Face Recognition Technique Based on Eigenfaces Method

Transcription

1 Face Recognition Technique Based on Eigenfaces ethod S Ali * and KA AL-Phalahi ** * Remote Sensing Unit, College of Science, University of Baghdad, Iraq, Baghdad, Al- Jaderyia ** Department of Computer Science, College of Science, University of AL-Nahrain, Iraq, Baghdad, Al-Jaderyia Sensingremote@gmailcom Abstract A robust recognition technique for identifying and recognizing human-face images is presented The recognition process utilizes the mean reduced faces to produce the Eigenface basis for the face space s eigenvalues and eigenvectors are computed, using covariance matrix algorithm The least square criterion is then utilized to determine the similarity between the existed (in Database file) faces with a new face s images A threshold value is designed to differentiate between existed and non-existed stored face s images 1 Introduction Face Recognition has a fundamental importance in our social relationships, being extremely valuable to our simple and daily activities Nowadays, Face recognition motivates great research efforts, because it satisfies many criteria in choosing the ideal biometrics solution; say it is fast, convenient and essentially remote It is very useful to identifying individual in international traffic points, in crime scenes, in access control and in many other fields The idea concerning measure comparison in which biometrics characteristic are extracted from the face image to compare with the measures of another face in order to succeed in face recognition [1] Face Recognition is part of a larger context called Biometrics that give us the notion of life measure, it can be defined as the physiologic or psychological characteristics that can be used to verify an individual's identity Biometrics techniques are divided in two categories: physiologic and psychological The physiologic biometrics is based only on the physiologic aspects of the body, and the most common are: face, fingerprint, hand geometry, iris and retina The psychological biometrics is based mainly on the psychological aspects, and the most common are: handwritten signature and voice The biometrics system is essentially a pattern recognition system that makes a personal identification determining the authenticity of a specific physiologic or psychological characteristic of an individual The biometrics systems are subjected to the Principle of Threshold Accordingly, a face is recognized if its features lie inside on acceptance range [] This principle defines some uncertainty degree in results that imply obtaining more than one answer as a searching result, eventually needing human intervention for the correct alternative choice Based on psychological point of view, there are two face recognition levels: entrance level and subordinate level In the entrance level, all the faces are noticed as an only face category, and in the subordinate level, the individual faces are distinguished by more detailed characteristics [1] 1

2 Problem of Face Recognition Given a training set of face images (as those shown in fig1), they represent some face space with high dimensionality; the problem is to verifying if a new face image belongs to one of the individuals or not Here we need to match this new image to one of existing face images in database and perform face recognition making use of Eigenfaces Approach [3] Generally, face recognition methods are framed in three different categories: Template-based, Feature-based and Appearance-based [4] Template-based method represents the faces by means of two-dimensional template with values representing the facial ellipse borders and of all faces organs It can also be presented as multiple templates for the face representation, under several angles and points of view Another important approach is the use a group of smaller facial characteristics models, corresponding to the eyes, nose and mouth, for an only point of view The most attractive advantage of this model is its simplicity, while its disadvantage is to need of great amount of memory and its inefficient comparison method Feature-based method it considers the positions and sizes of the facial organs, as eyes, nose, mouth, etc, in the face representation This method consumes very less computer resources than the template-based method, facilitating larger processing speed, with good acting with face database in varied scales Appearance-based method it intends to project the face images in a low dimension subspace, to obtain the face representation The Eigenfaces space is an application of this method It is built on Principal Component Analysis, from the projection of the images of the training set into the face space with low dimension [3] (1) () (3) (4) (5) Figure1: Training set of five face images, each of pixels size 3 Principle Component Analysis (PCA) It is a way for identifying patterns in data, and expressing the data in such a way as to highlight their similarities and differences Since patterns in data can be hard to find in data of high dimension, where the luxury of graphical representation is not available, PCA is a powerful tool for analyzing data The other main advantage of PCA is that; you can use it to compress the data size, ie by reducing the number of dimensions, without much loss of information [5] The main advantages that are gained from the PCA are: 1 Smaller representation of database because we only store the training images in the form of their projections on the reduced basis Noise is reduced because we choose the maximum variation basis and hence features like background with small variation are automatically ignored 4 The Recognition ethodology Suppose you have face images of the training set are submitted to a face detection algorithm All face images must be in same size (eg n n pixels) These

3 images are firstly arranged in an array, as column vectors, each of N 1 dimension (N= n n) This arrangement occurs by taking every row of the trained images and concatenating them, each one after to the other; as given by: 1,1,1 3,1 N,1 1 1,, 3, N, 1,3,3 3,3 N,3 3 1,, 3, N, (1) Thus, the average face Ψ of all training set plus the test image can be represented by [5]: 1 1, k k 1 1, k k , k N,1 k 1 () 1 1 N, k k 1 This column vector image Ψ N,1 can easily be retransformed into D image space Ψ(n,n) by inserting it in an empty array of size n n pixels Figure shows the average of the training set, shown in fig1 Figure: The average face of the training set shown in fig1 Once calculating the Ψ average face, a new Φ group of images is set up, obtained from the difference between each image of the training set and the average face; ie i i for i 1,,, (3) Each Φ, (referred as eigenface), will go far away from the average face, as shown in fig3 3

