# Analyzing Facial Expressions for Virtual Conferencing

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3 Animating Virtual Humans 3 Teture and depth information from a 3D laser scanner. 4 Control points of the shaped spline surface. control points instead of appling transformations on each verte, which reduces the computational compleit. Conventional B-splines suffer from one well-known drawback: since the re defined on a rectangular topolog, the don t refine curved areas locall. To overcome this restriction, we use triangular B- splines. 7 This spline scheme, based on triangular patches (shown in Figure 2a), can easil be refined while still preserving the above mentioned properties of normal B-splines. For rendering, we approimate the smooth spline and subdivide each patch into a number of planar triangles, leading to a mesh as illustrated in Figure 2b. We can var the number of triangles to get either a good approimation or higher frame rate during rendering. The resulting triangular mesh is defined b a discrete set of vertices on the mathematicall defined spline surface. We need to compute the B-spline basis functions 7 onl at the discrete verte positions on the surface (this can be done offline). Once we have determined the basis functions, we calculate the position of the vertices v j b v = N c j ji i i I j (1) with N ji the precalculated basis functions of verte j with N ji = 1 i I j (2) where I j is the inde set of verte j and c i the ith control point. The inde set I j usuall contains three to si indices for the control points that influence the verte s position. To individualize the generic model, we use a 3D laser scan of the person with a neutral epression. The scan provides us with information about color and depth as shown in Figure 3. We map the teture on the 3D model and optimize the control points position to adapt the spline surface to the measured data. After the optimization, shape and teture coincide with the person s appearance. The model can now be deformed to show other epressions rather than the neutral one of the scan. 5 Different snthesized epressions. Modeling facial epressions To estimate the FAPs requires animating our model to create different facial epressions. We simplified this task b using splines because the alread constrain the neighboring vertices motion. To parameterize the facial epressions, we adapted the MPEG-4 Snthetic-Natural Hbrid Coding (SNHC) group s proposal. 9 According to that scheme, ever facial epression can be generated b a superposition of 68 action units. These include both global motion (such as head rotation) and local motion (ee or mouth movement). Currentl, 46 of these 68 FAPs are implemented. To model the local movements, our generic face model contains a table describing how the mesh s con- 72 September/October 1998

4 trol points are translated or rotated for each FAP. This is done onl for the small number of control points shown in Figure 4. For a given set of FAPs that specif a person s epression, all positions of the control points are updated. Then the verte locations are computed according to Equation 1 b a linear combination of the control points. Figure 5 shows eamples of rendered epressions for different persons. Camera model The camera model describes the relation between our virtual 3D world and the 2D video frames. It s used for both rendering and parameter estimation. We use the perspective projection as shown in Figure 6, where the 3D coordinates of an object point [ z] T are projected into the image plane according to z Y X, Y X Object Image plane 6 Camera model and its associated coordinate sstems. X = X f Y = Y f z z (3) Here, f and f denote the focal length multiplied b scaling factors in the - and -directions, respectivel. These scaling factors transform the image coordinates into piel coordinates X and Y. In addition, the allow the use of non-square piel geometries. The two parameters X and Y describe the image center and its translation from the optical ais due to inaccurate placement of the charge-coupled device (CCD) sensor in the camera. To estimate the FAPs, we must model the real camera used for recording the video sequence in our snthetic world. The four parameters f, f, X, and Y are therefore obtained from an initial camera calibration using Tsai s algorithm. 1 At the decoder we can then use arbitrar camera parameter settings if we don t want to reconstruct the original image eactl. This lets us zoom into the scene if desired. Motion estimation and facial epression analsis Our motion estimation algorithm analzes a speaking person s facial epressions b estimating changes of FAPs. We use the whole face image for the estimation, in contrast to feature-based approaches that eploit the information of discrete feature point correspondences. Estimating 3D motion vectors from 2D images proves difficult. The errors of the estimates become ver large if we do not determine eactl the position of the small number of features. Therefore, we set up equations at each piel location of the image, leading to a large number of correspondences used for parameter estimation. To keep the computational compleit low, we developed a linear algorithm for the estimation that solves the large set of equations in a least-squares sense. The small errors that arise due to linearization are corrected using a feedback structure in a hierarchical framework. Feedback loop The motion estimation algorithm presented here esti- Camera image Snthetic image I(n) Î(n 1) Model Analsis Shape Teture Epressions Snthesis Facial parameters Model update mates the FAPs from two successive frames using the shape and teture information from the 3D model. An eas wa of doing this is to estimate the motion between two camera frames and move the 3D head model according to these estimates in the virtual world. However, small errors in the estimation result in placing the 3D model whose shape information proves necessar for computing the motion incorrectl. In the net frame, the facial parameters become even worse because the shape does not recover from the model eactl. To avoid error accumulation in the long-term parameter estimation, we use a feedback loop 11 as depicted in Figure 7. The head s model moves according to the parameters estimated from two successive frames. Rendering the model with a modified shape and position generates a snthetic image. The estimation is then performed between the actual camera frame I(n) and the snthetic image of the previous frame ^ I(n 1), which assures that no misalignment of the model occurs. An error in the estimated parameters again leads to placing the model incorrectl. However, the error can be removed during the estimation in the net frame because no mismatch eists between the 3D model and the sntheticall rendered image ^ I(n 1). 7 Feedback structure of the coder. IEEE Computer Graphics and Applications 73

