Flexible Registration of Human Motion Data with Parameterized Motion Models

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1 Flexible Registration of Human Motion Data with Parameterized Motion Models Yen-Lin Chen Texas A&M University Jianyuan Min Texas A&M University Jinxiang Chai Texas A&M University Figure 1: Our registration method automatically registers two motions by registering each motion with the parameterized walking model. Abstract This paper presents an efficient model-based approach for automatic human motion registration, which builds temporal correspondences between structurally similar but distinctive motion examples. The key idea of the model-based registration process is to construct a parameterized motion model from a set of preregistered motion examples. With such a model, we can register an input motion with the parameterized motion model by continuously deforming the model to best match the input motion. We formulate the registration process in a gradient-based nonlinear optimization framework by minimizing an objective function that measures differences between the input motion and deforming motion. We also develop a multi-resolution optimization process to efficiently estimate the model parameters as well as the temporal correspondences between the input motion and deforming motion. We demonstrate the performance of our approach by testing the algorithm on difficult motion sequences and comparing with alternative approaches. 1 Introduction With the proliferation of motion capture data, how to analyze and process a large set of motion capture data becomes increasingly ylchen@cs.tamu.edu jianyuan@cs.tamu.edu jchai@cs.tamu.edu Copyright 2009 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions Dept, ACM Inc., fax +1 (212) or permissions@acm.org. I3D 2009, Boston, Massachusetts, February 27 March 1, ACM /09/0002 $ important. One important and challenging motion processing problem is motion registration, which finds temporal correspondences between structurally similar motion sequences. Motion registration has many important applications; for instance, registered motions have been used for motion interpolation [Bruderlin and Williams 1995; Guo and Roberge 1996; Wiley and Hahn 1997; Rose et al. 1998; Park et al. 2002; Kovar and Gleicher 2004; Mukai and Kuriyama 2005], motion transfer [Hsu et al. 2005; Heck et al. 2006] and realtime motion control [Cooper et al. 2007]. Figure 2: Motion registration with dynamic time warping: (left) walking with arm waving. (middle) sneaky walking. (right) the red and green curves show the result from dynamic time warping and ground-truth result from manual registeration respectively. Note that image intensities visualize the frame-by-frame distances between two testing motion sequences. The higher the intensity values; the larger the frame-by-frame differences. One popular solution for automatic motion registration is dynamic time warping [Myers and Rabiner 1981]. The approach formulates the registration process as a discrete optimization problem and applies dynamic programming techniques to minimize motion differences between two motion sequences. The approach runs fast and has demonstrated a good performance for many applications. However, when two motions contain very different style variations (e.g. walking with arm waving and sneaky walking ), dynamic time warping often produces wrong results (see Figure 2). This paper presents a model-based registration technique for automatic and robust motion registration (see Figure 1). The key idea of

2 Figure 3: System overview. the model-based registration process is to register an input motion with a parameterized motion model constructed from a large set of preregistered motion examples. The parameterized motion model is a multi-dimensional morphing function that efficiently models motion variations embedded in the training examples. To register an input motion with the parameterized model, we continuously deform the parameterized model to best match the input motion. Mathematically, we formulate the registration process in a continuous optimization framework by minimizing an objective function that measures differences between the input motion and deforming motion. We develop a multi-resolution optimization process to efficiently compute the model parameters as well as the temporal correspondences between the input motion and deforming motion. We evaluate the performance of our approach by testing the algorithm on a variety of motion sequences including walking, running, and jumping. Our experiments show that the model-based registration process can produce much better results than dynamic time warping. We apply the parameterized model along with robust statistics to register spurious motions or motions corrupted with outliers. The registration framework is also very flexible and can be used for registering motions in a different format. For example, we demonstrate that we can extend the model-based registration process to register 2D video data. 2 Background Robust registration of human motion data has been an important part of many animation applications [Bruderlin and Williams 1995; Guo and Roberge 1996; Wiley and Hahn 1997; Rose et al. 1998; Park et al. 2002; Kovar and Gleicher 2003; Kovar and Gleicher 2004; Mukai and Kuriyama 2005; Hsu et al. 2005; Cooper et al. 2007]. In this section, we briefly review research on human motion registration. One approach requires the user to specify a set of key frames in input motions and then uses piecewise linear interpolation to estimate an appropriate time warping function [Rose et al. 1998; Park et al. 2002; Mukai and Kuriyama 2005]. An accurate alignment of human motion data usually requires specification of a large number of key