Real-time Character Posing Using Millions of Natural Human Poses

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1 Real-time Character Posing Using Millions of Natural Human Poses Xiaolin K. Wei and Jinxiang Chai Texas A&M University Abstract We resent intuitive interfaces for interactively osing 3D human characters. The user can create desired fullbody oses by directly dragging oints, modifying bone directions, or secifying distances between two oints in 2D screen sace. Designing such an interface for full-body ose modeling is challenging because many unnatural oses might be consistent with the ambiguous user inut. The system automatically learns a ose rior from a huge database which contains about 2.8 million rerecorded oses and uses it to remove the ambiguity. We formulate the roblem in a maximum a osteriori (MAP) framework by combining the rior with user-defined constraints. Maximizing the osterior allows us to generate an otimal and natural full-body ose that satisfies the user-defined constraints. Our system runs in real time; it is also simle and easy to use. We evaluate the erformance of our aroach with cross validation tests and comare with alternative techniques for character osing. 1. Introduction Our objective in this aer is to build an interactive system that allows novice users to ose a full-body human character quickly and easily. Alications of such a system include raid rototying of 3D animation, real-time game character control, interactive robot maniulation, real-time collision avoidance, and human comuter interactions. We resent an intuitive interface for osing a 3D full-body character in real time. The system allows the user to generate a wide variety of natural oses with minimal inut. The user can ose a desired 3D ose with a variety of 3D or 2D constraints, dragging a oint, modifying the distance between two oints, and sketching orientation of any bones on the screen. Our system starts with a full-body character under a default ose. In the oint dragging interface, the user first selects a character oint on the 2D screen sace; the user then drags the oint on the screen sace to indicate a desired osition for the chosen oint. Points can be drawn anywhere on the 2D screen sace from any camera view. The system oses the character based on these inuts in real time. The user can continue to refine the model until a desired ose is achieved. xwei@cs.tamu.edu jchai@cs.tamu.edu Building such an interface for 3D human ose modeling is difficult because the information from the user is often ambiguous. In our system, the inuts are a very small set of user-defined control oints, e.g. a dragging oint. This information is quite low-dimensional as comared to a tyical ose model, which is commonly reresented by about fifty of DOFs. The user s inuts, therefore, cannot be used to fully determine a natural ose configuration because they will be consistent with many disarate solutions. Some solutions might corresond to unnatural oses and not be what the user intends to model. One aealing solution to avoid unnatural oses is to imose riors from a data set of natural oses. Previous datadriven IK systems either use a linear combination of examle oses [WH97, ISC01, KG04] or a style-based robabilistic model [GMHP04] to constrain the solution sace. The systems have achieved imressive erformance for osing a character with articular actions or styles, such as oint reaching, kicking, walking, basketball shooting, or baseball swinging. However, neither aroaches scale u well to the size and heterogeneity of a ose database. Therefore they might not be suitable for osing a character for general actions such as osing a character from hotos, unless the database is consistently and correctly labeled. This aer develos an efficient data-driven IK algorithm using riors learned from a huge database. The rior describes the like-

2 2 Xiaolin K. Wei & Jinxiang Chai / Technical Reort lihood function over character oses and measures how natural a character ose is. We formulate the interactive character osing roblem in a maximum a osterior (MAP) framework by combining user-defined constraints with a rior embedded in the database. We model the rior as a mixture of factor analyzers [GH97] and learn it automatically from 2.8 millon re-recorded human oses (htt://moca.cs.cmu.edu/). Maximizing the osterior (likelihood of character oses given user-secified constraints) generates a natural and most desirable character oses that achieves the goal secified by the user. We demonstrate the ower and flexibility of this aroach by interactive osing of 3D characters