nips nips2006 nips2006-134 knowledge-graph by maker-knowledge-mining

134 nips-2006-Modeling Human Motion Using Binary Latent Variables

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Author: Graham W. Taylor, Geoffrey E. Hinton, Sam T. Roweis

Abstract: We propose a non-linear generative model for human motion data that uses an undirected model with binary latent variables and real-valued “visible” variables that represent joint angles. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. Such an architecture makes on-line inference efﬁcient and allows us to use a simple approximate learning procedure. After training, the model ﬁnds a single set of parameters that simultaneously capture several different kinds of motion. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line ﬁlling in of data lost during motion capture. Website: http://www.cs.toronto.edu/∼gwtaylor/publications/nips2006mhmublv/

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract We propose a non-linear generative model for human motion data that uses an undirected model with binary latent variables and real-valued “visible” variables that represent joint angles. [sent-6, score-0.748]

2 The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. [sent-7, score-1.17]

3 We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line ﬁlling in of data lost during motion capture. [sent-10, score-0.862]

4 edu/∼gwtaylor/publications/nips2006mhmublv/ 1 Introduction Recent advances in motion capture technology have fueled interest in the analysis and synthesis of complex human motion for animation and tracking. [sent-14, score-0.877]

5 Models based on the physics of masses and springs have produced some impressive results by using sophisticated “energy-based” learning methods[1] to estimate physical parameters from motion capture data[2]. [sent-15, score-0.407]

6 The simplest way to generate new motion sequences based on data is to concatenate parts of training sequences [3]. [sent-17, score-0.721]

7 Another method is to transform motion in the training data to new sequences by learning to adjusting its style or other characteristics[4, 5, 6]. [sent-18, score-0.614]

8 Data from modern motion capture systems is high-dimensional and contains complex non-linear relationships between the components of the observation vector, which usually represent joint angles with respect to some skeletal structure. [sent-20, score-0.686]

9 To model N bits of information about the past history they require 2N hidden states. [sent-22, score-0.349]

10 componential) hidden state that has a representational capacity which is linear in the number of components. [sent-25, score-0.271]

11 2 An energy-based model for vectors of real-values In general, using distributed binary representations for hidden state in directed models of time series makes inference difﬁcult. [sent-27, score-0.477]

12 Typically, RBMs use binary logistic units for both the visible data and hidden variables, but in our application the data (comprised of joint angles) is continuous. [sent-29, score-1.111]

13 The graphical model has a layer of visible units v and a layer of hidden units h; there are undirected connections between layers but no connections within a layer. [sent-31, score-1.795]

14 The main advantage of using this undirected, “energy-based” model rather than a directed “belief net” is that inference is very easy because the hidden units become conditionally independent when the states of the visible units are observed. [sent-35, score-1.436]

15 The learning rule is: ∆wij ∝ vi hj data − vi hj recon , (4) where the ﬁrst expectation (over hidden unit activations) is with respect to the data distribution and the second expectation is with respect to the distribution of “reconstructed” data. [sent-38, score-1.005]

16 The reconstructions are generated by starting a Markov chain at the data distribution, updating all the hidden units in parallel by sampling (Eq. [sent-39, score-0.607]

17 2) and then updating all the visible units in parallel by sampling (Eq. [sent-40, score-0.711]

18 For both expectations, the states of the hidden units are conditional on the states of the visible units, not vice versa. [sent-42, score-1.085]

19 The learning rule for the hidden biases is just a simpliﬁed version of Eq. [sent-43, score-0.342]

20 1 The conditional RBM model The RBM we have described above models static frames of data, but does not incorporate any temporal information. [sent-46, score-0.294]

21 We can model temporal dependencies by treating the visible variables in the previous time slice as additional ﬁxed inputs [10]. [sent-47, score-0.51]

22 We add two types of directed connections (Figure 2): autoregressive connections from the past n conﬁgurations (time steps) of the visible units to the current visible conﬁguration, and connections from the past m visibles to the current hidden conﬁguration. [sent-49, score-2.126]

23 The addition of these directed connections turns the RBM into a conditional RBM (CRBM). [sent-50, score-0.326]

24 1 For any setting of the parameters, the gradient of the quadratic log likelihood will always overwhelm the gradient due to the weighted input from the binary hidden units provided the value vi of a visible unit is far enough from its bias, ci . [sent-54, score-1.164]

25 Figure 1: In a trained model, probabilities of each feature being “on” conditional on the data at the visible units. [sent-55, score-0.552]

26 , t − n, the hidden units at time t are conditionally independent. [sent-62, score-0.497]

27 The only change is that when we update the visible and hidden units, we implement the directed connections by treating data from previous time steps as a dynamically changing bias. [sent-64, score-1.014]

28 The contrastive divergence learning rule for hidden biases is given in Eq. [sent-65, score-0.423]

29 5 and the equivalent learning rule for the temporal connections that determine the dynamically changing hidden unit biases is: (t−q) t−q (6) ∆dij ∝ vi ht data − ht recon . [sent-66, score-0.91]

30 j j Hidden layer j i (t−q) where dij is the log-linear parameter (weight) connecting visible unit i at time t − q to hidden unit j for q = 1. [sent-67, score-0.912]

31 Similarly, the learning rule for the autoregressive connections that determine the dynamically changing visible unit biases is: (t−q) ∆aki where unit i. [sent-70, score-0.961]

32 (7) is the weight from visible unit k at time t − q to visible The autoregressive weights can model short-term temporal structure very well, leaving the hidden units to model longer-term, higher level structure. [sent-72, score-1.636]

