THE capability to precisely synthesize online fullbody

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1 1180 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER 2014 Sparse Constrained Motion Synthesis Using Local Regression Models Huajun Liu a, Fuxi Zhu a a School of Computer, Wuhan University, Wuhan , China {huajunliu, fxzhu}@whu.edu.cn Abstract Based on sparse control constraints, one difficulty for synthesizing natural human motions is that lowdimensional control information can not be directly used to construct high-dimensional human poses. This paper introduces a novel and powerful local dimensionality reduction approach for synthesizing accurate and natural full-body human motions. The approach is to construct a group of online local dynamic regression models from a pre-captured motion database as a prior to support the full-body human action synthesis. By synthesizing a variety of human motions from as possible as few sparse constraints provided by users, the paper verifies the effectiveness of the proposed approach. Compared with previous statistical models, our model can synthesize more accurate results. Index Terms Human motion synthesis, Sparse constraints, Data-driven animation I. INTRODUCTION THE capability to precisely synthesize online fullbody human motions in real time would be applied to many areas, such as real sport training, rehabilitation, and realtime control of game virtual characters or robotic systems. Creating such a system has already been partially solved by commercially mocap equipments (such as, Vicon, XSens etc.), but their approaches are very expensive for a general family use. They also need complex operations which require the user to wear skintight clothing along with about 50 retro-reflective markers which are carefully positioned, 18 inertial or magnetic sensors, or a full-body exoskeleton to provide supports for motion capture. Recently, major game console companies, including Microsoft, Sony, and Nintendo, have developed next generation hardware devices to capture online performances of individual players. One of the advantages for these devices is their cheap price and suitable for common uses. However, low-dimensional signals from the devices are the main challenge for an accurate full-body human motion control, since a typical human body model is represented by more than 50 degrees of freedom (DOF). Building such an animation synthesis system is inherently an ill-posed problem, because user s inputs essentially are This work is supported by the National Basic Research Program of China (973 Program) (GrantNo.2011CB302306), National Science and Technology Support Program (Grant No. 2012BAH35B02), and the National Nature Science Foundation of China (GrantNo , ), Natural Science Foundation of Hubei Province of China (GrantNo. 2013CFB300), Research Fund for the Doctoral Program of Higher Education of China (GrantNo ). not enough to adequately determine a high-dimensional human pose. One attractive approach to eliminate reconstruction ambiguity is to learn a prior from pre-captured human poses. Previous researches often utilize principle component analysis (PCA) models [1] or principle component regression (PCR) models [2] to constrain the reconstruction space. Their systems work well for a large number of pre-captured motion data and they can model a virtual character s actions although its movement is highly nonlinear. Different from previous approaches, a new local dimensionality reduction method is proposed in our paper. While running, our system uses pre-captured mocap data to learn a group of local regression models to constrain the reconstruction space. We search the mocap database for K nearest motion examples which are similar to the recently already synthesized poses q t 1,...,q t m, and then use these motion sequence q tk 1,...q tk m along with their subsequent poses q tk, k= 1,...K, as training data to learn a predictive model for the reconstruction of the current pose q t. For linear regression learning approaches, the training data can be divided into two parts: input data and output data. Our proposed model has the following features: first, like the other local models, it is time-varying because, at each moment, a new local model is produced for the next pose prediction, and it scales up well to the size and heterogeneity of motion database. However, different from theirs, our proposed model estimates an projection direction and output data with a linear combination of basis regression equations or functions, therefore, it can add more spatial-temporal information than previous ones which just reduce dimensionality on input data. Our testing results also approved that our model is more powerful than previous models for synthesizing accurate motions. Using constrained maximum a posteriori (MAP) framework for human poses estimation can produce a natural motion sequence that best matches the control inputs assigned by the user. For this reason, we also formulate the online motion reconstruction problem in a MAP framework by utilizing a prior from online local regression models and a likelihood term from user-specified sparse constraints together. Our animation system can synthesize variously natural motions based on as possible as few sparse constraints (e.g., several joint positional trajectories) for an accurate online motion reconstruction doi: /jmm