4 (1) () (3) (4) (5) Figure3: ean reduced (eigenfaces) of the 5 training set of images, shown fig1 From the group of Φ images, the covariance matrix Cov can be computed as: Cov T (4) Where: T represents matrix transposition As an example, for the set of eigenfaces show in fig3, the covariance matrix (size 10 10) is symmetric around the diagonal, as shown in table-1 below: Table-1: The elements of the symmetric covariance matrix for the tested set of eigenfaces Eigenfaces eigenface 1 eigenface eigenface 3 eigenface 4 eigenface The eigenvalues and eigenvectors V of a square symmetric matrix Cov are, respectively, scalars and nonzero vectors that satisfy the following matrix product formula: [ Cov][ Vi ] i[ Vi}, for i 1,,, (5) Computation of the eigenvalues and eigenvectors can be performed by fast algorithm following the procedures given in [6] As an example, the eigenvalues and the eigenvectors for the set of eigenfaces shown in fig3 are: Eigenvalues Eigenvectors eigenface 1 eigenface eigenface 3 eigenface 4 eigenface If a new face image to be verified is entered with the training set, the matrix in eq(1) becomes: 4

5 1,1,1 3,1 N,1 1 1,, 3, N, 1,3,3 3,3 N,3 3 1,, 3, N, 1, 1, 1 3, 1 1 N, 1 (6) Suppose an existed image within the trained set has been selected to be verified, as illustrated in fig4 (1) () (3) (4) (5) + Figure4: The Training set of face images plus an existed test face to be verified Following the same procedures being done for the trained set (mentioned above), the eigenvectors for the new set of images will be: Eigenvectors eigenface 1 eigenface eigenface 3 eigenface 4 eigenface 5 eigenface As it is obvious, the similarity between the verify face and the trained set can be represented by the minimum distance test (ie utilizing the ean-square-error SE criterion), given by: in{ SEK } in{ ( VK, i V 1, i ) }, for K 1,,, (7) i The in{se} between trained eigenfaces and the verifying eigenface is, obvious, between V 4 and V 6 ; ie in{se K }=SE 4, as listed below: SE SE 1 SE SE 3 SE 4 SE

6 Let us now examine a different scene for an existed face, as illustrated in fig5 below; (1) () (3) (4) (5) + Figure5: The Training set of face images plus a verify existed face of different scene Once again, the eigenvectors of the new set of images are: Eigenvectors eigenface 1 eigenface eigenface 3 eigenface 4 eigenface 5 eigenface The SE between trained eigenfaces and the verifying eigenface, respectively by substituting (=5, 4, 3,, and 1) in eq(7) are as listed below: SE/ SE 1 SE SE 3 SE 4 SE As it is obvious, face 4 yields minimum SE for the first four elements of the eigenvectors, despite the huge differences between face 4 and the verifying face (ie both belong to the same person) 5 Conclusion: A very encouraging matching and verifying result has been satisfied by implementing the eigenfaces algorithm The result can be improved if pure face images were adopted (ie background free), and having same scales (ie viewed by the same camera at a fixed distances from the person s face, and using unvaried 6

7 illumination) However, certain image preprocessing operations may still required to enhance the results (eg image normalization, image re-centering, etc) References: [1] D Waldoestl, D, Lizama, E, and Nickolay, B, An eigenface based automatic face recognition system Fraunhofer, Germany, (1997) [] Turk,, and Pentland, A, Face recognition using eigenfaces e-dia Laboratory, IT Press, (1991) [3] Turk, A, and Pentland, A, Eigenfaces for recognition Journal of Cognitive Neuroscience, (1994) [4] Pablo Navarrete and Javier Ruiz del Solar Analysis and comparison of eigenspacebased face recognition approaches Universidad de Chile,Chile,( 00) [5] Turk, A, and Pentland, A, Eigenfaces for recognition Journal of Cognitive Neuroscience, (1994) [6] Harris, F J "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform" Proceedings of the IEEE Vol 66 (1978) ** * األستاذ الدكتور صالح مهدي علي و خمائل عباس الفالحي *وحدة االستشعار عن بعد/كلية العلوم / جامعة بغداد **قسم علوم الحاسبات/ كلية العلوم/ جامعة النهريين العراق بغداد الجادرية الخالصة: تم استحداث تقنية متقنة لتميز صوور وجووإ ساسوااية تتضومن التقنيوة اسوتخدام موا يعورر بجوور وجووإ الحاتيوة وحسوا المتجهات والقيم الحاتية لها ومن ثم مقاراتها باستخدام معيوار المربوا األصوغر لبيواى مودش التشوابال تو االخوتالر بوين تلو الجور تستخدم البحث قيم عتبة تعتمد عدد مكواات متجال الترابط الحاتي للتميز بين الجور المخزواة في قاعوة البيااوات والجور المدخلة حديثا 7