johnston2,” A new
homogeneity-based approach to edge detection using PSO, 24th
International Conference Image and Vision Computing New Zealand
(IVCNZ 2009)”, 2009 IEEE
5. Mahdi Setayesh, Mengjie Zhang and Mark Johnston, “Improving
Edge Detection Using Particle Swarm Optimisation”,2010,IEEE

Edge detection using evolutionary algorithms new

Recommended

More Related Content

Viewers also liked (20)

Similar to Edge detection using evolutionary algorithms new (20)

Recently uploaded (20)

Edge detection using evolutionary algorithms new

Editor's Notes