with oint constraints, distance constraints, direction constraints, and fixed constraints. The constraints are secified on either the 3D sace or the 2D screen sace. We have found that a first-time user can learn to use the system within a minute, and be able to create desired character oses within tens of seconds. Our system can generate a wide variety of natural oses. One benefit of the riors learned from a huge database is its generalization ability. The current CMU database includes a wide variety of behaviors and styles from different subjects. The learned rior from such a huge database can be used to generate oses for new behaviors, styles and skeletal models. We demonstrate generalization ability of the system by osing a character on random hotos. We show the sueriority of our algorithm by comaring with standard IK, style-based IK, and other alternative datadriven IK methods. The quality of our system deends on model riors learned from the database. We therefore evaluate the quality of reconstructed oses in terms of the imortance of model riors by comarison against ground truth data. 2. Background Inverse kinematics is one of the most imortant techniques for generating animation with kinematic constraints and has been studied in comuter animation as well as robotics. Three distinct aroaches have been used: analytical, numerical, and data-driven. Analytical inverse kinematics [KB82, Cra86] use a closed-form inverse of nonlinear direct kinematics functions. This aroach shows good erformance in some class of structures such as a single limb of human, but lacks generality for osing a full-body human character. Numerical algorithms formulate the inverse kinematics roblem as an otimization roblem which measures how well a desired ose matches kinematics constraints [GM85, ZB94, YN03]. There are two advantages of using numerical aroaches for inverse kinematics. First, they are alicable to general articulated bodies like full-body human characters. Second, it is very easy to add various forms of kinematics constraints, such as oint and orientation constraints, into otimization. However, inverse kinematics for full-body human characters is an ill-oses roblem. Many disarate and unnatural solutions might be consistent with kinematic constraints unless the user secifies a very large set of constraints across the entire ose such as in full-body motion cature or the otimization starts with a good initial guess. The numerical aroach has also been used for retargeting and editing catured motion data for new characters and alications [Gle98, LS99, CK02]. Our work builds on revious data-driven aroaches for inverse kinematics [WH97,ISC01,KG04,GMHP04,CH05]. One solution is to use a linear combination of examle oses to constrain the solution sace for inverse kinematics [WH97, ISC01, KG04]. Grochow and his colleagues [GMHP04] alied a global nonlinear dimensionality reduction technique, a Gaussian Process Latent Variable Model [Law04], to human motion data and then used the learned style-secific robabilistic model to comute oses from a small set of user-defined constraints. GPLVM works well for action-secific or style-secific oses. However, it might not be aroriate for our alication because of the size of our database (2.8 millon oses). The erformance of the GPLVM deteriorates as the size and heterogeneity of the database increases. Local statistical models are sufficient if the user rovides a small number of continuous control signals (the erformance animation roblem). Chai and his colleagues [CH05] used a series of local statistical ose models constructed at runtime to reconstruct full body motion from continuous, low-dimensional control signals obtained from video cameras. Online local models are more aroriate for creating animations (a sequence of oses) from continuous temoral constraints. They are not aroriate for our alication because user-defined constraints might not be continuous. More distantly-related revious work looks at estimating the ose of a character from 2D images [Bra99, Tay00, RS00] or 2D hand-drawn sketches [DAC 03, TBvdP04]. Our system is different in that we focus on new, interactive grahics alications and real-time synthesis and our system can ose a full-body character with just a few user constraints. We model the rior as a mixture of factor analyzers [GH97] and learn it automatically from a re-recorded motion cature database. The MFA model has also been successfully alied to model the rior for many highdimensional nonlinear data such as handwritten digits [HDR97] and images [BW00], and facial deformation [LCXS07].