frames. An alternative approach for motion registration is dynamic time warping [Bruderlin and Williams 1995; Kovar and Gleicher 2003; Kovar and Gleicher 2004; Hsu et al. 2005; Cooper et al. 2007]. Bruderlin and William introduced a basic dynamic time warping algorithm for motion registration and then used the registered motions for interpolation applications. Kovar and Gleicher [2003] improved dynamic time warping techniques by imposing monotonic and slope constraints on time warping functions. Recently, Hsu and Popovic [2005] proposed an iterative motion registration algorithm that estimates time warping functions as well as per-frame scale factors between the input motions. Dynamic time warping could also be performed in a continuous optimization framework. For example, Ramsay and Li [2002] introduced a continuous optimization framework for registration of various forms of 1D time series. Our work differs from previous approaches because our approach is data-driven. We register input motions by registering each motion with a parameterized motion model constructed from a large set of pre-registered motion examples. Our experiments show that the model-based registration significantly improves the accuracy and robustness of the motion registration process. Another benefit of model-based registration is its flexibility to register spurious motions or motions corrupted with outliers. The parameterized model also allows us to register 2D video data, a capability that has not been demonstrated by previous registration methods. 3 Overview The key idea of our approach is to construct a parameterized motion model from pre-registered motion examples and then deform the parameterized model to best match input motions. Figure 3 shows an overview of our system. The system contains three major components: Motion preprocessing. We pre-register a set of structurally similar but distinctive motion examples with a semi-automatic method. Motion parameterizations. We apply statistical analysis techniques to the registered motion data and construct a parameterized motion model to model motion variations in the training data. We represent the model with a small number of parameters λ 1,..., λ M. Motion registration. We deform the parameterized model to best register an input motion by minimizing the difference between the input motion and deforming motion. We formulate this as an optimization problem and automatically compute the model parameters ˆλ 1,..., ˆλ M as well as the time warping function ŵ 1,..., ŵ T in a coarse-to-fine manner. 184

3 Figure 4: The top five eigen-modes for walking motion. We describe each of these components in more detail in the next section. 4 Motion Data Preprocessing and Parameterizations This section discusses how to preprocess a set of motion examples in the database (section 4.1), how to use them to build a parameterized motion model (section 4.2), and how to apply the parameterized model for automatic motion registration (section 4.3). In the following, we will focus our discussion on constructing the parameterized model for walking. The basic reconstruction scheme that will be proposed in this section can easily be extended to other actions such as running and jumping. 4.1 Motion Data Preprocessing We construct the parameterized motion model from a set of prerecorded motion examples. We require all examples must be structurally similar. A set of walking examples, for instance, must all start out on the same foot, take the same number of steps, have the same arm swing phase, and have no spurious motions such as a head-scratch. To build the parameterized model for walking, we will record a database from an actor performing walking with various styles (different speeds, step sizes, directions, and stylized walking). We assume the database motions are already segmented into walking cycles. If the database motion contains multiple walking cycles, we manually segment the motion into multiple cycles. We denote the set of motion examples in the database as {x n(t) n = 1,..., N}, where x n(t) is the joint angle measurement of a character pose at the t-th frame for the n-th motion example. To register motion examples in the database, we pick one example motion x 0 as the reference motion and use it to register the rest of database examples {x n n = 1,..., N} with appropriate time warping functions. We register motion examples in a translation- and rotation-invariant way by decoupling each pose from its translation in the ground plane and the rotation of its hips about the up axis [Kovar and Gleicher 2003]. To ensure the quality of training data, we choose to use a semiautomatic process to align all motion examples in the database. To align each database example {x n(t) n = 1,..., N} with the reference motion x 0(t), we first manually select a small set of key frames, instants when important structural elements such as a footdown occurs. We then use the key frames to divide the example motion into multiple subsequences. The starting and ending frames of each subsequence are specified at the key frames. We use dynamic time warping to automatically align each subsequence. Finally, we use the estimated time warping function to warp the motion examples {x n(t) n = 1,..., N} into a canonical timeline { x n(t) n = 1,..., N} specified by the reference motion. 