5 Animating Virtual Humans 8 Transformation from FAPs to image points. FAPs 3D motion equation Estimating the 3D motion of fleible bodies from 2D images proves difficult. However, we can constrain the deformation of most objects to simplif the estimation process. In our algorithm we use a parameterized head model whose local deformations are a function of the 68 unknown FAPs. For each 3D object point of the surface, we can set up one linear 3D motion equation that determines how the point moves in the 3D space if the FAPs change. Instead of the si parameters specifing a rigid bod motion, we now have 68 unknowns. Due to the large number of equations for the parameter estimation, we still have an over-determined linear sstem of equations that we can solve easil. To set up the 3D motion equation, we must combine several transformations, shown in Figure 8, to take into account the dependencies between the FAPs and the model s 3D object points. First, the surface s control points are moved according to the given FAPs. Using the basis functions of the splines, the algorithm calculates the position of the vertices from the control points. Three vertices form a triangle, and the 3D motion of all object points inside this triangle specified b their barcentric coordinates is determined. Finall, the 2D image point is obtained b projecting the 3D point into the image plane. We incorporated these transformations all linear ecept for the projection into our parameter estimation algorithm. The new control point position c i can be determined from the position c i in the previous frame b where 3D model 9 Approimation of rotations. Control points Basis functions c = c + FAP d i i k ik k FAPk = FAP k FAPk Vertices Barcentric coordinates d ik α k r i 3D object points (4) (5) is the change of the facial animation parameter k between the two frames and d ik the 3D direction vector of the corresponding movement. Strictl speaking, Equation 4 is valid onl for translations. If a number of control points rotate around given O Camera model α k 2D object points aes b some action units, the description for the motion of control points becomes more complicated due to the combination of rotation (defined b rotation matrices) and translation. The order of these operations can no longer be echanged, and the use of matri multiplication results in a set of equations that is nonlinear in the parameters that must be estimated. However, we can also use the linear description from Equation 4 for rotation if we assume that the rotation angles between two successive frames are small. Then, the trajector of a control point i that rotates around the center O can be approimated b its tangent d ik as shown in Figure 9. This tangent differs for all object points, but we have to set up Equation 4 for all points individuall anhow because of local deformations in the surface. For a rotation b the angle α k, α k = FAP k s k (6) defined b the facial animation parameter changes FAP k and the corresponding scaling factor s k, the length of the translation vector d ik can be calculated b d ik = FAP k r i s k (7) Here, r i is the distance between the object point and the given rotation ais. With this assumption (the direction of d ik is specified b the direction of the tangent), Equation 4 can also be used for rotation, leading to a simple linear description for all FAPs. Additionall, we can estimate both global and local motion simultaneousl. The small error caused b the approimation is compensated after some iterations in the feedback structure shown in Figure 7. Having modeled the shift in control points, we can determine the motion of the triangular mesh s vertices using Equation 1. The local motion of an object point is calculated from that using 2 2 = λmv m = λm Nmj c m= (8) where λ m are the barcentric coordinates of the object point in the triangle that encloses that point. The motion equation for a surface point can be represented as = + FAP k t k = + T FAP k j J m= (9) where t k s are the new direction vectors to the corresponding FAP calculated from d k b appling the linear transforms of Equations 1 and 8. T combines all the vectors in a single matri and FAP is the vector of all FAP changes. The matri T can be derived from the 3D model. Equation 9 then describes the change of the 3D point location as a linear function of FAP changes FAP. Due to the presence of local deformations, we cannot describe the transformation with the same matri T for all object points (as in the case for rigid bod motion) but have to set T up for each point independentl. j 74 September/October 1998

