Patent Publication Number: US-7218760-B2

Title: Stereo-coupled face shape registration

Description:
TECHNICAL FIELD 
   This invention is directed towards face recognition and more particularly relates to recognizing facial features by locating points on the facial features using multiple images of a face. 
   BACKGROUND 
   A three dimensional object can be represented in two dimensions. In fact, representing a three-dimensional object by using two-dimensional views has advantages in object modeling and synthesis. In such two-dimensional representations, the three-dimensional features of the object need not be explicitly recovered and this avoids difficulties in three-dimension based methods. Rather, it is conventional to use view-based models to represent the object with multiple two-dimensional view projections. When representing an object with more than one two-dimensional view, a pixel-wise correspondence map is usually required between each of the two-dimensional views. Alternatively, a sparse correspondence map between a small set of feature points, or edges of features, on the object can be used between each of the two-dimensional views. The correspondence map can be computed and applied to separate the shape of the object from the texture of the object. As such, both the shape of the object and the texture of the object, from a particular viewpoint, can be modeled in a linear subspace. 
   When representing an object with more than one two-dimensional view, it may be advantageous to establish points to represent features on the object (feature points). A feature point based correspondence between multiple two-dimensional views is advantageous in some applications because it is more robust in dealing with light intensity and color variations, and can involve less computation than establishing a dense representation of the object. Accordingly, to accurately model an image class of an object, two problems can be addressed and solved. The first problem is that of locating feature points on features of the object by using a training set of two-dimensional views. Once the feature points of the features on the object are located, the second problem is that of establishing the underlying correspondence between two or more sets of feature points from a corresponding number of two-dimensional views. 
   An additional degree of difficulty arises when locating features in a complex and non-rigid object using multiple two-dimensional views. These difficulties can be addressed by using prior knowledge regarding the object itself. For instance, a deformable model of the object is an example of such prior knowledge. The deformable model can provide constraints on the location of features on the object. These constraints, which can be derived from image data with respect to the object, can be used to deal with the problems like segmentation of the object or the detection of features on the object. In particular, the Active Shape Model (ASM) as proposed by Cootes et al. (Active Shape Model, T. F. Cootes, C. Taylor, D. Cooper, and J. Graham. Active shape models—their training and their applications. Computer Vision and Image Understanding, 61(1):38–59, January 1995) provided the advantage that the instances of the model of the object can be deformed only in those ways that were learned from the training set from which the model was derived. That is, the model can accommodate considerable variability in segmentation of the object, or in the detection of its features, but the model should still be specific to the class of the object that the model represents. ASM uses the Principle Component Analysis technique (PCA) to model an object by both the two-dimensional shape variations of the object and the local grey level structures of the object. In particular, ASM is a process that includes interrogating two-dimensional images of the object and approximating the shape of features on the object using points (feature points) that respectively represent each feature on the object. 
   When two or more different two-dimensional views of the same object are given, the features on the object for each view can be matched to a model of the object by using ASM. After the model matching for each view is performed, it would be desirable to find the correspondence between the respective feature points of the features of the object for the different views, such as by implication across each of the different views. The detected feature points for each feature on the object, however, may not be geometrically consistent across the different views. This inconsistency occurs because ASM only considers a single view rather than the correspondence between the different views. The matching of the model to each of the different views could benefit from the use of a multi-view geometry. While this can be accomplished, it requires that all key feature points of each feature on the object remain visible in each of the two-dimensional views. 
   One technique for using ASM involves using a set of training examples of one face view from different viewpoints. From these views of the one face, a set of feature points of facial features on the face can be manually labeled. This manual labeling represents a deformation of the face into its different facial features and respective points that make up the facial features. For instance, these features can include the nose, eyes and mouth. The feature points are those points that mark the facial features on the face. ASM uses the set of training data representing the deformation of the face to analyze facial features on a different face by using views of the different face. This conventional ASM technique, however, suffers from inaccuracy in locating facial features in the views of the face being analyzed. Moreover, the conventional ASM technique can only deform the face being analyzed in the ways that the face in the set of training data had been deformed. One partial solution to overcome the inherent inaccuracy is to use a larger training database. Such a solution is only partial because it does not take into consideration the local grey-level model fitting for the different views of the face. Local grey-level model fitting tends to interpret the data so as to move facial features toward the strongest photometric edge, which may not necessarily be the actual edge of a facial feature—thus introducing further inaccuracy. Moreover, using a larger training database may further decrease accuracy because the additional data tends to further extend the acceptable facial feature shapes into an inaccurate range for the face being analyzed. 
