ISSN : 0975-2927
EISSN : 0975-9166
HIREMATH P.S.1*, MANJUNATH HIREMATH2*
1Department of Computer Science, Gulbarga University, Gulbarga-585106, Karnataka, India
2Department of Computer Science, Gulbarga University, Gulbarga-585106, Karnataka, India
* Corresponding Author : manju.gmtl@gmail.com
Received : 06-11-2011 Accepted : 09-12-2011 Published : 12-12-2011
Volume : 3 Issue : 4 Pages : 185 - 190
Int J Mach Intell 3.4 (2011):185-190
DOI : http://dx.doi.org/10.9735/0975-2927.3.4.185-190
Conflict of Interest : None declared
Acknowledgements/Funding : The authors are indebted to the referees for their helpful comments and suggestions. The authors are grateful to the University Grants Commission for the financial support for this research work under UGC-MRP F.No.39-124/2010 (SR) dated 27.12.2010
Face detection is a necessary first-step in face recognition systems, with the purpose of localizing and extracting the face region from the background. It also has several applications in areas such as content-based image retrieval, video coding, video conferencing, crowd surveillance, and intelligent human–computer interfaces. In this paper, we propose a novel approach for the detection of human face in a digital image based on the fuzzy spatial interrelationships of only the prominent facial features of the face, namely, eyes and mouth. A fuzzy face model is constructed for the face detection algorithm. The experimentation has been done using several face databases. The experimental results show that the proposed algorithm performs satisfactorily with an average accuracy of 96.10% and is efficient in terms of accuracy and detection time despite the exclusion of other facial features, namely, nose, eyebrows and ears.
Biometric, face detection, fuzzy face model, feature extraction.
Computer vision, for example, aims to duplicate human vision. Face detection is a necessary first-step in face recognition systems, with the purpose of localizing and extracting the face region from the background. It also has several applications in areas such as content-based image retrieval, video coding, video conferencing, crowd surveillance, and intelligent human–computer interfaces. Of late, the face detection problem has received considerable attention among researchers. The human face is a dynamic object and has a high degree of variability in its appearance, which makes face detection a difficult problem in computer vision. A wide variety of techniques have been proposed, ranging from simple edge-based algorithms to composite high-level approaches utilizing advanced pattern recognition methods.
A survey of literature on the research work focusing on various potential problems and challenges in the face detection and recognition can be found in [2-4] . Face detection using fuzzy pattern matching method based on skin and hair color has been proposed by Wu H.Q et al. [5] . This method has high detection rate, but it fails, if the hair is not black and the face region is not elliptic. In [6] , the face regions are detected using quantized skin color region merging and wavelet packet analysis. This method efficiently detects the faces with different size and poses. However, it is computationally expensive due to its complex segmentation and higher detection time.
A geometrical approach for facial feature generation based on the spatial relationships among them is expected to be less sensitive to the variations in the illumination conditions of the input image. In [7] , the facial features are detected in a gray scale image using only the geometrical approach, which requires more computational time for the processing of the input image and the grouping process performed before the facial feature extraction. Further, this approach is improved by Hiremath and Danti [11] [12] by using fuzzy mathematical approach for face model construction including the features, namely, the eyes, mouth, nose, ear and eyebrows, which are shown to be the discriminating features especially in the case of upright frontal human face detection. In this paper, we propose a novel fuzzy face model approach for the detection of human face in a digital image based on the fuzzy spatial interrelationships of only the prominent facial features of the face, namely, eyes and mouth, in order to reduce the detection time without sacrificing the accuracy.
In the proposed approach, the input image is preprocessed and then the eyes are searched on the basis of geometrical knowledge of the symmetrical relations between eyes. The other prominent feature mouth is searched with respect to the detected eyes using fuzzy rules and the face detection algorithm. The fuzzy rules are derived from the knowledge of the relative positions of the facial features in the human faces and the trapezoidal fuzzy membership functions to represent the uncertainty of the locations of the facial features due to variations in poses and facial expressions. The input image is expected to contain single frontal view face. For experimentation, the dataset contains 700 test images that are drawn randomly from the standard databases, viz. MIT, ORL, color FERET, Biometric Ideal database and CMU databases. The block diagram of the proposed approach is shown in the [Fig-1] .