3 Xiaolin K. Wei & Jinxiang Chai / Technical Reort Problem Statement We formulate interactive character osing roblem in a maximum a osteriori (MAP) framework. From Bayes theorem, the goal of MAP is to infer the most likely ose given the user-defined constraints c: argmin r(c )r() r( c) = argmin r(c) r(c )r() argmin where r(c) is the normalizing constant that ensures that the osterior distribution on the left-hand side is a valid robability density and integrates to one. And we reresent each ose with a 40-dimensional vector,, each dimension reresenting a joint angle value. In our imlementation, we minimize the negative log of r( c), yielding the following energy otimization roblem for the character ose : (1) ˆ = argmin lnr(c ) lnr() (2) where the first term measures how well a character ose matches the user-secified constraints and the second term measures the a riori likelihood of the ose using the knowledge embedded in the motion cature database. Otimizing the energy function allows us to generate an otimal, natural ose that satisfies user-defined constraints. The model riors are learned from the catured natural human oses off-line, while the other two stages are erformed online based on inut from the user. We describe these comonents in detail in the next three sections. 4. User Constraints The system allows the user to secify various forms of constraints for interactive character osing. All the constraints can be secified either on 2D screen sace or in 3D sace. For simlicity of descrition, we limit our discuss on the 2D constraints. The user can sketch out the character ose in greater or lesser detail with the following user constraints Point Constraints This constraint allows the user to select a set of oints on the character model and secify where the oints should ma to on the screen sace (Figure 1). More secifically, the user first selects a set of 3D oints {x i i = 1,...,N} and then secifies a corresonding set of 2D target ixels {z i i = 1,...,N} of where the oints should ma to on the screen sace. The user selects each 3D oint by selecting a 2D screen ixel. We erform ray tracing with this ixel to choose the corresonding 3D oint on the character. Given these inuts, the roblem is to find a character ose () so that each selected 3D oints (x i ) rojects onto the corresonding 2D screen osition (z i ) in the current camera Figure 1: Point constraints. Left: The user selects a set of oints (red) and secifies the desired screen rojections (green); Right: The resulting ose. view (Figure 1). We describe the selected oint x i in its local coordinate system. The otimization term for oint constraints can be described as follows: E = 1 N i g i (;x i ) z i 2 (3) where the vector-valued function g i is the comosition of forward kinematics function and rojection function from 3D to 2D in the current camera viewoint Distance Constraints This constraint allows the user to select any air of oints (x i and x j ) and control the distance between the two in 2D screen sace. This constraint is articularly useful for osing characters from hotograhs. Figure 2 shows an examle of the user inuts. The user selects the 3D oints by selecting 2D ixels as in the oint constraints case. The current distances between the airs of oints are dislayed, and the user can secify new distances. Let d denote the user-defined target distance, N D be the number of airs of oints, and let x i and x j ma to the screen ixels y i and y j resectively. The energy term can be defined as follows: E d = 1 N D ( y i y j d) 2 = 1 N D ( g i (;x i ) g j (;x j ) d) 2 (4) where the summation is for all airs of i, j Orientation Constraints This constraint allows the user to select any bones and secify the orientations in 2D screen sace. Figure 3 shows an examle of the user inuts. Let v i denote the orientation of a selected bone in the local coordinate and a denote the user-defined target orientation, M be the number of bones selected. The energy term can be defined as follows: E o = 1 M m( g m (;v i ) a ) 2 (5) where the vector a is the desired orientation on the screen sace and reresents the cross roduct of two vectors.

4 4 Xiaolin K. Wei & Jinxiang Chai / Technical Reort Figure 2: Distance constraints. Left: The user selects airs of vertices and secifies the distances between each air in screen sace; Middle: The generated 3D ose in the same viewoint; Right: The generated 3D ose from a new viewoint. Figure 4: Fixed constraints. Reducing the 3D distance between the right leg and left hand might also change the ositions of the left shoulder; Middle: Secifying one fixed oint allows the shoulder to stay unchanged; Right: The resulting ose from a new viewoint. Figure 3: Orientation constraints. Left: The user selects a set of bones and secifies the desired orientation on the screen sace; Right: The resulting ose Local Control: Fixed Constraints Because of natural correlation of human motion, the movement between differen joints might not be indeendent. If the user edits the ose with one of the above constraints, the regions of the character that the user did not select might still change. For examle, if the