   In addition to the foregoing problems, ASM is not consistent in finding the same facial features in two slightly different views of the same face. ASM does not always guarantee that the features identified in training data for a training object will yield similar features when searching two slightly different views of another object. This inability can be attributed to illumination changes in the object as a result of rotating the object in different two-dimensional views, or it can be attributed to different initial parameters. Two negative results can occurs when using conventional ASM in this environment. One result is that the conventional ASM model will wrongly identify features on an object or will inaccuracy locate the feature points for features on the object. Either way, different two-dimensional views of the same object, when using conventional ASM, will yield features that do not match up between the different two-dimensional views. In consequence, the correspondence between the identified features of the different views is inaccurate when using conventional ASM. 
   If would be an advance in the art to develop a technique that will accurately and consistently identify the same features in different views of the same object. 
   SUMMARY 
   An implementation of the invention identifies facial features by locating points for the facial features, such as eye corners and nose tip. To do so, a training set of multiple two-dimensional views of a face are used to develop a set of training data. The set of training data is used with two different two-dimensional views of a face in a mathematical model. The mathematical model is used to identify both inner and outer facial features on the two different two-dimensional views, thus presenting a stereo-coupling mechanism for identifying facial features on each of the two different views of the face. The mathematical model uses epipolar geometry as encoded within a fundamental matrix to constraint the regions on each of the two different views at which facial features will be located. The mathematical model finds a geometric correspondence between the points for each facial feature, respectively, on each of the two different views of the same face. 
   In another implementation of the invention, outer and inner facial features of a face model are matched with that of a first model for a first face image and with that of a second model for a second face image. Each of the matching outer and inner facial features of the first and second models is adjusted using the corresponding epipolar constraint for the first and second models. The first and second face images are images the same face captured at the substantially the same respective camera orientation. In other implementations, the images have a face pose range differing by the yaw. 
   In yet another implementation of the invention, an initialization is performed by using a face model for first and second models for respective first and second face images. Each of the first and second models has outer and inner facial features defined by a plurality points. A fundamental matrix is estimated for the first and second models. The points are updated for each of the inner facial features of the first and second models by using the respective local texture for each point. Each of the inner facial features of the first and second models is then updated. The points for each of the inner facial features of the first and second models are updated using the fundamental matrix and the corresponding epipolar constraint. An update is then performed for each of the outer facial features of the first and second models. If the first model has converged within a predetermined tolerance of the face model, a representation is output of the inner and outer facial features of the first model. If the second model has converged within a predetermined tolerance of the face model, a representation of the inner and outer facial features of the second model is output. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete understanding of the implementations may be had by reference to the following detailed description when taken in conjunction with the accompanying drawings wherein: 
       FIGS. 1   a – 1   b  illustrates a mechanism for matching corners of different facial features by points that form an outline around each facial feature on two different two-dimensional views of the same face, where the face is in two (2) different positions, and where the mechanism uses a fundamental matrix estimation. 
       FIG. 2  illustrates a decomposition of a face into inner and outer facial features, each being outlined by a line connecting a plurality of points. 
       FIGS. 3   a – 3   b  show respective two-dimensional views of a face in different poses, where the views represent starting images that can be used by implementations of the invention. 
       FIGS. 4   a – 4   a  are epipolar geometric illustrations depicting the correspondence between points on two different two-dimensional views of an image in accordance with an implementation of the invention. 
       FIGS. 5   a – 5   b  represents, in accordance with an implementation of the invention, a first iteration of a stereo-coupling mechanism for identifying the corresponding facial features on the two different views of  FIGS. 3   a – 3   b , respectively, by using epipolar geometry as encoded within a fundamental matrix. 
       FIGS. 6   a – 6   b ,  7   a – 7   b , and  8   a – 8   b  represent respective iterations of the stereo-coupling mechanism as was used with respect to  FIGS. 5   a – 5   b.    
       FIG. 9  is a flow diagram, in accordance with an implementation of the invention, of a procedure for facial feature detection that uses a stereo-coupling mechanism, where the procedure can be used on images seen in  FIGS. 3   a – 3   b  to accomplish the respective iteration results seen in  FIGS. 5   a – 5   b  through  8   a – 8   b.    
       FIG. 10  is a block diagram, in accordance with an implementation, of a networked computer that can be used to implement either a server or a client. 
   

