The document presents a major project on face recognition using Discrete Wavelet Transform (DWT) and Principal Component Analysis (PCA) at the University College of Engineering, Rajasthan Technical University. It outlines the algorithms for image processing, highlighting the use of wavelet transformation to reduce image size and PCA to extract features for recognition, ultimately calculating the Euclidean distance between test and training images for identification. Additionally, it details the steps for database generation and testing with a focus on the use of wavelet and PCA techniques.

1. MAJOR PROJECT
PRSENTATION
Face Recognition using Discrete Wavelet
Transform and Principle Component Analysis
UNIVERSITY COLLEGE OF ENGINEERING
RAJASTHAN TECHNICAL UNIVERSITY, KOTA
Submitted To:
Mr. S.R. KAPOOR
Associate Professor
Mr. VIVEK SRIVASTAVA
Associate 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)

2. 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.

3. • 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.

4. Original Image
After DWT

5. 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:
𝐶 𝑛∗𝑛 = 𝐴 𝑚∗𝑛
𝑇
∗ 𝐴 𝑚∗𝑛
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.

6. • 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, 𝑦𝑖 of the input data, 𝑥𝑖 can be calculated by
the following equation:
𝑦𝑖 = 𝑤 𝑇
(𝑥𝑖 − 𝑥)

7. 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.

8. 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.

9. Block Diagram
Training
Data Set
Wavelet &
PCA
Testing
Data Set
Wavelet &
PCA
Extracted
Features
Extracted
Features
Euclidean
Distance Result