2 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER Figure 1. Based on user-specified sparse constraints, our system can automatically synthesize realistic human motions. The blue points are sparse control points. of a full-body virtual character (see Figure 1). By online synthesizing a variety of human actions, such as walking, golf swinging, running, jumping, and boxing, the effectiveness of our model has been demonstrated in our implementation. Based on the same motion capture database and sparse control constraints, the synthesized results are better than the ones created by previous models. When the database is appropriate, the results are even comparable in quality to the ground truth data which were captured by the commercial equipments. II. RELATED WORK We discuss related work in utilizing sparse control constraints and statistical motion models based on data-driven approach for full-body human motion reconstruction. A. Sparse-constrained optimization A number of researchers have developed approaches that use sparse constraints provided by sensors to control high-dimensional human motions. For example, Shotton [3] and Wei [4] used a single depth camera to track and reconstruct various human motions. No markers were acquired to attach on user s body in their approaches, however, no less than 15 control points needed to be used to segment the human body. Semwal [5] combined the inverse kinematics algorithm and the sparse constraints from eight magnetic sensors together to provide an analytic solution for human motion control. Chai and Hodgins [1] used six to nine retro-reflective markers as the control points for online human motion reconstruction. Slyper and Hodgins [6] used five inertial sensors for realtime upper-body control. Recently, Liu and colleagues [2] reached a full-body human motion control using the positional and orientational constraints from six inertial sensors. Compared with theirs, this paper can use only four positional control points for realistic full-body human motion synthesis. Note that Tautges and colleagues [7] utilized sparse constraints provided by four accelerometer sensors to control a full-body human motion. However, their method can just closely approximate a performed motion because of missing positional and orientational constraints. Different with their control constraints, this paper applies positional constraints for motion synthesis to get a better results. In general, all of these approaches were using pre-recorded motion data as the supplement to balance the missing constraints of the sparse controls, and our work also adopts the same idea which is using sparse constraints and a statistical model calculated from a prerecorded motion capture data for human motion synthesis. B. Data-driven human motion reconstruction It is one of popular ways to construct statistical models of human motions for interactively controlling an avatar in real time. Statistical motion models are often described as several mathematical functions that represent human motion by a set of parameters associated with probability distributions. So far, using pre-captured motion data to learn statistical motion models have been used for key frames interpolation [8], motion styles synthesis [9] or speech-driven facial expressions [12, 13], interactive creation of a character s pose using a mouse [10] or control of human actions using vision-based tracking [1], realtime human motion control with inertial sensors [2] or accelerometer sensors [7], synthesizing human motion by using multifactor model [16], building physically-valid motion models for human motion synthesis [11] and so forth. Our approach is also to learn a statistical dynamic model from human motion capture database, however, the dynamic behavior of our model is controlled by a continuous sparse control constraints rather than a discrete hidden state as in [9, 12, 13] which using Hidden Markov Models (HMMs), so the control will be more flexible. Different with Gaussian Process Latent Variable Model (GPLVM), a global and nonlinear dimensionality reduction technique which works well with a small homogenous data set applied in [10, 14], this paper proposes a local dynamic model which can be applied for a large and heterogeneous motion database. Among above-mentioned statistical models, our work is most relevant to local models constructed in the subspace for online control of human motions [1, 2], because all of them are built during runtime and based on training data which are closed to the current reconstructed motion. Nevertheless, there exists a very significant difference. For dimensionality reduction methods, the training data can be divided into two parts: input and output data. If the modeling process has the ability to find the structure along with the parameters of a function so that it optimally represents a group of a given projection direction and output data, the prediction will be more effective. The methods [1, 2] they proposed are reducing dimensionality

