EDGE DETECTION USING EVOLUTIONARY ALGORITHMS

UNDER THE GUIDANCE OF DR. DEBASHIS GHOSH

Submitted by:Priyanka SharmaM.Tech IInd year

CONTENTS

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

INTRODUCTION

Edges are significant local

changes of intensity in an 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

A Tulips image

Edges of the Tulips image

b

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

Matrix generated by the Part of the image

REFLECTANCE ILLUMINATION SHADOWS

2.Non-geometric eventsReflection of lightIlluminationshadows

1. Geometric eventsDiscontinuity in depth and/or surface colour and texture

CAUSES OF INTENSITY CHANGES

Edge formation due to discontinuity of surface

Application of edge Detection

IMAGE RECOGNITION

SEGMENTATION

IMAGE FUSION

IMAGE TRACKING

DIFFERENT TECHNIQUES OF EDGE DETECTION

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.

Sobel

Roberts Prewitt

Marr

The IITR image

Canny

STEPS IN EDGE DETECTION

ENHANCEMENT

DETECTIONFILTERING

LINKLOCALISATI

ON

INPUTIMAGE

EDGES OFTHE IMAGE

Problems regarding Edge Detection

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.

PROBLEMS WITH GRADIENT BASED EDGE DETECTORS

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.

Edges of noisy image and blurred image using sobel operator

Evolutionary Algorithms

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.

VARIOUS HEURISTIC ALGORITHMS

•MIMICS THE BEHAVIOUR OF ANTS FORAGING FOR FOOD

ANT COLONY OPTIMIZATION

•COMES FROM SEARCH AND THE OPTIMAL FORAGING OF BACTERIA

BACTERIA FORAGING ALGORITHM

•SIMULATES THE BEHAVIOUR OF FLOCK OF BIRDS

PARTICLE SWARM OPTIMIZATION

•INSPIRED FROM DARWINIAN THEORY

GENETIC ALGORITHM

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

BACTERIA FORAGINGALGORITHM

INTRODUCTION OF BFA

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 from attaining local optimum.

Reproduction stage Of Bacteria

19

Operation of Bacterial ForagingStart

Initialization

MovingTumble / Swim

End of Nc?

End of Rep.?

End of Eli.?

End

Yes

No

Yes

No

Yes

No

Reproduction

Elimination

Evaluation

p: Dimension S: Population Size Nc: Chemotactic steps

NS: Swim Length Limitation

Nre: Reproduction Steps

Ned: Elimination-Dispersal Steps

Ped: Elimination Rate dlt(i): random number on [-1,1].

where i from 1 to p. c(i): Step Size for the dimension.

Operation of Bacterial Foraging(2)

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(1)

(2)

(3)

(4)

Modified Bacterial Foraging Technique for Edge Detection

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.

A Cameraman Image Edge Detected using BFOAWith split ratio 4

Edge detected using BFOA With split ratio 12

RESULT OF BACTERIA FORAGING ALGORITHM

Results

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.

PARTICLE SWARMOPTIMIZATION

INTRODUCTION of PSO

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.

DEFINITION OF PSO

CONTD…

The velocity update equation is given by

The next position of the particle will be

PSO based algorithm for edge detection

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”

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 movement directions from a pixel to one of eight neighbours

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.

Two New Factors 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 of PSO algorithm

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.

For each particle’s position (p) evaluate fitness

If fitness(p) better than fitness(pbest) then pbest= pL

oop

un

til a

ll

par

ticl

es e

xhau

st

Set best of pBests as gBest

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

Loop

unt

il m

ax it

er

Stop: giving gBest, optimal solution.

A Test ImageEdge Detected Using Sobel Operator

Edge Detected using PSO

RESULTS OF PSO

AA noisy Image Output Using Sobel Operator

Output Using PSO

Advantages of 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

CONCLUSION AND FUTURE WORK

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.

REFERENCES

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

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