   DETAILED DESCRIPTION 
   The present invention is directed towards face modeling and identification of facial features. Implementations of the present invention use epipolar geometry in face shape analysis to determine facial features, such as the nose, eyes, eye brows, mouth, etc. This detailed description presumes that the reader has an understanding of epipolar geometry. 
   Estimating the Fundamental Matrix 
     FIGS. 1   a – 1   b  show two target images that are calibrated by an estimate of the fundamental matrix E between them. One example of a formula for computing the fundamental matrix E for a pair of images is given by Zhang et al. (Z. Zhang, Determining the epipolar geometry and its uncertainty: a review. The International Journal of Computer Vision, 27(2):161–195, 1998). The two images are taken by a static camera while the head is in a frontal position and moving in the yaw direction between the two views. Because the illumination changes when the head is rotating, the color of the same physical point in the two images appears to be different. As such, it is advantageous to identify facial features of the face because the identification of facial features is more robust to intensity variations than optical flow based methods. The estimation of the fundamental matrix E can include four (4) different steps: 1) approximate the localization of faces by determining differences between the two different images; 2) detect the corners of each facial feature in the images; 3) match the corners of each facial feature by a correlation between the two different images; and 4) reject the false matches and estimate the fundamental matrix by least median squares.  FIGS. 1   a – 1   b  shows a pair of face images and the set of corner matches for facial features that are established with this technique. Nevertheless, a face model is needed for more accurate correlation of facial features between the two different images. Such a face model, as shown in  FIG. 2  and discussed below, is a representation of facial features, e.g., nose, eyes, eye brows, mouth, etc. 
   Decomposition of a Face Shape Model 
   A training set of face shapes, T={S i |iε0˜N} can be provided, where a shape vector is represented by S i =(&lt;x 1 ,y 1 &gt;, &lt;x 2 ,y 2 &gt;, . . . , &lt;x K ,y K &gt;) εR 2K , K=83. S i , a shape vector, represents the points that make up different features on a face (feature points). As seen in  FIG. 2 , a face has been decomposed into inner facial features (eyes, nose, and mouth), each of which is seen outlined by a line connecting a plurality of points.  FIG. 2  shows 63 points that make up these three different inner facial features. The face has also been decomposed into outer facial features (a pair of eyebrows and a silhouette of the jaw, chin, and cheeks), each of which is seen outlined by a line connecting a plurality of points.  FIG. 2  shows 19 points that make up these two different outer facial features. As such, a total of 83 points make up five (5) different facial features as seen in the composite of the decomposed facial features at the bottom of  FIG. 2 . 
   The points on the silhouette are helpful since they can help segment the region of the face from its background. Due to the self occlusion introduced by head rotation in the yaw direction, however, the points on the silhouette are difficult to accurately associate to two different views of the same face in that these points will not comply with the epipolar constraint. To overcome this difficulty, the decomposed face model is used. As showed in  FIG. 2 , the shape vector S i  is divided into two parts, the inner vector S in  and the outer vector S out . S in  denotes the 64 points that make up the three inside facial features and outer vector S out  denotes the other 19 points that define the eye brows and the silhouette or face contour. Of course, a different number of points could be selected to represent each of the facial features. Another reason to separate out the silhouette of the jaw, chin, and cheeks is due to the fact that their local grey-level model is less stable than the points that make up the three inner facial features, if the backgrounds that are presented in the training images are cluttered. Considering that the periphery of the eyebrows are more difficult to detect than other inner facial features, and are more likely to be affected by other factors such as by different hairstyles, the eyebrows are also assigned the S out  shape vector. 
   After aligning all shape vectors (S in , S out ) to the tangent space of the mean shape  S  in an iterative ASM procedure, a set of normalized shape vectors S i =T X     i     ,Y     i     ,S,θ (Ŝ i ) is obtained, where T represents a Euclidean transformation by performing a rotation θ, a scaling S and a translation by (X 1 ,Y 1 ). An example of such an iterative ASM procedure that can be used is given by Cootes et al., discussed above, 
   Following the decomposition strategy, each aligned face Ŝ i  is decoupled into two vectors Ŝ i =&lt;Ŝ in ,Ŝ out &gt;. Two low dimensional shape spaces, U F  and U in , are computed using the Principle Component Analysis technique (PCA) of ASM as Ŝ i =  S +U F b i , Ŝ in =  S   in +U in b ini , where U F  is the matrix consisting of k principal modes of variations in Ŝ i  and U in  is the one learnt from Ŝ in . For each point j of each facial feature in the shape i of the training set, a gray level profile g ij  centered around the j is extracted. The derivation vector d ij  of g ij  is calculated and normalized as: {circumflex over (d)} ij =d ij /Σ k d ij,k , where k is the index of points along the profile. PCA is used again to model the variation of the vectors {circumflex over (d)} ij . One example of the PCA of ASM, as used herein, is given in Cootes et al., discussed above. 
   Stereo-Coupled Model Searching 
   A stereo-coupled model of matching corresponding facial features of two views of the same face starts with an initial guess of the face position and the mean shape vector in both images. ASM is applied to each of the two views to update each point of each facial feature according to local texture statistics (e.g., photometric data proximal each point). To do so, the points are moved along a direction that is perpendicular to the model boundary. The quality of the fit is then evaluated, and from this, a new position for each point can be proposed. The best match is often found on a strong edge based upon the magnitude of the photometric data. 
   The next step involves finding the most plausible shape which satisfies both the prior shape distribution and the epipolar constraint. Model fitting can be formulated as finding the optimal parameter set c of the shape models in the two images, to minimize a loss function L(c) with two constraints, i.e., 
   