The input image may be color or gray scale image which is not too dark or too bright. If the input image is an RGB color image, it is converted into gray scale image. The
gray scale image is filtered using the Sobel horizontal edge emphasizing filter and utilizing the smoothing effect by approximating a vertical gradient. In the filtered image, objects of interest (facial features) are brighter than the background. In order to make the essential facial features clearly visible, filtered image is converted into binary image by simple global thresholding [1] . Further, the image is denoised by morphological operations, in which opening operation is performed to remove noise, and then the closing operation is performed to remove holes. Then the active pixels are grouped into maximal connected blocks to get the labeled regions or blocks. After the labeling process, for each feature block, its center of mass (), orientation θ, bounding rectangle and the length of semi major axis are computed.
The facial feature blocks in the labeled image are evaluated in order to determine which combination of feature blocks is a potential face [12] , in which we first search eyes and then other facial features, such as mouth with respect to eyes. The eyes are detected by exploiting the geometrical configuration of the human face. Initially, we select any two feature blocks arbitrarily and assume them as probable eye candidates, the corresponding center of mass () and orientation θ are computed. The line passing through the center of both the feature blocks is called as the horizontal-reference-line (HRL). The slope angle θHRL is constrained within the range of -45o to +45o. If the current pair of the feature blocks does not satisfy this orientation constraint, then they are rejected and another pair of feature blocks from the remaining feature blocks is taken for matching. Only for the accepted pairs of the features, the normalized lengths of the semi-major axis l1 and l2 are computed by dividing the length of the semi-major axis by the distance D between these two features. The θ1 and θ2 are the orientations of the above accepted blocks. The evaluation function Eeye is computed to check whether the current pair of features is a potential eye pair or not. If the evaluation value is greater than an empirical threshold value 0.56, then we accept these two feature blocks as the potential eye pair candidate. For this potential eye pair candidate, we construct the fuzzy face model and search for the mouth feature [12] , which is described in the Appendix. Once the potential eyes are found, the fuzzy face model is constructed as shown in the [Fig-2] . A line perpendicular to the HRL at the mid-point of the two eyes is called as vertical reference line (VRL). Let (p,q) be the mid-point of the line segment joining the centers of the two eye candidates. These two reference lines are used to partition the facial area into quadrants as shown in [Fig-2] . The vertical and horizontal distances of the mouth facial feature is estimated in terms of the distance D between the centers of the two eyes on the basis of the observations from several real faces. The notation Vmouth and Hmouth denote the vertical and horizontal distances of the centers of mouth. The support regions of the facial features are determined using the empirical values given in the [Table-1] .
Let a feature block K be a potential mouth feature. The horizontal distance Hmouth and the vertical distance Vmouth of the centroid of the Kth feature from the VRL and HRL, respectively, are computed using the equation:
Hmouth = , Vmouth =
Treating Hmouth and Vmouth as the fuzzy quantities to represent the possible location of the potential mouth feature, the fuzzy membership values µHmouth and µVmouth respectively, are defined using trapezoidal fuzzy membership function and the statistical distribution of these values for the images in the chosen data set. In particular, the membership function µVmouth is defined as following:
If Vmouth ≤ minVmouth,
µVmouth(Vmouth) =0.
If (min Vmouth ≤ Vmouth ≤ α),
µVmouth(Vmouth) = .
If (α ≤ Vmouth ≤ β),
µVmouth(Vmouth) =1.
If (β ≤ Vmouth ≤ max Vmouth),
µVmouth(Vmouth) = .
If(Vmouth ≥ maxVmouth),
µVmouth(Vmouth) = 0.
where = mouth-0.5σ and
+ 0.5σ; and minVmouth, maxVmouth,
and σ are the minimum, maximum, mean and standard deviation of the vertical distances of the centroid of the mouth feature, respectively, which are the empirical values obtained from the chosen data set presented in [Table-1] , and are used to determine the support region for the potential mouth feature is the set of values Hmouth and Vmouth, whose fuzzy membership values are non-zero. The [Fig-3] shows the graph of the trapezoidal fuzzy membership function µVmouth for the vertical distance of the mouth facial feature.
