MAJOR PROJECT PRSENTATION

Face Recognition using Discrete Wavelet Transform and Principle Component

Analysis

UNIVERSITY COLLEGE OF ENGINEERINGRAJASTHAN TECHNICAL UNIVERSITY, KOTA

Submitted To:Mr. S.R. KAPOORAssociate ProfessorMr. VIVEK SRIVASTAVAAssociate Professor

Submitted By:Mukesh Kumar Jatav (11/045)Mukesh Taneja (11/046)Pawan Kumar (11/051)Prabhat Sharma (11/053)Praveen Kumar Bhushan (11/055)

WAVELET TRANSFORMATION:

• Wavelet transform is one of the transformation methods that used to transform signal into the low resolution data by the filters.• The wavelet transformation for an mxn (or 2-dimensional signal)

image usually computes by Discrete Wavelet Transform (DWT).• The result of wavelet transform is created by passing the image

through 4th order Symlet filter of level 2.• The image is decomposed into 4 subbands, denoted by LL, HL, LH, HH.

• The subband denoted by LL is approximately at half resolution of the original image. While the subbands HL and LH contain the changes of image. The subband HH contains the detail in the high frequency of the image.

• the low-frequency components only can be sufficient for recognition. So, if we want to reduce size of the original data by applying wavelet transform, the LL subband of wavelet decomposition is used.

Original Image

After DWT

PRINCIPLE COMPONENT ANALYSIS• PCA represents the image of size mxn pixels by mxn dimensional

vectors, and uses those vectors for computing the mean of vector. • All vectors are subtracted by the mean of vector. The covariance

matrix is the product matrix between the subtracted mean vector and its transpose, as C is expressed as followed:

where C is the covariance matrix, A is the subtracted mean data matrix, m and n are the dimension of the vector data for train.

• The eigenvectors and eigenvalues are computed from the covariance matrix. The eigenvectors with the highest eigenvalue are selected.• The transformation matrix (w) is formed from these eigenvectors in

the column manner.• The extracted feature, of the input data, can be calculated by the

following equation:

Algorithm for Database Generation• Read person name from data folder.• Create a cell array for database.• Take five image one by one for training.• Apply Discrete Wavelet Transform with 4th order Symlet Filter of level 2.• Apply Principle Component Analysis on LL subband.• Take 1st column of extracted features after applying PCA for five images

of a person.• Take mean of extracted features of every person.• Save it into cell array for creating a database.

Algorithm for Test Image• Take an image for testing.• Apply Discrete Wavelet Transform with 4th order Symlet Filter of level

2.• Apply Principle Component Analysis on LL subband.• Take 1st column of extracted features after applying PCA.• Calculate the Euclidean distance between the test image and training

images of database.• Minimum distance between test image and training image gives the

output of the system.

Block DiagramTraining Data Set

Wavelet & PCA

Testing Data Set

Wavelet & PCA

Extracted Features

Extracted Features

Euclidean Distance Result

Thank You