Frontal Facial Symmetry Detection Using Eigenvalue Method

Facial symmetry is correspondence of face components on the both sides of face, left and right of a dividing line or about a center or an axis. Most of the research use face component like eyes, nose and ears component to identify facial symmetry. In this paper we suggest to add mouth as another face component to increase accuracy in facial symmetry detection. The results of facial symmetry detection are used for authentication process, analysis in medical, psychology and anthropology scope. By using MATLAB 7.1 we develop a program that can analyze face,asymmetry or not with utilizing eigenvalue. The contribution of this analysis is to know whether eigenvalue is suitable or not in analyzing facial symmetry.

As one of the most successful applications of image analysis and understanding, face recognition has recently received significant attention, especially during the past few years.Undoubtedly if face recognition attract researchers from many disciplines such as image processing, pattern recognition, neural networks, computer vision, computer graphics, and psychology.One of Face Recognition topic is Facial Symmetry Detection.
Symmetry means exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.In mathematic, symmetry defines as an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane.Facial symmetry is correspondence of face components on the both sides of face, left and right of a dividing line or about a center or an axis.Many paper and article from previous works claim that facial symmetry detection is a difficult task, for example in Y.Liu's paper that used eyes and nose to detect facial symmetry [1] and Maria Chan's that measure the position of face component to center line to detect facial symmetry [2].
The main point of facial symmetry is the same position and distance of face components both in left side and right side.But there is a problem in measuring position and distance of face components.Eigenface method is the answer for this problem.
Eigenface are a set of eigenvectors used in the computer vision problem of human face recognition.Basically, eigenfaces are a set of "standardized face ingredients", derived from statistical analysis of many pictures of faces.Any human face can be considered to be a combination of these standard faces.The higher the value, the closer the face is to that eigenface.Remarkably, it does not take many eigenfaces summed together to give a fair likeness of most faces.Also, because a person's face is no longer recorded by a digital photograph, but instead as just a list of eigenface values (one value for each eigenface in the database used), much less space is taken for each person's face.Eigenface consist of two, eigenvalue and eigenvector.
Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144) The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems, to name only a few.Each eigenvalue is paired with a corresponding so-called eigenvector (or, in general, a corresponding right eigenvector and a corresponding left eigenvector; there is no analogous distinction between left and right for eigenvalues).
Measurement of facial symmetry have many advantages.In Psychology and anthropology, symmetry face are more useful then asymmetry face.Psychologists and anthropologists have considered facial asymmetry as a critical factor that can be used to evaluate attractiveness and expressions [3], even though most of it was done qualitatively using human observers.The approach that we want to do in this paper is to know whether eigenvalue is suitable or not in analyzing facial symmetry.

APPROACH
The general concept of the process is to measure distance between each face component and calculate the eigenvalue of each distance [4].The eigenvalue of left side will be compare with right side.
Liu in his paper, proposed that to do facial symmetry detection, there are three point of face components used.Left eye, Right eye and nose which compose a triangle.By using only three face components, detection of facial symmetry will not be maximum.Example, if the detecting face have an abnormal mouth position, it will be a problem.In figure 1, if only used three components the face will be detected as symmetry face.Whereas, the mouth position is not symmetry.
To reduce this misidentification, we proposed to add mouth as another face component to increase accuracy in facial symmetry detection.Distances between each face component are distance from points existed in the face component square [4].There are center point of right eye square, left eye square, mouth and nose.
From measurement above, we got eight distances which

EXPERIMENTAL RESULT
This experiment is conducted by using face database from Student Image database from Gunadarma University.All of the images are in frontal position.The image will be grouped which consist of 8 images of each, to make block matrix of eigenvalue.By checking eigenvalue, we can analyze facial symmetry.
We divided the experiment into two based on the combination of input data.

Facial Symmetry Detection with Randomize Data
In this experiment, we use 150 image data which consist of 8 face component distance of each.All of image data will be rendomized and grouped into 50 blocks of matrix with 8 image each group.So, From 50 blocks of matrix will be occured some repeating in use of image data.
From analysis of eigenvalue and eigenvector table, there are some images that have same value of j2-j3, j4-j5, or both of it.There are 101 images classified as partial symmetry image, 48 images classified as absolute symmetry and 104 images classified as not symmetry.
In this experiment, the repeated images are grouped into different matrix block combination.So, it can influence the calculation result.There are 4 images that classified in absolute symmetry class only, image 35, 58, 96 and 137.It is 2,6% from image database.It shows that success rate of this method is still small.

Figure 1 :
Figure 1: Analyze facial symmetry by using three components

Figure 2 :
Figure 2: Face components that will be used in this analysis

Figure 3 :
Figure 3: Eight distance that will be used in this analysis

Figure 5 :
Figure 5: Eigenvector and eigenvalue from first experiment

Figure 6 :
Figure 6: Symmetry face result from first experiment

Figure 7 :
Figure 7: Eigenvector and eigenvalue from second experiment

Figure 8 :
Figure 8: Symmetry face result from second experiment

Figure 9 :
Figure 9: Symmetry face result from first and second experiments

Table 1 :
First experiment matrix example

Table 2 :
Second experiment matrix example