To evaluate Kth feature block in the support region for mouth, the value of the evaluation function Ek given by the following equation is computed.
The Ek value ranges from 0 to 1 and represents the probability that the feature block K is a mouth. The evaluation value Emouth is a fuzzy quantity represented by the set of Ek values with their corresponding fuzzy membership values µk; and the membership value µmouth corresponding to Emouth is obtained by the min-max fuzzy composition rule:
µk = min(µhmouth, µvmouth), for each k,
µmouth = max{µk}
The feature block having the evaluation value Emouth with the corresponding µmouth found in the support region of the mouth is the potential mouth feature with respect to the current pair of potential eye candidates.
The overall fuzzy evaluation E for the fuzzy face model is defined as the weighted sum of the fuzzy evaluation values of the potential facial features, namely, Eeye, Emouth for the eye and mouth respectively. The weights are adjusted to sum to unity as follows:
E = 0.9 Eeye + 0.1 Emouth
and its membership value µE is obtained by the fuzzy composition rule: µE = min{µmouth}, since the eyes are considered as the most important facial feature, the weight for eye is set to be higher than the other facial features. The mouth feature is assigned the second weight.
The above procedure is repeated for every eye pair candidate leading to the set of fuzzy faces. These fuzzy faces are represented by the set of E values with their corresponding membership values µE. Finally, the most probable face is obtained by the defuzzification process as follows:
For the set Ω of E values, find the maximum membership value µEmax given by:
µEmax = max{µE}
Then the E value corresponding to µEmax is the defuzzified evaluation value ED of the face. If there are more than one E value corresponding to µEmax, the maximum among those values is the defuzzified evaluation value ED of the face.
Fuzzy face detection algorithm:
An algorithm for the detection of single face in the given image, using the fuzzy face model, is as given below:
Step 1: Input the labeled image.
Step 2: Select any pair of feature blocks to be probable eye candidate blocks in the input image.
Step 3: Compute the slope angle θHRL of the two feature blocks and if it is 45o, then compute the evaluation value Eeye. If the Eeye is greater than the empirical threshold value 0.53, then these feature blocks are accepted as the potential eye candidates. Further, with respect to these potential eye candidates, construct the fuzzy face model.
Step 4: For searching mouth, choose any feature block K located in the support region of the mouth determine its horizontal and vertical distances hmouth and vmouth respectively. Then compute evaluation value Ek.
Step 5: Determine fuzzy evaluation value Emouth of the mouth and its membership value µmouth by computing the membership values µk of Ek for every feature block K in support region of the mouth using the min-max fuzzy composition rule.
Step 6: Compute the overall fuzzy evaluation value E of the fuzzy face with respect to the eye pair candidate, and also compute the membership value µE using fuzzy composition rule.
Step 7: Perform the defuzzification process. For the set Ω of {E, µE} values find the maximum membership value µEmax. Then the E value corresponding to µEmax is the defuzzified evaluation value ED of the face. If there is more than one E value corresponding to µEmax, the maximum among these values is the defuzzified evaluation value ED of the face.
The potential eyes, mouth features corresponding to the overall evaluation value ED is greater than the empirical threshold 0.53. Otherwise, the input image contains no face.
The effectiveness of the proposed approach is demonstrated with the compound data set containing 660 test images chosen randomly from the standard databases viz., MIT, Color FERET database, BioMetric Ideal Test database, CMU image Database, Georgia Tech Face Database, Indian Face Database, LFW Face Database, The BioID Face Database. The implementation is done on DELL OptiPlex 380 PC, Intel Core 2 Quad PC@2.66 Ghzmachine using MATLAB 7.9.The experimental results of the face detection by the proposed method is shown in [Fig-4] .
To demonstrate the effectiveness of the proposed approach, our test images in the dataset are expected to contain single frontal face with varying size, poses, expressions, head tilts, lighting conditions and background. In the dataset, we have used both color and gray scale images excluding too dark or too bright images to achieve satisfactory results. The proposed approach will precisely locate the facial features and shows detected face in a box.