3 1182 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER 2014 only on the input data, however, our proposed method focuses on finding the relationship between projection directions and output data, so it can give a more accurate prediction. The experiments in Section 5 show that the proposed method can produce more accurate results than the previous methods. In addition, for the equivalently accurate requirements, our approach needs fewer control information than theirs for the power of the proposed model. III. OVERVIEW OF ONLINE SYNTHESIS SYSTEM Our animation synthesis system automatically transforms control inputs from user-specified sparse constraints into realistic human motions by building a group of online local regression models at run time, and then using those models combined with the sparse constraints (e.g., userspecified joint positional trajectories) for human motion synthesis (see Figure 2). We assume human actions can be represented as an m-order Markov chain, so the current pose q t can be thought to only depend on previous m synthesized poses Q t,m = [q t 1,..., q t m ]: Pr(q t q t 1,..., q 1 ) = Pr(q t q t 1,..., q t m ). where the likelihood term E control measures to what extent the generated pose q t matches the user-specified constraints c t, and the prior term E prior measures the naturalness of the synthesized pose. An optimal estimate of the synthesized motion produces a natural human motion that achieves the goal specified by the user. IV. ONLINE SYNTHESIS OF HUMAN BEHAVIORS Using sparse constraints to synthesize human motion is difficult because the control constraints provided by the user can not fully constrain the entire human model to stay in the natural-looking space. So our solution is to utilize a group of local regression models to solve the issue of reconstruction ambiguity. The results in Section 5 show our proposed model can achieve more accurate results than previous ones. A. Control Consistency E control measures how well the locations of corresponding joints in the reconstructed human pose fit the control inputs obtained from user-defined constraints: E control = ln pr(c t q t ) f(q t ; s) c t 2 (3) where q t, s and c t are vectors. q t is joint angles of the synthesized pose at frame t, s is the character s skeletal size and c t is the user-specified constraints for the pose at frame t. The forward kinematics function f calculates the global coordinates value of the current pose q t. Figure 2. System overview. The proposed local regression modeling approach adds local spatial-temporal directions into the models for constraining the transformation of poses in the configuration space, predicts how humans move in each region and constrains the reconstructed motion to stay in the space of natural-looking human motion. We use the online constructed model to generate the desired pose q t from various forms of kinematic constraints c t specified by the user. We optimize the motion synthesis process in a MAP framework by estimating the pose q t which is most satisfied by user s input c t along with previous reconstructed pose sequence Q t,m : arg max qt pr(q t c t, Q t,m ) arg max qt pr(c t q t ) pr(q t Q t,m ) (1) By applying the negative log to the posteriori distribution function pr(q t c t, Q t,m ), we can convert the constrained MAP problem into an energy minimization problem: arg min qt ln pr(c t q t ) + ln pr(q t Q t,m) (2) }{{}}{{} E control E prior B. Online Local Regression Modeling In this subsection, we propose to automatically build sequential online local regression models to adequately constrain the synthesized pose to stay in the naturallooking solution space. A novel local linear model is proposed to avoid the problem of finding an appropriate structure for a global dynamic model, which would necessarily be high-dimensional and nonlinear. We adopt K-nearest neighbor search algorithm to find the K motion examples in the database which are similar to the already synthesized poses, and use these motion examples along with their subsequent poses for our online model learning. To predict the current pose q t at frame t, the first step is to search in the motion database, and find the closest motion segments which are most similar to the recently constructed one Q t,m = [q t 1,...,q t m ], we choose the K nearest motion segment examples [q tk 1,...,q tk m] along with their subsequent poses q tk, k=1,...,k as the training data to learn a predictive model via statistical model learning methods for the current pose q t. Suppose a linear relationship exists between an input joint angle vector x = [q t 1,...,q t m ] and an output joint angle vector y = q t. For simplicity, the prediction function for each DOF in output q t is learned separately. By subtracting the means from input training data and output training data, we assume the mean values of x and y are zeros. Therefore, the function of proposed model which is represented using linear regression as