7 . Animating Virtual Humans 11 PSNR after global and global plus local motion compensation. PSNR (decibels) Global + local motion Global motion Frame time, the threshold G used to detect outliers for the motion estimation reduces from 5 (first level) to.5 (highest resolution), which means that at higher levels more piels become classified as outliers. Eperiments with this hierarchical scheme showed that it can estimate displacements of up to 3 piels between two frames. Eperimental results To validate the estimation algorithm, we performed eperiments with snthetic and real video. To create the snthetic sequences, we rendered the 3D model with known FAPs, which let us compare the estimated FAPs with original ones. For real sequences recorded with a camera, we had to individualize the generic 3D model to the person in the video using a 3D laser scan of that person. Unfortunatel, we couldn t determine the accurac of the estimated FAP values for real image sequences, since we didn t know their correct values. Therefore, we could onl compare the reconstructed snthetic image with the original camera frame. The error measure that we used for that purpose is the peak signal noise ratio (PSNR), defined as 12 Camera frames (left) and corresponding reconstructed snthetic frames (right). PSNR = 1 log N 1 i= ( Iorig, i Isnth, i ) (18) In this equation I orig,i is the luminance component of piel i of the original camera image with values from to 255, and I snth,i is the corresponding value in the snthetic image. N denotes the number of piels in the image. filtered and subsampled versions of the camera frame I(n) and the snthetic frame ^ I(n 1). Due to using lowresolution images, the linear intensit assumption remains valid over a wider range. For subsampling, simple moving average filters reduces aliasing. A Gauss filter to smooth the edges before estimating the motion further filters the resulting images. The estimated parameter set generates a motion-compensated image b moving the 3D model and rendering it at the new position. Due to the motion compensation, the differences between the new snthetic image and camera frame decrease. Then, the procedure is repeated at higher resolutions, each time ielding a more accurate motion parameter set. Note that we use the same camera frame in all levels, and that the snthetic image is changed from ^ I(n 1) to ^ I(n) iterativel. In our current implementation we use three levels of resolution starting from piels. For each new level the resolution doubles in both directions, leading to a final Common Intermediate Format (CIF) resolution of piels. At the same Snthetic sequence In the first eperiment we created a snthetic sequence (1 frames) with a resolution of piels (CIF resolution). Rendering the 3D model with well-defined FAPs and a viewing angle of about 25 degrees achieves this. We estimated 1 FAPs for ever fifth frame using the proposed algorithm and compared the results to the correct values. Table 1 shows the relative error averaged over all estimates. The values in the table were measured relative to the maimum of each value that corresponded to an etreme epression. In this eperiment we used the FAPs for global motion of the head (FAPs 48, 49, 5), opening of the jaw (FAP 3), and movements of eelids (FAPs 19, 2), eebrows (FAPs 35, 36), and lip corners (FAPs 12, 13). The accurate values for the estimated FAPs also resulted in an ecellent reconstruction of the original frames. Because we used the same model for creating the sequence and estimating the parameters, we achieved a nearl perfect reconstruction. You can see this in Figure 11, where we plot the measured PSNR between the original and snthetic image. Averaging the PSNR values computed onl in the facial area and not for the background leads to a value of about 7 decibels. For comparison, Figure 11 also shows the PSNR for the reconstructed sequence we generated using onl global motion parameters (head translation and rotation). 76 September/October 1998

