Eigenface

Eigenface Tutorial

Keywords: Matlab, Face Recognition, Eigenfaces, Computer vision

         


This picture represents the set of images used to create our eigen space for face recognition. The goal of this tutorial is to apply the eigenface approach to recognize someone's face. The overall
problem is to be able to accurately recognize a person's identity and take some action based on the outcome of the recognition process. Recognize a person's identity is important mainly for security  reason, but it could also be used to obtain quick access
to medical, criminal, or any type of records. Solving this problem is important because it could allow personnel to take preventive action action, provide better service - in the case of a doctors appointment, or allow a person access to a secure area. This
tutorial will shows you how to build a face recognition program using Matlab.

Motivation and Audience

This tutorial has been developed to get people interest on computer vision and face recognition; in addition to give you some guidance on how to approach the problem. The reader should have the following
background and interests:

Moderate Matlab knowledgeBeing familiar with Linear Algebra conceptsDesire to learn about face recognition using MatlabIn addition, would like to learn more about computer visionThe rest of the tutorial is presented as follows:

Parts List and Sources
Construction
Programming
Final Words
 

Parts List and Sources

US-based vendors to obtain material to complete this tutorial include 
Mathworks

To complete this tutorial, you'll need the following items 

 

Software	VENDOR	Version	PRICE	QTY
Matlab	Mathworks	6.1	$500	1

Construction

This section gives step-by-step instructions along with photos and formulas on how to recognize faces and implemented into Matlab. All the necessary files to complete this tutorial would beprovided.

Steps

The first step is to obtain a set S with M face images. In our example M = 25 as shown at the beginning of the tutorial. Each image is transformed into a vector of size N and placed into the set.



After you have obtained your set, you will obtain the mean image Ψ

 





Then you will find the difference Φ between the input image and the mean image



Next we seek a set of M orthonormal vectors, un, which best describes the distribution of the data. The kth vector, uk, is
chosen such that



is a maximum, subject to



Note: uk and λk are
the eigenvectors and eigenvalues of the covariance matrix C

 

We obtain the covariance matrix C in the following manner

 





AT



Once we have found the eigenvectors, vl, ul





These are the eigenfaces of our set of original images
 
Recognition Procedure
1. A new face is transformed into its eigenface components. First we compare our input image with our mean image and multiply their difference with each eigenvector of the L matrix. Each value would represent a weight and would be saved on
a vector Ω.


    


2. We now determine which face class provides the best description for the input image. This is done by minimizing the Euclidean distance



3. The input face is consider to belong to a class if εk is bellow an established threshold θε. Then the face image is
considered to be a known face. If the difference is above the given threshold, but bellow a second threshold, the image can be determined as a unknown face. If the input image is above these two thresholds, the image is determined NOT to be a face.
4. If the image is found to be an unknown face, you could decide whether or not you want to add the image to your training set for future recognitions. You would have to repeat steps 1 trough 7 to incorporate
this new face image.
See Results
 

The source code face recognition using Matlab is provided below: