Optimal Gabor Filters for High Speed Face Identification
Haiyuan WU
∗, Yukio YOSHIDA and Tadayoshi SHIOYAMA
Dept. of Mechanical and System Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan.
e-mail: [email protected]
Abstract
This paper describes a fast face identification method with Gabor filters. Two efforts are made to achieve the ac- ceptable processing speed: 1) we design the optimal Gabor filters with the arrangement theory that uses a few direc- tions and layers. 2) The transformation with Gabor filters (as called Gabor transformation) is only done over the re- gions around the facial feature points, not the whole input image. The facial feature points extraction is performed by detecting the facial organ regions with color information and edge information, followed by the corner detection in each detected facial organ region with the SUSAN operator.
1 Introduction
Face identification is very important for security, surveil- lance and telecommunication. Various approaches of face identification have been reported. Some of them are tem- plate matching [1], eigen face method [2], etc. There are also some methods using frequency information as feature vectors [3] [4] [5].
Gabor transformation is one of the recognition methods that use frequency domain information. It can analyze in- formation about both the spatial-domain and the frequency- domain simultaneously with a signal. However, the high computation cost of Gabor transformation hinders its use in real time image analysis, even with the help of FFT.
In this paper, we propose a novel method to distinguish an individual in high speed by using optimal Gabor filters.
In order to reducing the processing time, we design Gabor filters with a filter arrangement theory [6]. The resulting Gabor filters have only 4 directions and 3 layers, which are much simpler, compacter and more efficient. Another effort we have done is that we only apply the Gabor transforma- tion to the regions around the facial feature points, not the whole input images.
∗Currently, in Wakayama University, Japan
In the proposal method, we first detect face in an in- put image and estimate its pose by using color information.
Then we rotate the input image according to the estimated face pose to make the face upright. Next, we extract the facial organs with both color and edge information. After that, we merge the two eyes region into one and then ap- ply the Gabor transformation to it. The two outer corners of the two eyes are detected with an integral projection of a Gabor filter output. The detected two outer corners of the two eyes are then used to normalize the size and the pose of the face. The facial features are detected by applying the SUSAN corner detector in operator in each extracted facial organ region. Finally, we apply the Gabor transformation to each small region around the detected facial feature points and perform the face identification by comparing the simi- larity of the Gabor filter outputs with ones of each registered face.
2 Gabor Filter Design
2.1 Gabor Filter OutputLetf(x, y)be the intensity at the point(x, y)in an input image, a Gabor filter output at(x, y)is given by
z(x, y) = ∞
−∞f(x−t, y−s)e−t2+s2σ22ej2π(u0t+v0s)dtds, (1) where(u0, v0)is a particular 2-D frequency,j = √
−1. σ characterizes the spatial extent and the bandwidth of the fil- ter.e−t2+s
2
2σ2 ej2π(u0t+v0s)is the Gabor elementary function.
The Fourier transform of Gabor elementary function will be:
G(u, v) = 2πσ2e−
(u−u0)2+(v−v0)2 2σ2
uv . (2)
Here,σuv ≡1/2πσ. The output of Gabor filter describes the energy at spatial frequency(±u0,±v0)in the direction θof the input image.
2.2 Gabor Filter Design
The property of a Gabor filter is determined by the pa- rametersu0,v0andσ. It is well known that there is a trade- off relation between the frequency accuracy and the position accuracy according to the uncertainty principle. In order to design a set of Gabor filters that makes the product between frequency accuracy and position accuracy to be constant, we let the relation betweenσand radius frequencyr0show in the following
σr0= 1
κ; r02=u02+v02. (3) Here,κ(= 0.2)is a constant.
We consider four filter arrangements to cover the fre- quency plane uniformly as shown in figure 1(a) [6]. Here, r1, r2 (r1 > r2)are coordinates of radius frequency, and q1, q2are coordinates of the phase of the center frequency.
We can decide the grid point ci(i = 1,2,3,4) by the rj(j = 1,2) and theqk(k = 1,2). LetGi (see equation 2) be a filter that makescias the center frequency. We as- sume the pointP(r, q/2)exist, where the output of the four Gabor filters which the center is atci(i=1,2,3,4) respectly became equal, i.e. G1 =G2 =G3 =G4 =ε. Then the ratio ofr1andr2is as following.
r2 r1 = A
1−A, A= 1 2
1−
1−1 + 2κ2lnε cos2q/2
. (4) Here, εis a parameter that decides the density of the fil- ter arrangement,qis the arrangement angle. In this paper, based on the theory that expressed upward and the exper- iment result, we let ε = 0.125andq = 45o. Then, the parameters of Gabor filters are set as:
Low : r0= 0.2, σ= 4, Middle : r0= 0.28, σ= 2.8, High : r0= 0.4, σ= 2.
Figure 1(b) shows the designed Gabor filters. From this fig- ure, we can see that the filters are arranged without double.
3 Automatic Facial Feature Point Extraction
To realize a high-speed personal identification method, the designed Gabor filters are only applied to the small re- gions around the facial feature points, not the whole input image. In this section, we describe the method to extract the facial feature points automatically.
We have built two models to describe the skin color like- ness and the hair color likeness. With these models, we can obtain the SCSM (Skin Color Similarity Map; See figure 2(a)) and the HCSM (Hair Color Similarity Map; See fig- ure 2(b)) by estimating the skin color likeness and the hair
r2 r1 q2
q1 c1 c3 c4
c2
q
p
(a) (b)
Figure 1. (a)Arrangement diagram of Gabor fil- ters; (b)The designed Gabor filters
color likeness of each pixel in an input image [7]. Using both the SCSM and HCSM, we can extract the face region from an image by applying the integral projection method.
