comments. A modification of line Hausdorff distance for face recognition to reduce computational

 Abstract — Face recognition, that has a lot of applications in modern life, is still an attractive research for pattern recognition community. Due to the similarity of human faces, face recognition presents a significant challenge for pattern recognition researchers. Hausdorff distance is an efficient parameter for measuring the similarity between objects. Line Hausdorff distance (LHD) technique, which is the applying of Hausdorff distance for face recognition, gives high accuracy in comparing with common methods for face recognition. For fast screen techniques such as LHD, the computational cost is a key issue. A modified Line Hausdorff distance (MLHD) is proposed in this paper. The performance of the proposed method is compared with LHD method for face recognition in various conditions: 1) ideal condition of face, 2) varying lighting conditions, 3) varying poses and 4) varying face expression. It is very encouraging that the proposed method gives lower computational cost than LHD while keeping the accuracy of face recognition equal to the LHD


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Abstract-Face recognition, that has a lot of applications in modern life, is still an attractive research for pattern recognition community. Due to the similarity of human faces, face recognition presents a significant challenge for pattern recognition researchers. Hausdorff distance is an efficient parameter for measuring the similarity between objects. Line Hausdorff distance (LHD) technique, which is the applying of Hausdorff distance for face recognition, gives high accuracy in comparing with common methods for face recognition. For fast screen techniques such as LHD, the computational cost is a key issue. A modified Line Hausdorff distance (MLHD) is proposed in this paper. The performance of the proposed method is compared with LHD method for face recognition in various conditions: 1) ideal condition of face, 2) varying lighting conditions, 3) varying poses and 4) varying face expression. It is very encouraging that the proposed method gives lower computational cost than LHD while keeping the accuracy of face recognition equal to the LHD method.
Index Terms-Face cognition, Line Hausdorff Distance, Hausdorff Distance, Modified Line Hausdorff Distance.

INTRODUCTION
utomatic face recognition is an active research area and has had a lot of publications in last two decade years. Face recognition has lot of applications in modern life such as bank card identification, access control, 'mug shot' searching, security monitoring systems.
Face recognition is used for identification one or more persons from a still image or a video by comparing the input image with face images stored in database. Face features of images in database are extracted and stored offline. The same features of the input image are extracted too and comparing with the features of each model image in the database. Due to the similarity of human face, comparing techniques of face features still presents significant challenge for pattern recognition researchers. There were a lot of methods for face recognition have been proposed. However, there was no method is the best in comparing with other methods [1]. Line Hausdorff Distance (LHD), which proposed by Gao and Leung [2], gives high accuracy for face recognition in comparing with other common methods for face recognition. Moreover, LHD is also stable in various condition of face recognition such as: lighting conditions, varying pose conditions and varying face expressions. This makes LHD become more attractive for applying for face recognition applications, where the real lighting conditions, poses and face expressions are different from image with ideal conditions in database. In most face recognition systems, searching the best matching face in database is the most computational expensive operation due to the large number of images in the database. Efficient search method is more attractive for a face recognition system. The proposed method in this paper, Modified Line Hausdorff Distance (MLHD), give lower computational cost than LHD method while the accuracy for face recognition is equal to the LHD method. In the rest of paper, the review of LHD method is presented in section 2. The proposed method, MLHD, is continued in section 3. Section 4 is the comparing recognition rate of the proposed method MLHD with LHD method. The paper is closed in section 5 with some comments. The edges of an face image, which is the reflecting of large local intensity changes caused by the geometrical structure of the face, are the important features of human face. However, edge of an human face image has not used for face recognition until Takács [3]. Takács [3] and Gao [4], used Haudorff distance for matching dominant points of the edge map of a face image and called Modified Hausdorff Distance (MHD). Gao and Leung [2] also used Hausdorff distance for matching face image but using the lines, which is the connection of dominant points, of the edge map, called Line Hausdorff Distance (LHD).
Edge map of an face image is the map of dominant points of edge curve of face image. For generating an edge map, first, edge curve of the face image is extracted. There are a lot of edge extraction methods proposed. However, Heath et al. [5] showed that "no one single edge detector was best overall; for any given image it is difficult to predict which edge detector will be best". For generating the edge map of face image, we use the edge detector which is proposed by Babu [6] followed by a thinning process for one pixel width edge curve extraction. The Dynamic two strip (Dyn2S) [7] is applied on edge curve for generating the dominant points of the edge curve. An example of an edge map of a face image is shown in Fig. 1.
 is the smallest intersecting angle between two lines, W is a parameter determined by a training process.
The parallel distance and perpendicular distance as Eq. (3) and Eq. (4) is used for two parallel lines as Fig. 2.
In general, two lines are not parallel, so we must rotate the shorter line with its midpoint as rotation center before calculating   A primary line Hausdorff distance for measuring the similarity between lines could be defined as Hence, the complete version of LHD will become    Table 1. The proposed algorithm has matching time 40% less than the original LHD.
In general, the lines of face's LEMs is equally contributing in the face. So the matching time for proposed algorithm will be a half of the LHD algorithm.