foot osition is selected and changed, the hand ositions may also change even if there are no any constraints defined on the hands. We can use fixed constraints to allow some bones to maintain their ositions as much as ossible in the otimization (Figure 4). In this case, the user can choose one oint on the shoulder to be fixed. More secifically, the user selects N F total number of fixed oints (x i s). Let x i_original be the original 3D ositions of these oints. The otimization term is E f = 1 N F i x i x i_original 2 (6) Fixed constraints must be used with at least one of the other constraints described above. The overall objective function will have this term multilied by a user-defined weight added to it. The larger the weight is, the more these oints will try to stay the same. 5. Pose Priors There might be many character oses that satisfy the userdefined constraints. For examle, when the user selects one oint to edit the whole body, there might be many results that are consistent with this constraint. To remove ambiguities, we can constrain the generated model to lie in the sace of natural oses by imosing a rior on the generated model. We model the rior as a mixture of factor analyzers [GH97] and learn it automatically from a re-recorded ose database. The MFA model learns a robability density function (P.D.F) in the PCA subsace that rovides a model rior to measure the naturalness of character oses. A single factor analyzer (FA) assumes that an observed r-dimensional ose is generated as a linear transformation of some lower q-dimensional latent variable τ N (0,I) lus additive Gaussian noise ω N (0,Ψ). Ψ is a diagonal matrix. The generative model can be described as: = Aτ + ω + µ (7) Here, A R r q is a factor loading matrix. µ is a mean vector. The P.D.F. of the observed data in an FA model can be obtained by: r(;θ) = N (µ,aa T + Ψ) (8) A mixture of factor analyzers (MFA) is defined by a linear combination of K factor analyzers. The MFA model extracts a series of low-dimensional local linear manifolds underlying the given high dimensional data. The P.D.F. of the observed data by a mixture of K FAs is given by: r(;θ) = K k=1 π kn (µ k,a k A T k + Ψ k) (9) where π k is a mixing roortion (π k > 0 and K k=1 π k = 1). The system automatically learns the model arameters of the MFA model, Θ = {π k,µ k,a k,ψ k k = 1,...,K}, from examle data via exectation maximization techniques [GH97]. We minimize the negative log of r(), yielding the energy formulation: E r() = ln K k=1 π in (µ k,a k A T k + Ψ k) (10)

5 Xiaolin K. Wei & Jinxiang Chai / Technical Reort A smaller E r value means that is closer to the oses in the training database and therefore more natural. The inverse and determinant of the covariance matrices are recomuted for each factor to achieve a faster running time. MFA model has two arameters (K and q) which can be determined by cross-validation. In our exeriment, the number of local models, K, is set to 70, and the number of dimensions of the latent sace, q, is set to 5. The time comlexity for learning MFA riors is O(NKrq), which is linearly deendent on the size of a database N. The rior evaluation is also very efficient for inverse kinematics alication: it only requires O(Kr 2 ) for rior evaluation for a new ose. In contrast, the learning comlexity for the SGPLVM is O(N 3 ) and the evaluation cost for the IK alication is O(N 2 ).. 6. Runtime Otimization During runtime, the system otimizes in the original joint angle sace and finds the 3D ose () that best satisfies the user constraints (c). In our imlementation, we also add joint limit constraints into the system. The overall objective function is a weighted combination of the user-defined constraint terms (Equations 3, 4, 5, and 6) and the model rior term (Equation 10): ˆ = argmine + λ 1 E d + λ 2 E o + λ 3 E f + λ 4 E r Subject to l i i u i i = 1,...,52 (11) where the arameter i is the i-th joint angle and the scalars l i and u i are the lower and uer bounds for the joint angel i resectively. In our exeriments, the weights λ 1, λ 2, λ 3 and λ 4 are set to 1, 1000, 10 and 100 resectively. Each factor in the MFA model has a mean character ose. We initialize the otimization with the best mean ose among all factors. We use the Levenberg-Marquardt algorithm with boundary constraints in the Levmar library [Lou07]. The solution converges raidly enough to rovide real-time erformance, thanks to the good starting oint, the highly constrained search sace constrained enforced by ose riors, and the analytical evaluation of the jacobian matrix. 