1. Face Recognition Using Evolutionary Approaches
Aditya Ravindran
Richa Aggarwal
Neha Bhatia
Abhinav Sharma

2. Optimization
 Optimization is the selection of a best element (according to some criteria) from a set of available alternatives.
An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function.
The domain A of f is called the search space or the choice set, while the elements of A are called candidate solutions or feasible solutions. The function f is called an objective function
A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution.

3. Optimization problem representation
An optimization problem can be represented in the following way:
Given: a function f : A  R from some set A to the real numbers
Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A ("minimization") or such that f(x0) ≥ f(x) for all x in A ("maximization").
Maximization
Minimization

4. Evolutionary Approaches
An evolutionary algorithm is a  population-based optimization algorithm.
Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions.
Firefly algorithm is the two evolutionary approach used for implementing face recognition system.
This algorithm is used to explore the search space and find parameters to maximize a particular objective function.

5. Firefly Algorithm
The firefly algorithm (FA) is an optimization algorithm, inspired by the flashing behavior of fireflies.
The purpose of flashing is:
Attract mating partners.
Communication.
Attract potential prey.
Fireflies have unique flashing pattern and limited light intensity.
The three main assumptions of firefly algorithm are:
All fireflies are unisex.
Attractiveness is directly proportional to brightness and inversely proportional to distance.
Brightness or intensity is determined by objective function.

6. Flowchart of Firefly algorithm

7. Four-Peak function using Firefly algorithm

8. Parabolic function using Firefly algorithm

9. Rastrigin function using Firefly algorithm

10. Rosenbrock function using Firefly algorithm

11. Styblinski function using Firefly algorithm

12. Camelback function using firefly algorithm

13. Face Recognition System
Block diagram of the processed Face recognition system

14. DWT-Discrete Wavelet Transform
Image decomposition by DWT
Haar wavelet transform may be considered to simply pair up input values, storing the difference and passing the sum. This process is repeated recursively, pairing up the sums to provide the next scale: finally resulting in 2n−1 differences and one final sum.
DWT is used primarily for image compression.
LL component is derived by applying low pass filter on the image matrix-first horizontally, then vertically.
The LL component is used for feature recognition because it corresponds to the predominant information of the whole image.

15. Sample images from the database
Image Database
Sample images from the database

16. Face Recognition System output
Test images from ORL database shown in row 1 used for face recognition and output images corresponding to row 1 as shown in row 2 using firefly algorithm

17. Graphical analysis of Firefly based face recognition
Graph 1. Variation of recognition w.r.t Number of Images

18. Graphical analysis of firefly based Face Recognition
Graph 2. Variation of accuracy w.r.t Number of Images

19. References
[1] Saibal K. Pal, C.S Rai, Amrit Pal Singh, “Comparative Study of Firefly Algorithm and Particle Swarm Optimization for Noisy Non- Linear Optimization Problems”,vol.10,2012,pp:50-57
[2] Dian Palupi Rini, Siti Mariyam Shamsuddin and Siti Sophiyati Yuhaniz,” Particle Swarm Optimization: Technique, System and Challenges “, vol 14,pp:9, January 2011
[3] Xin-She Yang, “Firefly Algorithm, Stochastic Test Functions and Design”, Department of Engineering, University of Cambridge:March 9,2010,Vol.2,pp:78-84
[4] Kwang In Kim, Keechul Jung, and Hang Joon Kim, “ Face Recognition Using Kernel Principal Component Analysis”, ieee signal processing letters,vol.9,no.2,february 2002,pp:3