4 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER y = α T x + β y (4) where the input joint angle x is an m D-dimensional vector. D represents the dimension of DOFs for a human character and y is joint angle value for output. Regression coefficients are vector α, and β y represents a homoscedastic noise variable, which is independent of vector x. Moreover, given the K motion examples {(x k ; y k )}, k = 1,..., K which are similar to the current synthesized poses, and by minimizing the expected squared error K E = y k α T x k 2,we can get the coefficients α k=1 by the least squares solution, α = (X T X) 1 X T y (5) The row of the matrix X stores the input joint angle vectors x k, k = 1,..., K, and K output joint angle values are stacked in vector y. Our proposed method calculates projections of highest correlation between input joint angle matrix X and output vector y. These projections can be achieved by maximizing the squared relationship correlation 2 (Xu j, y) = (u T j XT y) 2 /u T j XT Xu j (6) where u j is one of the projection directions. Since each projection Xu j is orthogonal to others and its length is unit, we can get u T j XT Xu j = 1. Here, u j is one column of the matrix U that includes the eigenvectors of covariance matrix C = (X T X) 1 X T yy T X. In the proposed model, we project X onto U for only considering the projections. By minimizing y XUγ 2 with respect to the reduced coefficients γ, we can get α = Uγ = U(U T X T XU) 1 U T X T y (7) Because we predict each DOF in output q t separately, we just have one projection direction u for each time. The weight for each data point x k can be calculated by Gaussian functions, using their relative distance from the previous reconstructed poses Q t,m = [q t 1,...,q t m ] : ω k = exp( 1 2 (x k Q t,m ) T W (x k Q t,m )) (8) where W is the diagonal matrix which contains the weights for each DOF. In our implementation, we use an identity matrix to represent W. The eigenvectors are extracted from the matrix C ω = (X T DX) 1 X T Dyy T DX (9) where D is a diagonal matrix, containing ω k along its diagonal. Furthermore, the weighted regression coefficients can be represented as α ω = U(U T X T DXU) 1 U T X T Dy (10) Suppose there exists a Gaussian distributed noise variable β y, its standard deviation σ can be estimated by y k βx k, k = 1,..., K. In our experiment, a predicted function for each DOF of the synthesized pose is constructed, therefore, to predict the d-th DOF of the pose, we can describe our local regression model as q t,d = α T d,ω Q t,m + N(0, σ d ) (11) where q t,d, σ d are scalars, q t,d represents the d-th DOF of the t-th frame pose, and σ d represents the standard deviation for the d-th prediction function. α d,ω, Q t,m are vectors, α d,ω are the weighted regression coefficients for the d-th DOF, and Q t,m is reconstructed motion segment before current synthesized pose. The computational complexity for reconstructing a pose is O(Km 2 D 2 ). Here, K, m, D represents the number of training data, the previous m poses (window size) and the dimension of DOF for a human character, respectively. In our implementation, we maximize the probability of the pose q t based on previous synthesized motion sequence Q t,m : P r(q t Q t,m ) D d=1 exp[ (q t,d α T d Q t,m) 2 ] (12) σd 2 where q t,d, d = 1,..., D is the d-th degree of freedom of the current pose q t. The vector α d and the scalar σ d are the regression coefficients and standard deviation of the d-th prediction model. By minimizing the negative log of Pr(q t Q t,m ), the energy formulation can be reached as: E prior = d (q t,d α T d Q t,m) 2 σ 2 d (13) The final cost function for our pose synthesis is constitutive of the aforementioned terms: control term (Equation 3) and prior term (Equation 13). V. RESULTS AND COMPARISONS Software implementation. We have examined our algorithms with different motion sequences on a desktop PC with Intel Core 2.8 GHz CPU and 4 GB memory. Figure 3 are several interfaces of our prototype software. We adopt gradient-based optimization using Levenberg- Marquardt method [15] for the objective function which is defined in Equation (2), and use the most similar motion example which already exists in the database to initialize the optimization. In the implementation, the optimization converges fast. The computational efficiency of our animation system mainly relies on searching scope in the motion database, so we accelerate process for the K nearest neighbor search using the neighbor graph approach in [1]. We use two databases for our testing. One database has poses includes five full-body behaviors: golf swinging (2935 frames), jumping (5082), boxing (32852), walking (22846) and running (6173). The other has 1.2 M poses downloaded from the CMU database. All of them were recorded using a Vicon mocap system which has a frame rate of 120 fps. In our implementation, we downsampled the data to 60 fps in order to achieve more natural-looking motions for visualization. To balance the synthesis framerate and the quality of reconstructed motion, in our implementation, we choose window size m is 2, and our system can run at average 57 fps. We verified the effectiveness of proposed approach on various behaviors and evaluated the reconstructed results with ground-truth data.