4.2 Motion Parameterizations One way to parameterize the registered motions is to use a weighted combination of motion examples in the database. This model, however, does not offer a compact representation for human motion because the number of parameters linearly depends on the number of database examples. More importantly, the representation does not utilize spatial-temporal correlation embedded in the motion examples. A better way is to apply statistical analysis to model variations in the registered motion examples. We form a DT dimensional vector X n by sequentially stacking all poses of the pre-registered motion examples x n(t), t = 1,..., T, where D is the dimensionality of the full-body configuration space and T is the number of frames in the reference motion. We apply principle component analysis (PCA) to all pre-registered motion examples X n, n = 1,..., N. As a result, we can construct a parameterized motion model P using mean motion P 0 and a weighted combination of eigenvectors P m, m = 1..., M: P (λ 1,..., λ M ) = P 0 + M λ mp m (1) m=1 where the weights λ m are control parameters for the motion model and the vectors P m are a set of orthogonal modes to model motion variations in the training examples. Therefore, we can use the parameterized model to generate a motion instance as follows: p(t, λ 1,..., λ M ) = p 0 (t) + M λ mp m (t) t = 1,..., T (2) m=1 What remains is to determine how many modes (M) to retain. This leads to a trade-off between the accuracy and the compactness of the motion model. However, it is safe to consider small-scale variation as noise. We automatically determine the number of modes by keeping 99 percent of the original variations. Figure 4 shows the top five modes constructed from the pre-registered walking database. 4.3 Motion Registration We now focus our discussion on how to register an input motion y(s), s = 1,..., S with the parameterized motion model p(t, λ 1,..., λ M ), t = 1,..., T using an appropriate time warping function s = w(t). Note that modeling the time warping function w(t) only requires recovering the finite number of values that w(t) can take since the domain of t = 1,..., T is finite. We therefore represent the time warping function w(t) with T finite values of w(t): w(1),..., w(t ). The key idea of our model-based registration process is to continuously deform the parameterized motion model to produce a motion instance p(t, λ 1,..., λ M ), t = 1,..., T that best matches the input motion y(s), s = 1,..., S. We expect an accurate registration result will be achieved when the deforming motion p(t, λ 1,..., λ M ), t = 1,..., T is close to the input motion y(s), s = 1,..., S. 185

4 Figure 5: The multi-resolution optimization procedure registers an input motion with the parameterized motion model in a coarse-to-fine manner. We start the optimization in level 1. After the optimization in level 1 converges, we initialize the time-warping curve in level 2 by upsampling the estimated time-warping curve from level 1. We initialize the motion parameters with the optimized motion parameters in level 1. We repeat this process until the algorithm converges at the finest level. Note that the gray images visualize frame-by-frame distances between the input motion and deforming motion. In order to define the motion registration process, we must formally define the criterion to be optimized. Naturally, we want to minimize the error between the input motion y(s) and its closest motion instance p(t, λ 1,..., λ M ), t = 1,..., T with an appropriate time warping function s = w(t), t = 1,.., T. If t is a frame in the canonical timeline, then the corresponding frame in the input motion is w(t). At frame t, a motion instance generated by the parameterized motion model {λ 1,..., λ M } has the pose p(t) = p 0 (t) + M λmp m=1 m (t). At frame w(t), the input motion has the pose y(w(t)). We want to minimize the sum of squares of the difference between these two quantities: T M y(w(t)) (p 0 (t) + λ mp m (t)) 2 (3) t=1 m=1 where the sum is performed over all frames of the canonical time line. The above error can be computed as follows. For each frame t in the reference motion, we have the corresponding frame w(t) in the input motion. The input motion is then sampled at the frame w(t); typically it is linearly interpolated at this frame in the time coordinate of the input motion y. The goal of motion registration is thus to minimize the cost function defined in Equation 3 with respect to the motion parameters {λ 1,..., λ M } and the time warping function w(t), t = 1,..., T. Direct optimization of the above function might result in invalid time warping functions because time warping functions are constrained functions. In our experiments, we require that time warping functions satisfy the following conditions: Positive constraints: a time warping function should be positive: w(t) > 0. Monotonic constraints: a time warping function should be strictly increasing: w(t) > w(t 1). The monotonicity property makes sure that the time warping function is invertible so that for the same event the time points on two different time scales correspond to each other uniquely. Slope constraints: a time warping function should not be too 1 steep or too shallow: w(t) w(t 1) L. This prevents very short sequences matching very long ones. In our L experiment, we set L to 3. Rather than modeling a time warping function w(t) in the original time space, we choose to transform the w(t) into a new space z(t): z(t) = ln(w(t) w(t 1)), t = 1,...T (4) We choose w(0) to be zero and further have w(t) = t exp[z(i)], t = 1,..., T (5) i=1 Equation 5 makes sure monotonic constraint of the w(t) will be automatically satisfied if we conduct the optimization in the new space z(t). Thus, the cost function for the model-based motion registration process (Equation 3) can be re-written as follows: T t M E error = y( exp[z(i)]) p 0 (t) λ mp m (t) 2 (6) t=1 i=1 m=1 We also introduce a prior term to prevent the deforming motion moving away from the registered motion examples in the database. E prior = M λ 2 m m=1 σm 2 where σ 2 m is the m-th eigenvalue of the registered motion examples x n(t), t = 1,..., T. The overall objective function is a combination of the error term (Equation 6) and the prior term (Equation 7): {ˆλ m}, {ẑ t} = arg min {λm},{z i } αe error + E prior (7) Subject to ln L z t ln L t = 1,..., T (8) 186