7. Results Our system can generate a wide variety of natural oses with minimal user inut. This section first describes the database we used for modeling ose riors. We then show the effectiveness of our system by generating oses from various forms of user-defined constraints. We also evaluate the With a heuristically selected active set, the training and evaluation costs are O(NM 2 ) and O(M 2 ) resectively. imortance of the different ose riors for character osing with the same set of user constraints. We comare our method against alternative data-driven techniques for interactive character osing. Our result is best viewed in the accomanying video. Data. The training database consisted of 2.8 million frames or about 6.48 hours from CMU motion cature database (htt://moca.cs.cmu.edu). Those behaviors included locomotion (juming, running, hoing, walking), hysical activities (basketball, boxing, dance, exercise, golf, martial arts, swimming), interacting with the environment (ste tool, rough terrain, layground equiment) and common scenarios (cleaning, waiting, gestures). Results with different user constraints. We illustrate four tyes of constraints in the accomanying video: oint, distance, orientation, and fixed constraints. We also demonstrate how to use a dragging interface to ose a character based on reference hotos. Figure 7 shows a ose generated by dragging interface. The user can also act out a desired ose using a toy and then use the dragging interface to model the ose based on the hoto of the toy (see Figure 5). The imortance of riors. We evaluate how the database influences the final motion by keeing the user-defined constraints constant. We comare the results for a database of running and the whole database under the same set of constraints. We first test them on a set of constraints derived from a running ose. Then we test them on a set of constraints derived from a sitting ose. The accomanying video shows that we can generate a good running ose with both running and general database. As would be exected, the system fails to generate a good sitting ose if the ose rior is learned from running. Comarison with other techniques. We comare the MFA model used in this work against alternative methods. We tested the erformance of these algorithms in two databases: the whole CMU database and a database of 5000 oses randomly samled from the whole CMU database. IK erforms numerical otimization to solve inverse kinematics. PCA erforms an otimization in the PCA subsace without any model rior term. PPCA erforms an otimization in the PCA subsace with a Guassian model rior term. It assumes that the samles in the database are reresented by a multivariate Guassian distribution. SG- PLVM learns a global nonlinear embedding using a scaled gaussian rocess latent variable model [GMHP04]. LPCA first finds k samles in the database that best matches the user constraints by comuting a score for each samle based on the otimization objective function. It then erforms an otimization in the PCA subsace determined by the k nearest samles [CH05]. All these methods start with the same initial ose and user-defined constraints and adot the same otimization algorithms (Levenberg-Marquardt). We show a comarison of the ose reconstruction er-

6 6 Xiaolin K. Wei & Jinxiang Chai / Technical Reort oses in database 2.8M oses in database IK PCA PPCA SGPLVM 1.92 N/A LPCA MFA Table 1: Comarison of average reconstruction errors for different methods and different database sizes. The reconstruction error is obtained under the same set of six 3D-oint constraints: two shoulders, two legs and two hands. Figure 5: The user can also act out a desired ose using a toy and then use the dragging interface to model the ose based on the hoto of the toy. ror in Table 1, for the different techniques and for the two databases. We use cross validation to evaluate the reconstruction errors from different algorithms. The average reconstruction error is the L 2 distance between the actual ose and the reconstructed in osition sace (oint clouds). Our method (MFA) with riors learned from the whole CMU database roduces the smallest reconstruction error. IK and PCA roduces a larger error because the number of user secified constraints is usually small even when comared to the reduced dimensions of the PCA subsace. PPCA can remove the maing ambiguity from the lowdimensional constraints to the reduced subsace dimensions by the model rior. However, the full-body models are not as well aroximated by a global multivariate Guassian distribution because the size and heterogeneity of the database. SGPLVM with a 6-dimensional latent sace and active set size 200 generates better results than IK, PPCA, and PCA for the database of 5000 oses, but comutationally it is too exensive to evaluate its erformance for the whole database. In our exeriments, LPCA gives low errors on both databases. However, it needs to search in the whole database for examles close to user-defined constraints, which makes it imractical for real-time alications. Note that, for all these methods, the riors learned from the larger database result in the lower reconstruction errors. 