9 Animating Virtual Humans References 1. D.E. Pearson, Developments in Model-Based Video Coding, Proc. IEEE, Vol. 83, No. 6, June 1995, pp W.J. Welsh, S. Searsb, and J.B. Waite, Model-Based Image Coding, British Telecom Technolog J., Vol. 8, No. 3, Jul 199, pp K. Aizawa and T.S. Huang, Model-Based Image Coding: Advanced Video Coding Techniques for Ver Low Bit-Rate Applications, Proc. IEEE, Vol. 83, No. 2, Feb. 1995, pp I.S. Pandzic et al., Towards Natural Communication in Networked Collaborative Virtual Environments, Proc. Framework for Immersive Environments (FIVE) 96, 1996, 5. F.I. Parke, Parameterized Models for Facial Animation, IEEE CG&A, Vol. 2, No. 9, 1982, pp M. Rdfalk, Candide: A Parameterized Face, LiTH-ISY-I- 866, Image Coding Group, Linköping Univ., Linköping, Sweden, Oct., G. Greiner and H.-P. Seidel, Modeling with Triangular B- Splines, Proc. ACM/IEEE Solid Modeling Smp. 93, 1993, ACM Press, New York, pp M. Hoch, G. Fleischmann, and B. Girod, Modeling and Animation of Facial Epressions Based on B-Splines, Visual Computer, Vol. 11, 1994, pp SNHC Sstems Verification Model 4., ISO/IEC JTC1/SC29/WG11 N1666, Bristol, Great Britain, April R.Y. Tsai, A Versatile Camera Calibration Technique for High-Accurac 3D Machine Vision Metrolog Using Offthe-Shelf TV Cameras and Lenses, IEEE J. of Robotics and Automation, Vol. RA-3, No. 4, Aug. 1987, pp R. Koch, Dnamic 3D Scene Analsis through Snthesis Feedback Control, IEEE Trans. PAMI, Vol. 15, No. 6, June 1993, pp H. Li, P. Roivainen, and R. Forchheimer, 3D Motion Estimation in Model-Based Facial Image Coding, IEEE Trans. PAMI, Vol. 15, No. 6, June 1993, pp J. Ostermann, Object-Based Analsis-Snthesis Coding (OBACS) Based on the Source Model of Moving Fleible 3D Objects, IEEE Trans. Image Processing, Vol. 3, No. 5, Sept. 1994, pp D. DeCarlo and D. Metaas, The Integration of Optical Flow and Deformable Models with Applications to Human Face Shape and Motion Estimation, Proc. Computer Vision and Pattern Recognition (CVPR) 96, IEEE CS Press, Los Alamitos, Calif., 1996, pp P. Eisert and B. Girod, Model-Based Coding of Facial Image Sequences at Varing Illumination Conditions, Proc. 1th Image and Multidimensional Digital Signal Processing Workshop 98, IEEE Press, Piscatawa, N.J., Jul 1998, pp Peter Eisert joined the image communication group at the Telecommunications Institute of the Universit of Erlangen-Nuremberg, German in As a member of the Center of Ecellence s 3D Image Analsis and Snthesis group, he is currentl working on his PhD thesis. His research interests include modelbased video coding, image communication, and computer vision. He received his diploma in electrical engineering from the Universit of Karlsruhe, German in Bernd Girod is a chaired professor of telecommunications in the Electrical Engineering Department of the Universit of Erlangen-Nuremberg. His research interests are in image communication, 3D image analsis and snthesis, and multimedia sstems. He has been the director of the Center of Ecellence s 3D Image Analsis and Snthesis group in Erlangen since He received an MS from Georgia Institute of Technolog, Atlanta, and a PhD in engineering from the Universit of Hannover, German. Readers ma contact the authors at the Telecommunications Laborator, Universit of Erlangen, Cauerstrasse 7, D-9158, Erlangen, German, {eisert, nt.e-technik.uni-erlangen.de. International Smposium on Visualization Ma 1999 Vienna, Austria The IEEE Technical Committee on Computer Graphics is cosponsoring its first visualization conference in Europe. In conjunction with Eurographics, the TCCG will cosponsor the joint Eurographics-IEEE TCCG Smposium on Visualization on Ma 1999 in Vienna, Austria. A Program Committee will review both papers and case stud submissions. Attendance is open to all with strong representation epected from both sides of the Atlantic. There will also be other eciting events coordinated with the conference. For more information visit or the TCCG Web page at 78 September/October 1998

10 IEEE Computer Graphics and Applications 79

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