Since the shape of head is symmetrical, and it can be con- sidered as an elliptical sphere approximately, we can infer the roll angle of the head by estimating the axis of least in- ertia of the extracted face region (skin color region + hair color region) [8]. We then rotate the image to bring the axis of least inertia to the vertical direction (See figure 2(c)).
Then, we extract the EIM (Edge Intensity Map; See fig- ure 2(d)) and the ESM (Edge Sign Map; See figure 2(e)) from the face region. Using the SCSM, HCSM, EIM and ESM, we can obtain the regions of face organs (See figure 2(h)) including eyebrows, eyes, nose, and mouth from the image by applying the integral projection method [9].
To guarantee a high personal identification rate, the outer corners of two eyes need to be extracted precisely. We merge the regions containing two eyes into one. In this region, we apply the Gabor filter of the highest frequency in 4 directions (See figure 2(f)), and select the biggest out- put among them as the output of the Gabor transformation z(x, y)(See figure 2(g)).
z(x, y) =max{z(x, y; 0.4,0o), z(x, y; 0.4,45o), z(x, y; 0.4,90o), z(x, y; 0.4,135o)}. (5) Then we perform an integral projection for all pixels whose z(x, y)are greater than 0.4 onto the horizontal axis. The horizontal positions of the two eyes are determined by find- ing out the continuous regions from the horizontal integral projection where the integrated value is greater than 20 pix- els. We choose the outer sides of the two eye regions on the horizontal axis as the outer corners of the eyes.
We use the detected outer corners of the eyes to normal- ize the face size by scaling the face image so that the dis- tance between the two outer corners of the eyes becomes 50 pixels. The face pose normalization is performed by rotat- 2
(a)SCSM (b)HCSM (c)
(d) EIM (e) ESM (f) (g)
(h) (i)
Figure 2. Facial feature point extraction
ing the face image so that the line connecting the two outer corners of the two eyes becoming horizontal.
Finally, we use a SUSAN corner detector to detect the corner points in each extracted facial organ region. We choose the leftmost corner point and the rightmost corner point in each facial organ region as the facial feature points (See figure 2(i)) [10].
4 Recognition Method
Let F be the dictionary face image, which has been reg- istered before, and let H be the input image to be identified.
We use the outputs of designed 12 Gabor filters, which are applied to the 8 facial feature points and their vicinity as the feature vectors, which are used to compare an input image with the dictionary images. Figure 3(a) shows the 8 facial feature points Pi(i = 1,· · ·,8) we used. For each small image region around a facial feature point, we estimate the similarity between the small region of the input image and the one of the dictionary face image with a normal correla- tion method as following:
Mk = (fk•hk)
fk • hk ≤1, (6) fk = (fk1(i, j)· · ·fk12(i, j)),hk = (hk1(s, t)· · ·hk12(s, t)),
(7)
(a) (b)
Figure 3. (a) The sed facial feature Points; (b) An example of output of one Gabor filter
wherek(= 1· · ·8)indicates the number of facial features, (fk1· · ·fk12)and (hk1· · ·hk12) are the image set of the Gabor transformation of 4 directions and 3 stages of the input image and dictionary face image, respectively. Re- gion of Gabor transformation is the20×20pixels center- ing around(i, j),(s, t). Figure 3(b) shows an example of the output of one Gabor filter.
We define the similarityM¯ as the average of regular cor- relation of all feature points region. M¯ is calculated as fol- lowing:
M¯ =1 8
8 k=1
Mk. (8)
A face in an input image is identified as the face in the registered face image set that has the highest similarity.
5 Experimental Results
A: Facial Feature Point Detection
We first tested our automatic facial feature point detec- tion on over 100 still color images taken by a digital camera, and another over 100 images taken by a mobile phone with a mobile camera (made by Kyocera). We also tested with live video sequences and several movie videos. The pro- cessing time was about 0.15 second per frame. We show some results of automatic extracted facial feature points in figure 4. From this figure, we can see that almost all of the feature points are extracted precisely.
B: Face identification for size variation
In this experiment,35persons were registered in the dic- tionary image. 140(= 14×10)test images of14persons have been used to test our face identification algorithm. All the test images were taken in normal office environment without any special lighting. All the face in the images were in front pose, and the face size changed from120% to30% 3
relative to the size of the registered face. 130images were identified correctly. The failed10images were the images where the face size was smaller than45%. The reason was that the images were too blurred after scaling to the regular of size.
C: Face identification for face rotation
In this experiment,35persons were registered in the dic- tionary image.60(= 12×5)test images of12persons have been used to test our face identification algorithm. The rota- tional axis was perpendicular to the image plane and the ro- tation angle varies from±5to±30degrees. All test images were taken in normal office environment without any spe- cial lighting, and the face size in all test images was same.
51images were identified successfully, and9images failed.
Figure 5 shows some example of test images.
6 Conclusions
In this paper, we have proposed a new method for face identification, which is able to distinguish an individual in high speed by using Gabor filters. In this method, we have extracted the facial feature points automatically, and have used the Gabor filter outputs of extracted feature point’s vicinity for reducing the processing time.
Extensive experiments show the effectiveness of the pro- posed method for facial images with face size variation from 120% to 30% and the face rotation within the im- age plane from ±5 to±30 degrees. Also, the processing time of Gabor transformation is shortening to 3 seconds on a PC with a 533Mhz Celeron processor (the image size is 640×480pixels).
From now on, we are planning to inspect the efficacy and the effectiveness of this method furthermore by testing it with face images of more person and of some common face database.
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Figure 4. Some experimental results.
(a)120% (b)60% (c)30o
Figure 5. Some example of test images
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