A NEW ROBUST FACE DETECTION IN COLOR IMAGES Sanun Srisuk and Werasak Kurutach Advanced Machine Intelligence Research Laboratory Department of Computer Engineering Mahanakorn University of Technology, Bangkok, Thailand. sanun, werasak @mut.ac.th Abstract having both simple and complex background scenes. Skin color [2,3,6,9,11-14,18,20-22] has been widely used with In this paper, we propose a novel approach for robust skin shape analysis [6,13,18,21,22] and facial feature extraction segmentation and face similarity measure. The proposed [2,3,11,12,20], to speed up the face detection process and skin segmentation is a method for integrating the chromi- to reduce the false alarm rate. Although skin detection has nance components of any color model. The goal of the widely been investigated using so many approaches, i.e., method of skin detection is to select the appropriate color statistical analysis [10,11], fuzzy pattern matching  and model for verifying the skin pixel under different lighting color region mapping [18,21,22], there are still many open conditions and various types of skin color. The enhanced problems to be explored. Neural networks (NN) [8,9,17,20] Hausdorff Distance, called RAMHD, is used to measure the have been proposed for detecting faces in grey images. The similarity between the face edge and an elliptical model in computational complexity is very high because neural net- the skin area. This method is very robust to the occlusions works have to process many small local windows in the im- of the face edge. Finally, the results of face similarity mea- ages. In addition, support vector machines (SVM) [7,16] sure will be improved by updating the elliptical model. We have also been applied to the face detection. The two will show the performance of skin segmentation and face methodologies use the same approach in training with the similarity measure with real images. face and nonface database. The SVM performs slightly bet- ter and is approximately 30 times faster than the NN . In 1. INTRODUCTION recent years, the Hausdorff Distance (HD) [1,6,21,22] has been proposed for detecting human face by measuring the Automatically detecting human faces is becoming a very similarity between the elliptical model and the face edge. important task in various applications, i.e., human computer The advantage of using the elliptical ﬁtting technique is that interaction (HCI) and video indexing. In HCI, computers it is more robust against noise and changes in illumination. can adjust their behaviors by knowing the user’s feeling This paper presents a fast algorithm of face region detec- through his or her facial expressions. In this application tion based on color and shape analysis. Firstly, we will pro- the location of face must known a priori, before the ex- pose a novel method for integrating the well known color pression of the face can be analysed. In video indexing, models by using Bayesian estimation and fuzzy set based the human faces must be discovered as fast as possible due concept. Secondly, the shape analysis is performed by us- to the large video database. Although several methods are ing RAMHD, an enhancement of the conventional Haus- currently used to perform the face detection, there are still dorff Distance [4,5]. Finally, we will provide an efﬁcient many factors that make the face detection more difﬁcult, algorithm for updating the elliptical model. The algorithm such as scales, locations, orientations (upright and rotation), introduced here is faster and more reliable than others even occlusions and poses. However, a face detection technique in the case where the image contains multiple faces, failure that can be used