     
       
         
           
             
               
                 
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   subject to the constraints
 
{circumflex over (μ)}′ T E{circumflex over (μ)}=0  (3)
 
| b   i,k |≦3√{square root over (λ k )}  (4)
 
where d(x,y) is the Euclidean distance between points x and y, S in1  and S in2  are observed feature points after local texture based updating,
 
 S   in1 ={μ i |μ i   =&lt;x   in,i   ,y   in,i   &gt;,i =0˜63}
 
 S   in2 ={μ i ′|μ i   ′=&lt;x   in,i   ′,y   in,i   ′&gt;,i =0˜63}
 
and Ŝ in1  and Ŝ in2  denote the model instances:
 
 Ŝ   in1   =T   in1 (  S   in   +U   in   b   in1 )  (5)
 
 Ŝ   in2   =T   in2 (  S   in   +U   in   b   in2 )  (6)
 
The parameters b in1  and b in2  should satisfy the second conditions to generate a desirably accurate face shape.
 
   L(c) is used to evaluate the difference between model instances and observed feature points. Alternatively, in terms of the epipolar geometry, L(c) can also be viewed as a measure to find the correct corresponding points. During the searching procedure, a typical observed matching μ⇄μ′ among the shapes S in1 ,S in2  can be noisy and there it is desirable to recover the correct one. L(c) denotes the distance between original feature points μ, μ′ and correct corresponding points {circumflex over (μ)}, {circumflex over (μ)}′ where {circumflex over (μ)}, {circumflex over (μ)}′ are the points in the shape instances Ŝ in1 , Ŝ in2 . An assumption is made that there will be a Gaussian error distribution of μ, μ′ on the points {circumflex over (μ)}, {circumflex over (μ)}′, which will in turn minimize the loss function L(c) for the most likely values that will represent an accurate correspondence between points on the two different views. 
   A procedure for locating an accurate correspondence between points on the two different views involves the decomposition of a shape model and the combined constraints of both epipolar constraint (e.q.3) and prior shape constraint (e.q.4). In general, such a procedure begins by initializing shape models on two different views of the same face in terms of face detection results. An example of the initialization of shape models on two different views that can be used herein is given in Li et al. (S. Z. Li, Q. D. Fu, L. Gu, B. Scholkopf, Y. M. Cheng, H. J. Zhang. “Kernel Machine Based Learning for Multi-View Face Detection and Pose Estimation”. In Proceedings of 8th IEEE International Conference on Computer Vision. Vancouver, Canada. Jul. 9–12, 2001). After the shape models of the different views have been initialized, the points for each facial feature are updated independently using the texture (e.g., photometric data) proximal to each point. Then, the inner shape image is updated. To do, an initial estimate is given for the inner shape vectors S in1 , S in2 . This initial estimate is fitted to the image data for the two different views of the face. An optimization is sought for parameters of T in1 ,T in2 ,b in1 ,b in2  and a truncation of b in1 , b in2  is made within ±3√{square root over (λ k )} according to the prior shape constraint. After the truncation, an update is made to the points for the inner facial features (nose, eyes, and mouth) according to the epipolar constraint. 
   Since the points for the inner facial features for the two different views may not as yet satisfy the epipolar constraint, a nonlinear optimization solution is introduced to find the correct correspondence of {circumflex over (μ)}⇄{circumflex over (μ)}′ from the matching of μ⇄μ′. As shown by the epipolar geometric diagrams seen in  FIGS. 4   a – 4   b , l μ  is the epipolar line of feature point μ in the second view or image of the same face. A line l ⊥  is drawn orthogonal to l μ  from μ′, which intersects l μ  at point M. A line l v  going from e 2  through a point v on l ⊥  is an epipolar line. Thus, point v defines the pencil of epipolar lines in the second image. The pencil can be parameterized by a parameter λ, which is the signed distance between v and μ′. The parameter μ′ is projected to l v  to obtain {circumflex over (μ)}′. The parameter l {circumflex over (μ)}′  is the epipolar line of {circumflex over (μ)}′, in the first view or image of the same face. The parameter μ is projected to l {circumflex over (μ)}′  to obtain {circumflex over (μ)}. In order to find the optimal λ opt  to minimize L(c) as (2), a classical Levenberg-Marquardt optimizer can be used, were the initial value of λ is set to ½d(μ,M). Several iterations can be made in order to achieve an optimal value of λ. Lastly, all points S 1 ,S 2  for all facial features are updated as was done in the first step. 
