Dr. Pawan Kumar Deepak Kumar JhaAssistant Professor M.Tech. , CSE, 2nd Year

IITT College of Engineering Pojewal , Punjab

Punjab Technical University , Jalandhar

Estimation of Convolution Masks for Image Restoration Using Genetic

Algorithm

Abstract Model of image degradation and restoration Mathematical equations for degraded functions

and noises Algorithm for estimation of Convolution mask

using Genetic algorithm Simulation results Conclusions and References

Image restoration is carried out to recover a corrected image from a degraded image. In image restoration there is need to build the specific mathematical model for degradation hence there is need to know about the cause of degradation without which some time it becomes impossible to correct the image. In most practical cases there is not enough information available about the degradation, and is needed to be estimated either analytically or empirically. The level of problem of image restoration is further increased by the presence of noise, and more than one cause of degradation, as in these circumstances it becomes difficult to formulate the mathematical model or degradation function. By using Genetic Algorithm convolution mask generated for restore degraded images. The proposed algorithm has been tested on images simulated with the motion blurring and for the presence of noise.Finally the algorithm is applied to correct the motion artifact which is additive with noises in Computed tomography images.

Model of Image Degradation and Restoration

Degradation Restoration

Degradation function

(H)+ Restoration

Filterf(x , y)

Noisen(x , y)

g(x , y)

f^(x , y)

Steps involved in the process of Degradation/Restoration

First we take a degraded image as input for process.

For the restoration process to compensate the corruption present in the image, a filter mask will be modelled.

With modelled filter mask, restoration is carried out to get approximate image from corrupted image.

Motion artifact : is due to relative motion between the camera and the object. Mathematically can be represent as

H(u , v)=sin(πVTu)πVu

Where V:constant speed in direction of x-axisT:mechanical shutter open time

Most of the medical images get effected by this type of artifact.

Atmospheric turbulence in remote sensing or astronomy .This degradation caused due non-homogeneity in atmosphere that deviates passing of light rays.

In this paper we consider the types noises are present in the images as

salt and pepper Gaussian noises

5/ 62 2( , ) exph i j k i j

START

Initialization of Population size and no.of Generations

Stoppage conditions satisfied

Evaluate the fitness value of each individual

in each Generation

Selection of fittest individual for reproduction(mutation,

cross over elite child)

STOPOptimal convolution Mask(best fittest Mask)

Yes

NO

Initialization The algorithm starts with initialization of

individuals randomly. An array of individuals are called the Population The individuals are may be any one of the

followingBit strings (0101 ... 1100)Real numbers (43.2 -33.1 ... 0.0 89.2)

As in this work we consider the individuals as rational numbers which are in the range of [0 1]

Initialization of Population size and no.of

Generations

Next initialization of Generation limit At each generation successive operations are

performed on the current population that produces new generation population.

Initialization of Population size and no.of

Generations

Fitness function At each generation the fitness value or efficiency

of individuals are evaluated using fitness function. The individuals which have higher fitness values

that are consider for further process. The fittest individuals are considered for the

reproduction process.

Evaluate the fitness value of each individual in each

Generation

Reproduction Elite child

Crossover child

Mutation Child

Parents

Child

Selection of fittest individual for reproduction(mutation, cross

over elite child)

Stoppage conditions Fitness function value limit Fixed number of generations reached Allocated budget reached Time limit Combination of any of aboveIn this work we consider fixed number of generation as

stoppage condition.

Stoppage conditions satisfied

As the stopping conditions are satisfied, the algorithm halts, and the result obtained will be the best fittest individual .

Stop

Parameters consider for this paper Population size 100 Generation limit 500 Elite Count 4 Crossover Fraction 0.5 Tool used Image processing tool

box, Matlab

(a).Original CT scan image of abdomen

region

(b). Image corrupted by motion artefact (90o) and additive

noise Gaussian noise

(C).Restored image by using convolution mask obtained by genetic algorithm

(a).Original camera man

image

(b). Image corrupted by motion artefact (in 45o) and additive noise Salt

and Pepper noise

(C).Restored image by using convolution

mask obtained by genetic algorithm

In this paper we developed 3X3 and 5X5 convolution masks coefficients.

With the optimal filter mask is found, it can be used to restore other similar or related corrupted images, without having any prior knowledge about degradation function or additive noises.

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Yen-Wei Chen, Zensho Nakao and Xue Fang, “Parallelization of a Genetic Algorithm for Image Restoration and Its Performance Analysis”, IEEE 1996.

Mohsen Ebrahimi Moghaddam, “Out of Focus Blur Estimation Using Genetic Algorithm” Journal of computer science 4(4):298-304, 2008 ISSN 1549-3636.

Gonzalez R. C. and Woods R. E. “Digital Image Processing”, 2nd edition 1992. pp:222-225.

“Global Optimization Algorithms Theory And Application”, 2009 pp:141-142