in any real time application needs to sat- features and occlusions of the edge of faces. isfy a number of important criteria: (1) All the true faces The organization of this paper is as follows. In section should be detected as fast as possible. (2) Face detector 2, we present our contribution in the area of face detection, should be robust with repect to occlusion and failure of the which includes our proposed robust skin detection based on edge of face. (3) No false face should be detected. (4) Bayesian estimation and fuzzy membership concept, a fast All of faces should be found automatically without the re- and accurate face similarity measure based on robust Haus- quirement of system to adjust the parameters in the process. dorff Distance and a formulation for updating the elliptical (5) Face detector should discover the faces from images model. Section 3 will show and discuss the experimental re- sults of our face detection algorithm in real image. Finally, Ô´Û ½ ¾ µ is the a posteriori probability of Û , given conclusions will be presented in section 4. chrominance components ½ and ¾ . To solve the problem of ﬁnding an appropriate color model, the maximum a pos- teriori (MAP) is used, and deﬁned as 2. FACE DETECTION ALGORITHM Å Ö Ñ Ü Û Ô´Û ½ ¾µ In this section, we will present our face detection algorithm Ô´ ½ ¾ Û µ ¡ Ô´Û µ Ö Ñ Ü in three parts: skin detection using Bayesian estimation and Û Ô´ ½ ¾µ fuzzy set concept, face similarity measure using RAMHD Ö Ñ Ü Û Ô´ ½ ¾ Û µ ¡ Ô´Û µ (4) and a method for updating the elliptical model. From eq. (4), the probability Ô´ ½ ¾ µ can be dropped because it is a constant independent of Û . The result of 2.1. Skin detection under different races and varying il- MAP is Û that maximizes the probability of Ô´Û ½ ¾ µ. lumination conditions This implies that we should select the chrominance com- ponents if the result from eq. (4) is Û ½ (skin). Thus, the Color is a useful piece of information in computer vision decision function can be deﬁned as the followings: especially for skin detection. The skin detection is an early Ô´ ½ ¾ Û½ µ ¡ Ô´Û½ µ Ô´ ½ ¾ Û¾ µ ¡ Ô´Û¾ µ µ ½ ¾ ¾ Û½ (5) process used to avoid the exhausive search for faces. How- ever, there are many color models that can be used for dis- Ô´ ½ ¾ Û¾ µ ¡ Ô´Û¾ µ Ô´ ½ ¾ Û½ µ ¡ Ô´Û½ µ µ ½ ¾ ¾ Û¾ (6) criminating color information in modeling skin color. In , Liu has contended that there does not exist a single The chrominance components in a given color model will color space that is appropriate for all kinds of images. For be selected only if ½ ¾ ¾ Û½ . Let us denote « example, Hue (H) is not reliable for the discrimination task «½ «¾ «Ò « ¾ « be the selected chrominance com- when the saturation is low. Also, the distribution of skin area is consistent across different races in the Cb and Cr ponents, e.g. « À Ë Ö Á É . After the chrominance color spaces. Therefore, when we use different color mod- components of a given color model has been selected by us- els under uncontrolled conditions, the skin detection will ing Bayes theorem, the next process is to integrate them. consequently result in different ways. Vandenbroucke et al. If the selected chrominance components, «, are assumed  propose an hybridge color space using “knock out” al- gorithm. The best set of the three ones has been selected to be independent, these chromaticity values can be sepa- from 14 available color features for classifying soccer play- rately veriﬁed. Let us suppose that Ñ Ò and Ñ Ü (see ers. However, the accuracy of skin detection depends on Figure 1 (b)) are the respective boundaries of the range of both the color model and the method of skin classiﬁcation. human skin (deﬁned by user). It can be observed that most Hence, the challenge problem is how to select color models that suit skin pixel classiﬁcations under different conditions, of component values in any color space of a skin area are i.e., different races and varying illuminations. Here, we pro- distributed near the center of the range (i.e. ´ Ñ Ò · Ñ Ü µ ). ¾ pose a novel approach for selecting the appropriate chro- This behavior implies that these component values are im- maticity values from a given color model based on prob- portant information. Thus, we need a function that result in abilistic reasonings. It is well known that the robustness against changes in illumination can be accomplished if a the highest value when the component values fall near the color space efﬁciently separates the chrominance from the center of the human skin range. luminance information. So, in our system, the color model (R, G, B) of images is transformed to the well known color 1 pαi (X=x) representation systems. Then, the chrominance components Grade of Membership Function of the transformed color models are used to classify the skin pixel, by discarding the luminance value. The probability of skin or nonskin given ½ and ¾ is then computed by using 0.5 the Bayesian estimation: Ô´ Û µ ¡ Ô´Û µ Ô´Û ½ ¾µ ½ ¾ (1) Ô´ ½ ¾µ 0 0 100 200 300 400 500 600 700 800 900 1000 x 0 0 50 100 150 200 250 300 350 X 400 ½ and ¾ can be deﬁned as the chrominance compo- a b c d Xmin Xmax nents of a given color model, i.e. ¾ Ö Ü Ý (a) (b) À Ë Ö £ £ Ù£ Ú£ Á É ½ ¾ Ë . Ô´ ½ ¾ Û µ represents the probability of ½ and ¾ given class Figure 1: (a) Fuzzy membership function. (b) The distribu- Û . Û ¾ Û½ Û¾ denotes the skin (Û ½ ) and nonskin (Û ¾ ) tion of skin area in 1-D histogram. classes. Let Û½ ´ ½ ¾ µ and Û¾ ´ ½ ¾ µ be the 2-D his- togram of skin and nonskin areas in the chrominance com- ponents ½ and ¾ . ÆÛ is the total number of attribute val- The membership function is employed in our approach. ues in the 2-D histogram Û ´ ½ ¾ µ. The probability of ½ ¼ Ü ÓÖ Ü and ¾ , given Û , is then deﬁned as ¾´ Ü µ¾ Ü ´ · µ ´ µ¾ ¾ Ô´ ½ ¾ Û µ Û ´ ½ ¾µ (2) ½ Ü ¾´ µ¾ ´ · µ Ü ÆÛ µ¾ Ü ´ µ ½ ´ ¾ Ü (7) Ô´Û µ is the a priori probability of class Û deﬁned by Æ ½ ¾´Ü µ¾ µ¾ Ü ´ · µ Ô´Û µ È Û ´ ¾ (3) ¾´ Ü µ¾ ´ · µ Ü ÆÛ ´ µ¾ ¾ Direction of D1 The parameters and , where , are Direction of D2 r2x2+ r 2y 2- r2ry2= 0 y x x adjustable to reﬂect the meaning of the designed fuzzy ry membership function. The parameters and are deﬁned r8 r1 d' i as the respective lower and upper boundaries of any skin pk ej area in any color space. When Ü falls in the range from r7 r2 di to , the function ´Üµ will result in the value 1. Ü becomes rx r6 r3 less important information when it falls in the range from r5 r4 to or from to . The results from eq. (7) of each chrominance component are then integrated by Ë× Ò ´Ü Ýµ È « ¬ ¬ µ ¡ ´« µ Figure 2: Our new searching strategy ½ ´ · × Ò (8) ¼ ÓØ ÖÛ × where Ë× Ò ¢ ¼ ½ is the skin color likeness func- boundary. We try to ﬁnd which is closest to Ô along tion. The parameters ¬ ¾ «½Å Ò «¾Å Ò «ÒÅ Ò and ¾ «½Å Ü «¾Å Ü «ÒÅ Ü are the minimum and maximum the directions of ½ and ¾ . In order to accomplish values of the range of human skin in selected chrominance that task, the elliptical model can be automatically ´ ¬ µ ¢½ deﬁned in terms of Ö Ü ´ Ê Ñ Ü Ê Ñ Ò µ ¾ and ¿ components, respectively. The parameter ½¼¼ ÖÝ ´ Ê Ñ Ü Ê Ñ Ò µ ¾1 . ¿ is deﬁned as the length of the ranges from to and from Then, the algorithm of to . The parameter ´« µ is the weighting coefﬁcient asso- our new measure, called Robust Automatic Minimum ciated with chrominance component « . HD-RAMHD, can be carried out step by step as