   Generally, the shape of a face is approximated, in one implementation, by the foregoing steps so as to minimize an internal energy function. The epipolar constraint represents a special energy term that aims at finding the best correspondence between the points of the facial features for each of the two different two-dimensional views of the same face. 
     FIGS. 5   a – 5   b  through  8   a – 8   b  depict a result of respective iterations of one implementation of a stereo-coupled mechanism using epipolar geometry, where  FIG. 3   a – 3   b  represents the two initial views of the same face. As can be seen in the last views in  FIG. 8   a – 8   b , the stereo-coupled model accurately locates each facial feature in the two different views, where the convergence of the facial features in the respective views is similar. This convergence is possible because the geometry constraint imposed on inner facial features (eyes, nose, and mouth) regulates the correspondence mapping between the two different views models. 
   A procedure  900 , seen in  FIG. 9 , illustrates one implementation of the present invention having steps one (1) through eight (8) that are performed upon two (2) different views of the same face using a face model. The two views are taken at the same relative camera orientation to the face, where the face is rotated in the yaw direction between the two different views. The two views are processed simultaneously. Steps two through seven are repeated in iterations within procedure  900 . 
   The input to procedure  900  is two face images, an example of which is provided by  FIGS. 3   a – 3   b . This input is seen at step 1 in procedure  900  at blocks  902 – 904 , respectively, for the 1 st  and second face (e.g., the two different views of the same face). After step 1 of procedure  900 , step 2 proceeds in which the corner points of each facial feature on each face are detected in each of the two images by the initialization of the shape model on the first and second faces at blocks  908 – 910 . Blocks  908 – 910  can be executed simultaneously. With respect to the inner facial features, the corner points for the mouth include a plurality of mouth corners. The corner points for each of the eyes include a plurality of eyes corners, and a corner point for the nose includes a nose tip. 
   After the corner points of each facial feature are detected, the initialization of the shape model on the first and second faces at blocks  908 – 910  also includes establishing the correspondences between the two sets of corner points. Stated otherwise, blocks  908 – 910  call for the initialization of first and second models for respective first and second face images. This initialization uses a face model having outer and inner facial features, where each facial feature is defined by a plurality points, and where each of the first and second models has outer and inner facial features. By way of example,  FIGS. 5   a – 5   b  provide an example of the two different views upon which procedure  900  are applied.  FIG. 2  provides an example of the face model having both inner and outer facial features, each of which is defined by a plurality of points. The inner facial features in  FIG. 2  are a nose, a mouth and a pair of eyes. The outer facial features in  FIG. 2  are an arcuate bottom edge of the face and a pair of eyebrows. As can be seen by the initial input of  FIGS. 3   a – 3   b , the first and second face images are the same face captured at the substantially the same respective camera orientation. The respective face poses of the first and second face images are substantially the same as to pitch, substantially the same as to roll, and different as to the yaw in a range from about 3 degrees to about 10 degrees (10°). 
   Following the establishment of correspondence between the corner points of the facial features in the two different views, an estimation is made of a fundamental matrix ‘E’ for the first and second faces (models) at block  906 . Once example of a technique for estimating the fundamental matrix ‘E’ that can be used at block  905  of procedure  900  is described in Pentland et al., discussed above. 