Face recognition under ideal condition
In this experiment, we use a pair of frontal face, which is the ideal conditions picture, of each   Table 2.
With Bern University database, all methods give correct recognition of 100% because there are minor differences between two frontal face pictures. However, two frontal face pictures of AR database is taken within 2 weeks, this makes large difference between two pictures.
Here we see that the proposed method MLHD gives lower accuracy than LHD method for face recognition. However, the proposed method has computational complexities is a half in comparing with LHD method.

Face recognition under varying lighting
conditions In this experiment, 100 frontal face pictures of AR database are used as the database. Each person has 2 pictures with the left-light, 2 pictures with the right-light and 2 pictures with the bothlight. So with each lighting condition, we have 200 pictures as the input. The face recognition under varying lighting condition result is showed in Table 3.
In all conditions of the light, MLHD method archives equal recognition rate to the LHD method. This means MLHD method is stable with lighting conditions of the image as LHD method. This makes MLHD method, also LHD method, become more attractive with real applications, where the lighting conditions is not controlled, than common face recognition method as Eigenface.

Face recognition with varying poses
In this experiment, 30 frontal face pictures of Bern database are used as the database. With each person, we use one image of looking left, looking right, looking up and looking down. So we have 30 images as in put for each condition of pose. The face recognition with varying poses result is showed in Table 4.
The proposed algorithm, MLHD, gives higher accuracy for looking left and looking up of model's face while lower accuracy for others case of facing poses. In the average, the proposed algorithm give the same result as the LHD algorithm.

Face recognition with varying face expression
In this experiment, 100 frontal face pictures of AR database are used as the database. Each person has 2 pictures with each face expression: smiling, angry and screaming. The face recognition with varying face expression result is showed in Table 5.
The original LHD gives high accuracy for face recognition with smiling and angry expression of human face, however, low accuracy for screaming expression. The proposed algorithm gives slightly lower accuracy for smiling and angry expression than original LHD. However, with screaming expression, the proposed algorithm gives much higher than original LHD. As the result in Table  5, the proposed algorithm is more stable than original LHD for face recognition with varying face expressions.

CONCLUSION
LHD method is an advantage method for face   recognition in comparing with Eigenface, which is the most common method for face cognition used by most researchers of face recognition community. Beside getting higher recognition rate than Eigenface method, LHD method also shows that it is stable with various lighting conditions, varying poses and varying face expression. This paper has proposed MLHD method. MLHD method gives the same recognition rate as LHD method while getting lower computational complexities. For =2 Kcg , MLHD method gives a half computational complexities of LHD method. This is valuable which a face recognition application, where the number of image for searching is huge. Beside that, MLHD also shows that it is stable with non-ideal conditions of the image.