follows. ´« µ ÈÒÔ« Ô ´ Üµ Üµ Ò ´ « µ ½ (9) ½ « ´ step 1. Let ½ ½ ¾ ½ and ½ ¾ ¿ ¼½ ¼¾ ¼¿ ¼ be the interior and ¼ ¾ Ô« ´ Üµ is the probability generated by the 1-D his- ¾ ¾ ¾ togram of chrominance component « . Note that this his- exterior directions of searching. Initialize and ¼ to Ô togram is normalized by dividing all entries with the great- ( ¼ Ô ) and to 1 ( ½). est value. The threshold × Ò is deﬁned for making a deci- and ¼ , perform the following test: If sion whether a color pixel is skin or not. step 2. At each ½ Ò or ¼ , goto step 3. Otherwise, increase by 1 × Ò Ô« ´ Üµ (10) Ò ½ ( · ½) and repeat step 2. After completing the skin detection process, we deter- step 3. Compute the minimum distance mine each region Ê ´Ê Ñ Ò Ê Ñ Ü Ê Ñ Ò Ê Ñ Ü µ of the skin areas by directly evaluating their projections on the Ê ÅÀ Ô ´ µ x- and y-axis. Then, the color pixels in the region Ê are Ñ Ò´ Ô ¾ Ô ¼ ¾µ ´ ¾ µ ´ ¼ ¾ µ converted to a binary image by the method of gray scale Ô ¼ ¾ ´ ¾ µ ´ ¼ ¾ µ conversion and edge detection. In each region, we generate Ô ¾ ´ ¾ µ ´ ¼ ¾ µ the sets of the edge ´Ü Ý µ ½ ´ ¾ µ ´ ¼ ¾ µ ½ ¾ ¿ to be used for verifying whether the area Ê con- (11) tains an oval shape or not. repeat steps 1, 2 and 3 for all Ô ¾È . step 4. Calculate the similarity measure 2.2. Face similarity measure under partial occlusion Ê ÅÀ ´ È µ In this section, we will propose a robust method for face ½ ½ Ò ´È µ similarity measure under partial occlusions. This technique ½ È Ô · Ò´È µ (12) is based on a modiﬁed Hausdorff Distance combined with ¾ ÜÔ Ò È ´ µ Ô ¾È ´ Ê ÅÀ ´ µµ our new searching strategy as described in Figure 2. where Ò ´È µ and Ò´È µ are the respective cardinalities of From Figure 2, ¾ ½ and ¼ ¾ ¾ , ½ Ò, the two point sets Ô ¾ È Ê ÅÀ ´Ô µ and È . are two points in the xy-plane that lie on the straight Ê ÅÀ ´Ô µ measures the distance of each point Ô ¾ È line ½ and ¾, respectively. ½ and ¾ are called to its nearest neighbor in in the directions of ½ and ¾ . If some points in È near some points in , both ex- the interior and exterior directions of searching. Let È pressions ½ ÜÔ Ò ´È µ Ô ¾È ´ Ê ÅÀ ´Ô µµ and Ò ´´È µµ ½ ¾ be a point of the binary image, and È ÒÈ Ô½ Ô¾ Ô¿ Ô È Ô ´Ù Ú µ ½ È be a 1 Note that we will provide an efﬁcient algorithm for automatically ad- set of ellipses each of which is a set of points on its justing the size of the elliptical model in the next section. in (12) will result in an approximated value of 1. The term ÖÝ . Let ÖÜ and ÖÝ are the x- and y-radius before updated. ÓÐ ÓÐ ´Ò ´È µ Ò´È µµ is designed to prevent the false detection, oc- The new radius can be evaluated by curing when the point Ô is too discarded by the func- ¼ ½ tion. In our system, it is assumed that the occluded areas ½ ÖÜ Ò Û ÖÜ ÓÐ · ÐÐ Ô× ´Þ µ (16) of the edge of face are less than 35%. Thus, the expression Ò´ ½µ Þ¾ ´Ò ´È µ Ò´È µµ ¼ is acceptable values. To justify the ½ similarity measure Ê ÅÀ È ¢ ¼ ½ , it can be and ¼ ½ shown that È ¯ Ê ÅÀ ´È µ Þ¼ µ ½ ½ ½, if and only if Ò ´È µ Ô ¾È ÖÝ Ò Û ÖÝ ÓÐ · ÐÐ Ô× ´ (17) Ò ´È µ ½, Ò´ Þ¼ ¾ ¾ ¾µ ´ Ê ÅÀ ´Ô µµ ¼ and Ò´È µ ¯ contains an oval shape, if and only if Ê ÅÀ ´È µ where Ò´ ½ µ and Ò´ ¾ µ are the cardinalities of the points Ò ´È µ ¼ , where ÓÚ Ð and Ò´È µ ÓÚ Ð ¾ ¼ ½ is the threshold sets ½ and ¾ , respectively. If the second terms of (16) and used to adjust the sensitivity of the face similarity measure. (17) are both positive, the elliptical model will be enlarged. To solve the problem of comparing È to the portions Otherwise, it will be reduced. The elliptical model can be of the set (e.g. as occurs when faces are partly oc- recreated using an updated radius Ö Ü Û and ÖÝ Û . Let ÆÜ and Ò Ò cluded or