5 where the weight α controls the importance of the error term. We analytically evaluate the jacobian terms of the minimization function and then run the optimization with the Levenberg- Marquardt algorithm with boundary constraints in the Levmar library [Lourakis 2007]. To improve the speed and robustness of our optimization, we develop a multi-resolution optimization procedure to estimate the motion parameters and time warping function in a coarse-to-fine manner. Figure 5 visualizes the basic concept of our multi-resolution optimization process. We first form the input motion y(s) and parameterized motion p(t, λ 1,..., λ M ) in coarse levels by downsampling both the input motion y(s), the mean motion p 0 (t), and base motions p m (t), m = 1,..., M. We start the registration process in the coarsest level (see Level 1 in Figure 5) and run the optimization to register the coarsest input motion with the coarsest parameterized motion. After the optimization in level 1 converges, we initialize the time-warping curve in level 2 by upsampling the estimated time-warping curve in level 1 and initialize the motion parameters in level 2 with the estimated parameters from level 1. We repeat this process until the algorithm converges at the finest level. In our experiments, we set the downsampling rate to 2. 5 Extensions This section explores the power and flexibility of the model-based registration framework. We first extend the framework for registering motions corrupted with outliers or spurious motions and then discuss how to extend the framework to register motions in a different form (video data). 5.1 Corrupted Motion Data The model-based motion registration framework can be extended to register spurious motions or motions containing outliers. For example, we can extend the framework to register walking with arm waving to the parameterized motion model even though the pre-registered walking database does not contain any arm waving motions. To deal with spurious motion or motion corrupted with outliers, we apply robust statistics to measure the error term. Robust estimation [Hampel et al. 1986] addresses the problem for finding the values for the parameters from the measurement data with outliers, which correspond to spurious patterns or corrupted degrees of freedom in our experiments. We define the error term as follows: E outliers error = T t=1 D d=1 ρ(y d(w(t)) p d (t, λ 1,..., λ M )) (9) where the function ρ is a robust function that is used to reduce the influence of outliers. y d (w(t)) and p d (t, λ 1,..., λ M ) represent the d-th DOF (degree of freedom) of the input motion and deforming motion at the frame t respectively. To increase robustness we will consider estimators for which the influence of outliers tends to zero. We choose the Lorentzian estimator but the treatment here could be equally applied to a wide variety of other estimators. A discussion of various estimators can be found in [Hampel et al. 1986]. More specifically, the Lorentzian function is defined as follows: ρ(r) = log(1 + 1/2(r/σ) 2 ) (10) where the scalar σ is a parameter for the robust estimator and r is the residual error between the input motion y d (w(t)) and the deforming motion p d (t, λ 1,..., λ M ). We experimentally set σ to 0.1. N M T L F walking running jumping Table 1: Details of the data we used. N is the number of motion examples. M is the number of motion modes. T is the number of total frames in the reference motion. L is the number of levels for multi-resolution representations. and F is the frame rate for motion databases (frame per second). 5.2 Video Data Another advantage of the model-based registration process is its flexibility to register various forms of motion data. We can register any 2D or 3D human motion data with the parameterized model as long as we can numerically measure the difference between the input motion and the parameterized motion model. Here, we focus our discussion on how to register a video sequence with the parameterized model but the treatment here could be equally applied to other motion formats. We pick a few interesting feature points in video and track their 2D positions y 2D (s) throughout the whole sequence [Wei and Chai 2008] (see Figure 10). We use the tracked 2D trajectories to register the input video data with the parameterized motion model. However, direct application of the registration framework for this problem might not work because the distance between the input motion (i.e. 2D trajectories) and the parameterized motion model depends on an unknown projection matrix which is a function of camera parameters c. One good way to address this problem is to simultaneously estimate model parameters {λ 1,..., λ M }, time warping function w(t) and camera parameters c using the 2D trajectories y 2D (s) and parameterized model p(t, λ 1,..., λ M ). We assume a weak perspective projection model, which is valid when the average variation of the depth of an articulated object along the line of sight is small compared to the distance between the camera and object. As a result, the unknown camera parameters c include scale parameter, camera orientation and position. The new error term can be defined as follows: Eerror video = T y t=1 2D (w(t)) fproj(g(p(t, λ1,..., λm )), c) 2 (11) where the function g is the forward kinematic function which maps the motion from the joint angle space to the 3D position space. The function f proj is a projection function which projects the 3D points into the 2D space with appropriate camera parameters c. 6 Results We show the performance of the model-based registration process in a variety of experiments. We compare with dynamic time warping and test the algorithm on corrupted motion data. We also show our algorithm can be used for 2D video data registration, a capacity that has not been demonstrated in previous motion registration approaches. Except the video data, the computational time for our model-based registration method ranges between one and two seconds on the Intel Core 2 Duo CPU. Our results are best seen in the accompanying video although we show sample frames of a few results here. Data. Table 1 summarizes the details of the three motion databases. The motion was captured with a Vicon motion capture system of 12 MXF20 cameras with 41 markers for full-body movements at 187