   In step 3 of procedure  900 , an update is made to the plurality of points for each of the inner facial feature of the first and second models (e.g., the first and second faces) by using the respective local texture for each point. This update occurs in blocks  912 – 914  of procedure  900 , where the local texture for each point includes photometric data at or proximal to the point. In step 4, at blocks  916 – 918 , an update is made to each of the inner facial features of the first and second models using the result of the updates to the points from step 3. 
   Steps 1–4 operate to update two different models, each representing a different view of the same face. In step 5, at block  920 , a unitary operation is conducted instead of a pair of operations as in steps 1–4. Block  920  uses the fundamental matrix and the corresponding epipolar constraint in order to update the plurality of points for each of the inner facial features of the first and second models. Stated otherwise, the operations that are conducted at block  920  refine the updated first and second models by using two constraints that are expressed mathematically in eq. (3) and eq. (4), above. 
   Step 6 returns to conducting a pair of operations at blocks  922 – 924 , where an update is made to each of the outer facial features of the first and second models. A pair of queries is conducted in the seventh step. These queries occur at blocks  926  and  928  for the first and second models, respectively. At block  926 , if the first model has converged within a predetermined tolerance of the face model, a representation of the inner and outer facial features of the first face model is output. Otherwise, steps 3–7 are repeated until the convergence for the first model is within the predetermined tolerance of the face model. Similarly, at block  928 , if the second model has converged within a predetermined tolerance of the face model, a representation of the inner and outer facial features of the second face model is output. Otherwise, steps 3–7 are repeated until the convergence for the second model is within the predetermined tolerance of the face model. An example of the result of four (4) iterations of steps 3–7 are seen, respectively, in  FIGS. 5   a – 5   b  through  8   a – 8   b.    
   Following the convergence of facial features between the two different views, the result of procedure  900  can be used in a face recognition process. For instance, identification can be made of the face of a person in a database that matches at least one of the first and second face images. Here, the matching process can uses the output representation of the inner and outer facial features of one or both of the first and second models. 
   A Computer System 
     FIG. 10  shows an exemplary computer system that can be used in the implementations described herein. Computer  1042  includes one or more processors or processing units  1044 , a system memory  1046 , and a bus  1048  that couples various system components including the system memory  1046  to processors  1044 . The bus  1048  represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. The system memory  1046  includes read only memory (ROM)  1050  and random access memory (RAM)  1052 . A basic input/output system (BIOS)  1054 , containing the basic routines that help to transfer information 
   between elements within computer  1042 , such as during start-up, is stored in ROM  1050 . Computer  1042  further includes a hard disk drive  1056  for reading from and writing to a hard disk (not shown), a magnetic disk drive  1058  for reading from and writing to a removable magnetic disk  1060 , and an optical disk drive  1062  for reading from or writing to a removable optical disk  1064  such as a CD ROM or other optical media. The hard disk drive  1056 , magnetic disk drive  1058 , and optical disk drive  1062  are connected to the bus  1048  by an SCSI interface  1066  or some other appropriate interface. The drives and their associated computer-readable media provide nonvolatile storage of computer-readable instructions, data structures, program modules and other data for computer  1042 . Although the exemplary environment described herein employs a hard disk, a removable magnetic disk  1060  and a removable optical disk  1064 , it should be appreciated by those skilled in the art that other types of computer-readable media which can store data that is accessible by a computer, such as magnetic cassettes, flash memory cards, digital video disks, random access memories (RAMs), read only memories (ROMs), and the like, may also be used in the exemplary operating environment. 