some features of faces are failed), we deﬁne the Ê ¼ ¼ function as ÆÝ denote ÖÜ Û ÖÜ and ÖÝ Û ÖÝ , respectively. We can Ò ÓÐ Ò ÓÐ ﬁnd the best matching from Ê ÅÀ ´È Ò Û ¨ Ø µ, where Ü ´ µ Ü Ü È Ò Û is an updated elliptical model, and Ø is ´Ø Ü ØÝ µ such that ¼ Ü (13) Ü ÆÜ ØÜ Ü · ÆÜ and Ý ÆÝ ØÝ Å Å Å Å Ý · ÆÝ . where is the threshold deﬁned for discarding any large value of Ü. In our experiments, the parameters and ÓÚ Ð 3. EXPERIMENTAL RESULTS are set to ¾ ¿ and ¼ , respectively. This means that the point Ô such that Ê ÅÀ ´Ô µ is indicated as the point in In our experimentation we have employed 475 real images the occluded areas, we will discard that point as a noise. If collected from various sources, i.e. internet and XM2VTS the condition ´ Ê ÅÀ ´Ô µµ holds for all Ô ¾ È , the database . Each of which contains multiple faces with distance from È to must be within the threshold . Thus, various sizes and different lighting conditions, most of the notion of resemblance encoded by this distance is that, faces are in a complex background scene. Parts of some the distance from set È to should be less than or equal to faces are occluded and some features of faces are failed. . This is an important advantage of our new measure, be- The database is composed of Asian, European and African cause it discards the large error rather than combining them faces. We implement the proposed method on Pentium III with the small one. In section 3, we will show the perfor- 450 MHz with 128 Mbytes of memory. mance of our new measure compared to others. To generate the statistics of skin and nonskin. The two best sets that most likely to the skin and nonskin areas 2.3. Updating the elliptical model should be carefully selected from the image database. The skin areas are easily collected from the part of human body, The accuracy of face similarity measure also depends on the size of the elliptical model. To achieve the most appropriate i.e., face, hand and arm. However, the nonskin areas are size of the elliptical model, Ö Ü and ÖÝ need to be updated not easy to gather, this is because the nonskin areas can be using the ellipse function represented by everything in the image database excluding Ûµ ÐÐ Ô× ´ Ü Ýµ ÐÐ Ô× ´ ÖÝ Ü¾ · ÖÜ Ý¾ ÖÜ ÖÝ ¾ ¾ ¾ ¾ (14) the skin area. Therefore, to collect a certain nonskin and to reduce the nonskin data set. The nonskin areas that are which has the following properties: most likely to be mistaken to the skin area are collected for ¼ ´Ü Ýµ × Ò× Ø ÐÐ Ô× ÓÙÒ ÖÝ building the statistical informations. This collection can be ÐÐ Ô× ´ Ü Ýµ ¼ ´Ü Ýµ × ÓÒ Ø ÐÐ Ô× ÓÙÒ ÖÝ greatly helping to make a decision in the case where a pixel ¼ ´Ü Ýµ × ÓÙØ× Ø ÐÐ Ô× ÓÙÒ ÖÝ (15) overlap between skin and nonskin classes. Refer to section 2.2, the idea of the directions of search- Our approach has three stages. In the ﬁrst stage, the re- ing can also be used to update Ö Ü and ÖÝ . The ellipse gions that may contain a skin color were extracted by the is divided into 8 regions , i.e. Ö , ½ (see Fig- method in section 2.1. Then, the RAMHD will be used in ure 2). Let È Å be a set of elliptical models at the po- sition Å , where Å is the position of the best match- the second stage to verify whether or not the skin areas con- ing of face similarity measure from section 2.2. The near- tain an oval shape. In our system, the facial feature does est neighbor of a point Ô ¾ È Å can be found using not neccessary to verify. This is because, the result that pro- steps 1, 2 and 3 of the RAMHD algorithm. At each Ô in duces from section 2.1 is only the skin area. Hence, if that the regions Ö¾ Ö¿ Ö Ö and Ö½ Ö Ö Ö the nearest neigh- bor of those points that does not rejected by