8. Discussion We have resented an aroach for interactive character osing from different kinds of user constraints (oint, distance, direction, fixed) while matching the statistical roerties of a database of millions of natural oses. The system first automatically learns a statistical model from examle oses and then enforces this as a rior to model the ose. The model rior, together with user-defined constraints, comrise a roblem of maximum a osteriori estimation. Solving the MAP roblem in a reduced subsace yields an otimal, natural ose that achieves the goals secified by the user. One of the key challenges in data-driven animation is how to generalize the motion data that are not in the database. One benefit of the MFA learned from a huge database is its generalization ability. The current CMU database includes a wide variety of behaviors and styles from different subjects. The learned rior from such a huge database can be used to generate oses for new behaviors, styles and skeletal models. We demonstrate this by osing a character on hotos with the riors learned from the same database. For examle, we find that the CMU database does not include similar oses shown in Figure 6. But the system is still able to create both oses. A general IK system for osing human characters can generate any desired oses for any characters. A data-driven aroach learned from a huge database offers same caability but with less ambiguity and fewer user interactions. In contrast, style-based or action-based IK has not demonstrated such kind of flexibility. The quality of the generated oses deends on both ose riors and user-defined constraints. Without the use of the ose riors, the system would not generate natural models unless the user accurately secifies a very detailed set of constraints or the system starts with a very good initial ose. When the user s inut conflicts with the ose riors, a tradeoff between the user inut and the naturalness of the ose can be achieved by adjusting their weights in the objective function. Our system allows the user to change this weight on the fly, thus roviding an interesting sectrum of ossibilities for the user to choose from. The system allows for a click done mode and a direct maniulation mode to create character oses. The user can choose the desired constraints and then click a button to generate the solution with the current constraints. This allows for lacing multile constraints in one otimization ste. This can lead to large scale changes, but all the constraints may not be satisfied if they come in conflict with allowing for natural oses. The direct maniulation interface allows a user to directly maniulate a character ose resented to them, using actions that corresond to the hysical world. Having real-world metahors for character oses and actions can make it easier for a user to learn and use an interface, and raid, incremental feedback allows a user to make fewer errors and comlete tasks in less time, because

7 Xiaolin K. Wei & Jinxiang Chai / Technical Reort Figure 6: The user can ose characters based on the reference hotos: (left) reference hotos; (right) generated oses in two different viewoints. they can see the results of an action before comleting the action. References [Bra99] B RAND M.: Shadow uetry. In Proceedings of IEEE International Conference on Comuter Vision (1999) [BW00] B ISHOP C. M., W INN J. M.: Non-linear bayesian image modelling. In Proceedings of ECCV [CH05] C HAI J., H ODGINS J.: Performance animation from low-dimensional control signals. In ACM Transactions on Grahics (2005). 24(3): [CK02] C HOI K.-J., KO H.-S.: Online motion retargeting. In Proceedings of ACM Symosium on Comuter Animation (2002). [Cra86] C RAIG J.: Introduction to robotics: Mechanics and control. Addison-Wesley. [DAC 03] DAVIS J., AGRAWALA M., C HUANG E., P OPOVI C Z., S ALESIN D.: A sketching interface for articulated figure animation. In Proceedings of the 2003 ACM SIGGRAPH/Eurograhics Symosium on Comuter Animation (2003). [GH97] G HAHRAMANI Z., H INTON G. E.: The em algorithm for mixtures of factor analyzers, [Gle98] G LEICHER M.: Retargeting motion to new characters. In Proceedings of ACM SIGGRAPH 1998 (1998) [GM85] G IRARD M., M ACIEJEWSKI A. A.: Comutational modeling for the comuter animation of legged figures. In Proceedings of the 12th annual conference on Comuter grahics and interactive techniques (Siggrah 85) (1985) [GMHP04] G ROCHOW K., M ARTIN S. L., H ERTZMANN A., P OPOVI C Z.: Style-based inverse kinematics. In ACM Transactions on Grahics (2004). 23(3): [HDR97] H INTON G. E., DAYAN P., R EVOW M.: Modeling the manifolds of images of handwritten digits. In IEEE Transactions on Neural Networks (1): [ISC01] III C. F. R., S LOAN P.-P. J., C OHEN M. F.: Artist-directed inverse-kinematics using radial basis function interolation. In Comuter Grahics Forum (2001). 20(3): [KB82] KOREIN J., BADLER N.: Techniques for generating the goal-directed motion of articulated structures. In IEEE Trans. Comuter Grahics and Alications (1982) [KG04] KOVAR L., G LEICHER M.: Automated extraction and arameterization of motions in large data sets. In ACM Transactions on Grahics (2004). 23(3): [Law04] L AWRENCE N. D.: Gaussian rocess latent variable models for visualization of high dimensional data. In Advances in Neural Information Processing Systems 16 (2004) [LCXS07] L AU M., C HAI J., X U Y.-Q., S HUM H.-Y.: Face oser: Interactive modeling of 3d facial exressions using model riors. In Proceedings of the 2007 ACM SIGGRAPH/Eurograhics symosium on Comuter animation (SCA) (2007). [Lou07] L OURAKIS M.: levmar: Levenberg-marquardt

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