6 Figure 6: Motion registration between two walking motions with different styles: (top) normal walking. (middle) the registered stylized walking from our method. (bottom) the registration result from DTW. The red circles highlight the differences of two results. Figure 7: Motion registration between sneaky walking and walking with arm waving : (top) sneaky walking. (middle) the registered walking with arm waving from our method. (bottom) the registration result from DTW. The red circles highlight the differences of two results. Note that pink and yellow colors highlight the left and right leg respectively. 188

7 Figure 8: Automatic segmentation and registration of a long walking sequence: (left). A long walking sequence is segmented into three distinct walking cycles, where green, orange, and blue colors indicate the first, second and third walking cycle respectively. (right). the three registered walking cycles. Figure 9: Robustness to outliers: (top) a long-distance jumping motion sequence corrupted with outliers throughout the motion. (bottom) the registered short-distance jumping sequence. Figure 10: Video registration: (top) the input video and tracked image features. (middle) the reconstructed/registered 3D motion from the estimated viewpoint. (bottom) the reconstructed 3D motion from a new viewpoint. 189

8 120Hz. The walking and running database include 200 and 100 preregistered motion examples with variations of speeds, step sizes, directions, and styles, respectively. The jumping database includes 50 registered motion examples with different jumping heights, jumping distances, directions and styles. The number of model parameters for the walking, running and jumping are 30, 20 and 18 respectively by keeping 99 percent of the motion variations. Comparisons. We report the superior performance of our algorithm by comparing with dynamic time warping. Figure 6 and Figure 7 show sample images of the side-by-side comparisons between our method and dynamic time warping. The dynamic time warping technique is based on minimizing the joint-angle motion difference across the entire sequence. The DTW implementation considers continuity, causality and slope limit described in the paper [Kovar and Gleicher 2003]. In the experiments, we set the slope limit to 3. Motion segmentation and registration. Our algorithm can be used to sequentially segment a long sequence of an input motion into multiple subsequences and then align each subsequence by registering them to the parameterized motion model. Figure 8 shows the results for automatic segmentation and alignment of a long walking sequence. The input sequence contains three walking cycles with distinctive motion styles. Corrupted motion data. The model-based registration process is robust to outliers and noise. Figure 9 shows sample frames of the registration results between a corrupted long distance jump and a short-distance jump. In the accompanying video, we also show our registration algorithm is robust to noisy motion data. Video data. We can use the parameterized motion models to register a video sequence. We first use an interactive spacetime tracking process to track 2D positions of a few interesting image features across the entire video sequence [Wei and Chai 2008] and then register the 2D trajectories with the parameterized model. Figure 10 shows sample images of the input video and the reconstructed 3D deforming motion seen from two different viewpoints (estimated viewpoint and new viewpoint). The testing video data contains two walking cycles and is downloaded from the public video database 1. It takes about 3.2 seconds to register 2D video data with the parameterized model on the Intel Core 2 Duo CPU. 7 Discussion We present an efficient model-based approach for automatic registration of human motion data. We construct a parameterized motion model from a set of pre-registered training examples and then deform the parameterized model to best register an input motion by maximizing the match between the deforming motion and input motion. We also introduce an efficient multi-resolution optimization algorithm to simultaneously compute the model parameters and time warping curves. One limitation of the model-based registration approach is that an appropriate set of training examples must be available and preregistered in the preprocessing step. To obtain a high-quality motion model, we choose to pre-register database examples with a semi-automatic method. This might become time-consuming when the number of examples in a database is large. One possible solution is to preregister a small set of examples in the database with the semi-automatic process and then use the model-based registration method to incrementally update the parameterized model. In the future, we would like to include more subjects, children to elderly people, and more motion variations to the training databases. We are also attempting to build parameterized motion models for 1 other actions. 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