   A number of program modules may be stored on the hard disk  1056 , magnetic disk  1060 , optical disk  1064 , ROM  1050 , or RAM  1052 , including an operating system  1070 , one or more application programs  1072  (such as a design application), other program modules  1074 , and program data  1076 . A user may enter commands and information into computer  1042  through input devices such as a keyboard  1078  and a pointing device  1080 . Other input devices (not shown) may include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are connected to the processing unit  1044  through an interface  1082  that is coupled to the bus  1048 . A monitor  1084  or other type of display device is also connected to the bus  1048  via an interface, such as a video adapter  1086 . In addition to the monitor, personal computers typically include other peripheral output devices (not shown) such as speakers and printers. 
   Computer  1042  commonly operates in a networked environment using logical connections to one or more remote computers, such as a remote computer  1088 . The remote computer  1088  may be another personal computer, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to computer  1042 . The logical connections depicted in  FIG. 10  include a local area network (LAN)  1090  and a wide area network (WAN)  1092 . Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets, and the Internet. When used in a LAN networking environment, computer  1042  is connected to the local network through a network interface or adapter  1094 . When used in a WAN networking environment, computer  1042  typically includes a modem  1096  or other means for establishing communications over the wide area network  1092 , such as the Internet. The modem  1096 , which may be internal or external, is connected to the bus  1048  via a serial port interface  1068 . In a networked environment, program modules depicted relative to the personal computer  1042 , or portions thereof, may be stored in the remote memory storage device. It will be appreciated that the network connections shown are exemplary and other means of establishing a communications link between the computers may be used. 
   Generally, the data processors of computer  1042  are programmed by means of instructions stored at different times in the various computer-readable storage media of the computer. Programs and operating systems are typically distributed, for example, on floppy disks or CD-ROMs. From there, they are installed or loaded into the secondary memory of a computer. At execution, they are loaded at least partially into the computer&#39;s primary electronic memory. The system described herein includes these and other various types of computer-readable storage media when such media contain instructions or programs for implementing the blocks described, in conjunction with a microprocessor or other data processor. The system described can also include the computer itself when programmed according to the methods and techniques described herein. 
   For purposes of illustration, programs and other executable program components such as the operating system are illustrated herein as discrete blocks, although it is recognized that such programs and components reside at various times in different storage components of the computer, and are executed by the data processor(s) of the computer. 
   CONCLUSION 
   Implementations enable the representation of facial features and the locating of points for the facial features, such as the eye corners, nose tips, etc. Correlation of the facial features for a pair of different views of the same face is found by using epipolar geometry. A mathematical model captures the shape variations on both inner facial features and the outer silhouette of the face. An algorithm uses a face model that is decomposed into inner and outer facial features in order to improve the matching of the facial features on the pair of different views of the same face. 
   Although the invention has been described in language specific to structural features and/or methodological acts, it is to be understood that the invention defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as exemplary forms of implementing the claimed invention.