5 1184 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER 2014 Figure 4. Comparison with three popular algorithms: GPLVM, local PCA and local PCR algorithms: (upper) motion synthesis using positions of six joints (head, the center of torso, two wrists and two ankles); (lower) motion synthesis using positions of four joints (two wrists and two ankles). TABLE I. RECONSTRUCTION ERRORS AND SYNTHESIS FRAMERATE ON DIFFERENT WINDOW SIZE m=1,2,3, Reconstruction error (degree) Synthesis framerate (fps) Figure 3. The interfaces of our prototype software. (upper) walking motion; (middle) golf swinging motion; (lower) jumping motion. The red lines are user-specified trajectory constraints, and the blue points are the point constraints at one frame on red trajectories. Testing on user-specified data. We tested our animation system by online synthesizing various human motions (walking, running, golf swinging, jumping and boxing) of an avatar based on four joint positional constraints specified by the user (left wrist, right wrist, left ankle and right ankle). Figure 7 is some frames of the results for online motion synthesis. Error evaluation. We used leave-one-out error evaluation method to verify the quality of synthesized motions by our approach. We choose one sequence of motion capture example as the testing data each time, and then we use the rest of motions as the searching data for our online motion reconstruction. We synthesized different human motions and calculated the average synthesis errors. Figure 4 shows the standard deviations and mean errors of the reconstruction errors for various behaviors (golf swinging, jumping, boxing, walking and running). Window size and synthesis framerate. The computational complexity of modeling process mainly depends on the dimensional number of input data (m D). Table 1 is the reconstruction errors and framerates under different window size m. We tested the window size from 1 to 4. In our implementation, we found our system runs in real time with the average framerate of 35 fps when m is 3, compared with 84 fps when m is 1. In addition, the reconstruction errors usually increase as window size is reduced. When more local spacial-temporal information is added to the prior learning, the effect of prediction will be more accurate. Comparing with previous algorithms. Based on leave-one-out error evaluation, we tested the performance of our proposed model compared with three popular approaches (Gaussian Process Latent Variable Model [10], local principle component analysis model [1] and local principle component regression model [2]) by reconstructing various human motions. Figure 4 is the comparison for mean errors and standard deviations on five different motion behaviors for all four techniques.

6 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER Figure 6. Frame-by-frame comparison for one testing sequence: (upper) walking motion; (lower) boxing motion. TABLE II. R ECONSTRUCTION ERRORS BASED ON DIFFERENT NUMBER OF CONTROL POINTS FOR DIFFERENT ALGORITHMS. GPLVM LPCA LPCR Our method Figure 5. The interfaces of comparison with two popular algorithms (local PCA and local PCR ) and ground truth data (green one). (upper) walking motion; (middle) golf swinging motion; (lower) boxing motion. In the evaluation, we also adopt six constraint points which were used in [2], the results show that, compared to the other three techniques, our method can achieve not only smaller mean errors but also smaller standard deviations. In another aspect, while just using four control points(two wrists and two ankles), previous methods can not synthesize natural-looking human data (See Figure 5). Figure 6 shows the frame-by-frame comparison of the reconstruction errors for one testing data. The assessment results indicate the synthesis results by our proposed method are better than the results created by the other two local methods. Different number of control points. We tested the different number of control points for four methods. We chose the number of positional control points from two to six. (1) Left wrist and right ankle; (2) left wrist and two ankles; (3) two wrists and two ankles; (4) root, two wrists and two ankles; (5) head, root, two wrists and two ankles. By testing on different motions, we got the conclusion that the reconstruction errors usually reduce as the number of constraints is increased. In addition, we also found that compared with the six constraint points (head, the center of torso, two wrists and two ankles) which was used in [2] to get a natural-looking reconstructed human motion, we can use as possible as few constraint points (4 constraint points: two wrists and two ankles) to achieve a comparable result with the mocap real data. Table 2 is the average reconstruction error comparison on different number of control points. Along with few constraint points are used, our model is still more powerful for accurate motion synthesis than the previous three methods. Testing on different database. Table 3 is the average reconstruction errors of five different actions from three algorithms for two different training database. The reconstruction errors are calculated using 3D positional constraints from six control points. We found that, for GPLVM method, the reconstruction error is great when using a large and heterogeneous database. When applying a small database, the reconstruction error is also larger than the local modeling approaches. For the other local modeling methods, when the size of training database is