the func- skin area contains an oval shape, it is assumed to be the tion are retained in ½ Þ½ Þ¾ Þ¿ Þ ½ Þ ¾ ½ and boundary of the human face. This can enormously reduce ¾ ¼ ¼ ¼ Þ½ Þ¾ Þ¿ Þ ¼ ¾ Þ ¼ ¾ ¾ , respectively. The points the computational complexity. Finally, the elliptical model in the sets ½ and ¾ are respectively used to adjust Ö Ü and will be updated by using the method in section 2.3. The results of the ﬁrst stage will subsequently effect the accuracy of the face similarity measure. So, it is seem im- portant that this stage must produces the results robustly and reliably. From Figure 3, we have shown the result of our skin detection when we apply to the images under different lighting conditions. Figure 3 (a), (b) and (c) show the effect (a) of dark, normal and bright illuminations. The results show on the right of Figure 3, one can see that the changing of illuminations does not signiﬁcantly effect to the results of our skin detection. Moreover, we do not need to adjust the range of human skin to suit each image. This is one of the key advantages of our proposal, because we do not require (b) one to prespecify the boundaries of the range of human skin for any particular image. Figure 4 (a), (b) and (c) shows the results of our skin detection under different races, the result is much more accurate and efﬁcient enough for using in the face detection stage. The example result of the method for updating an elliptical model can be shown in Figure 5. (c) In Figure 6, we present some results of our face detec- tion algorithm. We have tested the proposed method on a Figure 3: The results of skin detection under varying illu- large number of data set. The label in the bottom left cor- minations. ner (T/F/N/E/C) gives the numbers of total faces (T), found faces (F), not-found faces (N), false detection (E) and the computation time (C) of face detection. Figure 6 (a), (b) and (c) show the results of sample images with multiple faces of different sizes. No false alarm occurs in this samples. Moreover, all faces can be automatically discovered with- (a) out requirement a user-deﬁned parameter in the process. We present the results of our face detection with occluded faces in Figure 6 (d). In this case, the face detector still found the locations of these faces. Figure 6 (e) shows the result of section 2.1. In Figure 6 (f), it shows that the result of our face similarity measure is very robust even so many features (b) of the edge of face are disappeared. Table 1. The comparison of our algorithm with others. Found Not-Found False Time The proposed scheme 92.36% 7.64% 18.22% 846ms (c) M2HD  52.95% 47.05% 26.47% 2063s MEHD  66.3% 33.7% 28.4% 2230s HD  35.3% 64.7% 147.05% 1218300s Figure 4: The results of skin detection under different races. YES+HD  82.36% 17.64% 411.76% 56.75s HSV+AMHD  88.24% 11.76% 23.52% 773ms AMHD  64.71% 35.29% 32.35% 1853s Table 1 compares the accuracy and the computation time of our approach with others’ [1,4,5,6,21,22] based on the numbers of found faces, not-found faces, false detection and computation time. The successful rate of the proposed method is 92.36%, and the false alarm rate is also not bad. The accuracy of YES+HD and HSV+AMHD is close to the successful rate of our scheme. However, the techniques in Figure 5: The results of face detection before (left) and after [1,4,5,6,21,22] are less efﬁcient than our technique. This (right) updating the elliptical model. 5. REFERENCES ½ B. Takacs and H. Wechsler, “Fast searching of digital face libraries using binary image metrics”, IEEE Int. Conf. on Patt. Recog., pp. 1235- 1237, August 1998. ¾ C. Garcia and G. 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