The performance of our approach on the different databases used in the compound dataset is given in the [Table-2] .
The proposed approach has achieved good detection rate and time for the FERET and ORL databases due to the images containing simple backgrounds and reasonable variations
in poses, expressions and lighting conditions as compared to the images of MIT, CMU and CIT databases, whose images contain complex background and more variations in poses, expressions, orientations and lighting conditions. The comparison performance of proposed method with other face detection methods is given in the [Table-3] .
The eyes are searched by exploiting the geometrical configuration of the human face in which the symmetrical relations between the eyes are as shown in the [Fig-5] . All the feature blocks in the labeled image are evaluated in order to search eyes [11] [12] . Initially, we select any two feature blocks randomly and assume them as probable eye candidates. Their corresponding center of mass () and orientation θ are computed using the equations:
where (i,j) order central moments μi,j are given by:
and B denotes feature block. Let (x1, y1) and (x2, y2) be, respectively, the centers of right feature block and left feature block [Fig-4] . The line passing through the centers of both the feature blocks is called as the horizontal-reference-line (HRL) and is given by the equation:
ax + by + CHRL = 0
where, a = y2 - y1, b = x1 - x2, CHRL = x2y1 - x1y2, and the slope angle θHRL between the HRL and x-axis is given by:
θHRL = tan - 1(-a/b), - /2 ≤ θHRL ≤
/2
Since the proposed face model is a frontal view model, a face in a too skewed orientation is not considered in this model. Hence, the slope angle θHRL is constrained within the range of − 45o to 45o. If the current pair of feature blocks does not satisfy this orientation constraint, then they are rejected and another pair of feature blocks from the remaining feature blocks is taken for matching. Only for the accepted pairs of features, the normalized lengths of the semi major axis l1 and l2 are computed by dividing the length of the semi major axis by the distance D between these two features:
D = [ (x1-x2) 2 + (y1-y2)2 ] 1/2
The following evaluation function Eeye is computed to check whether the current pair of feature is potential eye pair or not:
Eeye = exp [ -1.2 ((l1 - l2) 2 + (l1 + l2 - 1) 2 + (θ1 - θHRL)2 + (θ2 - θHRL)2) ]
Here the term (l1 - l2) 2 enforces similar length between two eyes. The term (l1 + l2 - 1)2 enforces the distance D between two eyes to be twice the length of each eye. The term (θ1 - θHRL) 2 and (θ2 - θHRL) 2 enforces both the eyes to be aligned with the HRL. This evaluation function ranges from 0 to 1 and it can be given the interpretation of a probability value.
In this paper, a novel approach for the detection of human face in an image based on the fuzzy geometrical configuration of the prominent facial features of the face, namely, eyes and mouth, is presented. The feature extraction process is performed in the support regions, which are determined by the fuzzy rules. The single frontal human face in the images with different face sizes, head tilts, lighting conditions, expressions and background are detected successfully. The proposed approach is robust with better average detection rate of 96.10% approximately and takes less detection time as compared to the methods in [11] [12] .
The authors are indebted to the referees for their helpful comments and suggestions. The authors are grateful to the University Grants Commission for the financial support for this research work under UGC-MRP F.No.39-124/2010 (SR) dated 27.12.2010.
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 | Fig. 1- Block Diagram of the proposed Fuzzy face model Approach |
 | Fig. 2- Fuzzy face model with support region for mouth |
 | Fig. 3- Trapezoidal fuzzy membership function µVmouth for the vertical distance of the mouth feature. |
 | Fig. 4- (a) Original input image (b) Binarized image using Global Threshold (c) Feature extraction and probable eye pair detection (d) detected face |
 | Fig. 5- Symmetrical relations between eyes |
 | Table 1- Empirically determined distances Vmouth and Hmouth of the mouth feature (normalized by D). |
 | Table 2- Average detection rate for different face image databases. |
 | Table 3- The comparison of performance of the proposed method with other face detection methods |