7 1186 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER 2014 Figure 7. Key frames for online motion synthesis. From top to bottom: walking, golf swinging, running, jumping and boxing. The blue points are joint constraints. TABLE III. AVERAGE RECONSTRUCTION ERRORS FOR FOUR METHODS ON DIFFERENT DATABASE poses 1.2 M poses GPLVM LPCA LPCR Our method increased, the reconstruction error reduced. In addition, our proposed model can achieve the smallest reconstruction error than others. By testing on different database, we also verified the powerful of the proposed model. Limitations. There are three limitations for the proposed method. (1) Like other data-driven approaches, the database is crucial for the quality of synthesized motion. The system will not produce a desired motion if the training data does not contain any desired motion patterns. For example, if the walking motion pattern is not included in the database, our system will not be able to synthesize desired walking data. (2) Userspecified constraints are also crucial for the final results. In fact, if user-specified constraints are not natural or self-conflicting, the reconstruction result will not be a realistic human motion to satisfy user s constraints. (3) The motion data need to be previously arranged for online

8 JOURNAL OF MULTIMEDIA, VOL. 9, NO. 10, OCTOBER search. Like most local modeling approaches, a specific data arrangement structure is applied for motion data to accelerate the searching process. VI. CONCLUSIONS In this paper, a new local regression model is introduced for online reconstructing natural full-body human motion just based on as possible as few user-specified constraints. The proposed method, which is using datadriven approach, is to utilize several nearest motion examples to construct a group of online local regression models for online motion synthesis. However, based on the same defined constraints and motion database, the proposed method has better force of constraint than the previous local models and thus can synthesize more realistic human motions. Therefore, our proposed model is suitable for the next generation hardware devices to exploit the motion capture system for a common use. [15] M. I. A. Lourakis, levmar: Levenberg-Marquardt Nonlinear Least Squares Algorithms in C/C++., (2009) [16] G. Liu, M. Xu, Z. Pan, A. E. Rhalibi, Human Motion Generation with Multifactor Models. Journal of Visualization and Computer Animation 22(4): (2011) Huajun Liu received his B.S. and Ph.D. degree in School of Computer at Wuhan University in 2005 and He was a post-doctor in Wuhan University, a visiting researcher in Korea Institute of Science and Technology and a visiting scholar in Texas A&M University. Now he works in School of Computer, Wuhan University. His research interests include computer graphics (character animation, data-driven approaches for graphics and vision, interaction techniques for 3D graphics). Fuxi Zhu was born He received Ph.D. degree from School of Computer at Wuhan University. Now he is a professor in School of Computer, Wuhan University, China. His research interests include web knowledge mining in machine learning and parallel computing. REFERENCES [1] J. Chai, J. Hodgins, Performance animation from lowdimensional control signals, ACM Transactions on Graphics (2005), 24(3), pp [2] H. Liu, X. Wei, J. Chai, I. Ha, T. Rhee, Realtime human motion control with a small number of inertial sensors, In Proceedings of the 2011 symposium on Interactive 3D graphics and games (2011), pp [3] J. Shotton, A. Fitzgibbon, M. Cook, T. Sharp, M. Finocchio, R. Moore, A. Kipman, A. Blake, Real-time human pose recognition in parts from a single depth image. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2011),pp [4] X. Wei, P. Zhang, J. Chai, Accurate realtime full-body motion capture using a single depth camera, ACM Transactions on Graphics (2012), 31(6), Article No. 188 [5] S. Semwal, R. Hightower, S. Stansfield, Mapping algorithms for real-time control of an avatar using eight sensors, In Presence (1998), 7(1):1-21. [6] R. Slyper, J. Hodgins, Action capture with accelerometers. In 2008 ACM SIGGRAPH / Eurographics Symposium on Computer Animation (2008), pp [7] J. Tautges, A. Zinke, B. Kruger, J. Baumann, A. Weber, T. Helten, M. Muller, H. Seidel, B. Eberhardt, Motion reconstruction using sparse accelerometer data. ACM Transaction on Graphics (2011), 30(3), Article No. 18 [8] Y. Li, T. Wang, H.-Y. Shum, Motion Texture: A two-level statistical model for character synthesis, ACM Transactions on Graphics (2002), 21(3), pp [9] M. Brand, A. Hertzmann, Style machines, In Proceedings of ACM SIGGRAPH (2000), pp [10] K. Grochow, S. L. Martin, A. Hertzmann, Z. Popovic, Style-based inverse kinematics. ACM Transactions on Graphics (2004), 23(3): [11] X. Wei, J. Min, J. Chai, Physically valid statistical models for human motion generation, ACM Transactions on Graphics (2011), 30(3), Article No.19. [12] C. Bregler, M. Covell, M. Slaney, Video rewrite: driving visual speech with audio. InProceedings of ACM SIGGRAPH (1997), pp [13] M. E. Brand, Voice puppetry. In Proceedings of ACM SIGGRAPH (1999), pp [14] S. Levine, J. Wang, A. Haraux, Z. PopoviC, V. Koltun, Continuous character control with low-dimensional embeddings, ACM Transactions on Graphics (2012), 31(4), Article 28.