33 During training, the states of the hidden units are determined by both the input they receive from the observed data and the input they receive from the previous time slices. [sent-73, score-0.667]

34 The learning rule for W remains the same as a standard RBM, but has a different effect because the states of the hidden units are now inﬂuenced by the previous visible units. [sent-74, score-1.006]

35 Visible layer t-2 t-1 t Figure 2: Architecture of our model (in our experiments, we use three previous time steps) While learning a model of motion, we do not need to proceed sequentially through the training data sequences. [sent-76, score-0.282]

36 As long as we isolate “chunks” of frames (the size depending on the order of the directed connections), these can be mixed and formed into mini-batches. [sent-78, score-0.234]

37 7 by its expected value and we also used the expected value of vi when computing the probability of activation of the hidden units. [sent-86, score-0.348]

38 However, to compute the one-step reconstructions of the data, we used stochastically chosen binary values of the hidden units. [sent-87, score-0.382]

39 This prevents the hidden activities from transmitting an unbounded amount of information from the data to the reconstruction [11]. [sent-88, score-0.342]

40 4) we used the stochastically chosen binary values of the hidden units in the ﬁrst term (under the data), but replaced hj by its expected value in the second term (under the reconstruction). [sent-91, score-0.743]

41 We took this approach because the reconstruction of the data depends on the binary choices made when selecting hidden state. [sent-92, score-0.378]

42 Thus when we infer the hiddens from the reconstructed data, the probabilities are highly correlated with the binary hidden states inferred from the data. [sent-93, score-0.385]

43 The inference step, conditional on past visible states, is approximate because it ignores the future (it does not do smoothing). [sent-96, score-0.549]

44 Because of the directed connections, exact inference within the model should include both a forward and backward pass through each sequence (we currently perform only a forward pass). [sent-97, score-0.31]

45 We have avoided a backward pass because missing values create problems in undirected models, so it is hard to perform learning efﬁciently using the full posterior. [sent-98, score-0.257]

46 The processed data consists of 3D joint angles derived from 30 (CMU) or 17 (MIT) markers plus a root (coccyx, near the base of the back) orientation and displacement. [sent-101, score-0.278]

47 Each of the remaining joint angles had between one and three degrees of freedom. [sent-104, score-0.238]

48 All of the joint angles and the root orientation were converted from Euler angles to the “exponential map” parameterization [13]. [sent-105, score-0.391]

49 The autoregressive connections in our model can be thought of as doing a kind of “whitening” of the data. [sent-118, score-0.302]

50 Perhaps the most direct demonstration, which exploits the fact that it is a probability density model of sequences, is to use the model to generate de-novo a number of synthetic motion sequences. [sent-123, score-0.505]

51 Video ﬁles of these sequences are available on the website mentioned in the abstract; these motions have not been retouched by hand in any motion editing software. [sent-124, score-0.687]

52 Note that we also do not have to keep a reservoir of training data sequences around for generation - we only need the weights of the model and a few valid frames for initialization. [sent-125, score-0.427]

53 The visible units at the last few time steps determine the effective biases of the visible and hidden units at the current time step. [sent-127, score-1.654]

54 We always keep the previous visible states ﬁxed and perform alternating Gibbs sampling to obtain a joint sample from the conditional RBM. [sent-128, score-0.609]

55 This picks new hidden and visible states that are compatible with each other and with the recent (visible) history. [sent-129, score-0.715]

56 Generation requires initialization with n time steps of the visible units, which implicitly determine the “mode” of motion in which the synthetic sequence will start. [sent-130, score-0.803]

57 We used randomly drawn consecutive frames from the training data as an initial conﬁguration. [sent-131, score-0.213]

58 1 Generation of walking and running sequences from a single model In our ﬁrst demonstration, we train a single model on data containing both walking and running motions; we then use the learned model to generate both types of motion, depending on how it is initialized. [sent-133, score-0.837]

59 We trained2 on 23 sequences of walking and 10 sequences of jogging (from subject 35 in the CMU database). [sent-134, score-0.454]

60 Figure 3: After training, the same model can generate walking (top) and running (bottom) motion (see videos on the website). [sent-136, score-0.69]

61 Figure 3 shows a walking sequence and a running sequence generated by the same model, using alternating Gibbs sampling (with the probability of hidden units being “on” conditional on the current and previous three visible vectors). [sent-138, score-1.268]

62 Since the training data does not contain any transitions between walking and running (and vice-versa), the model will continue to generate walking or running motions depending on where it is initialized. [sent-139, score-0.834]

63 The order of the sequences was randomly permuted such that walking and running sequences were distributed throughout the training data. [sent-143, score-0.523]

64 We trained on 9 sequences (from the MIT database, ﬁle Jog1 M) containing long examples of running and jogging, as well as a few transitions between the two styles. [sent-145, score-0.332]

65 Training was done as before, except that after the model was trained, an identical 200 hidden-unit model was trained on top of the ﬁrst model (see Sec. [sent-147, score-0.214]

66 A video available on the website demonstrates our model’s ability to stochastically transition between various motion styles during a single generated sequence. [sent-150, score-0.701]

67 3 Introducing transitions using noise In our third demonstration, we show how transitions between motion styles can be generated even when such transitions are absent in the data. [sent-152, score-0.77]

68 1, where we have learned on separate sequences of walking and running. [sent-155, score-0.293]

69 To generate, we use the same sampling procedure as before, except that at each time we stochastically choose the hidden states (given the current and previous three visible vectors) we add a small amount of Gaussian noise to the hidden state biases. [sent-156, score-1.03]

70 This encourages the model to explore more of the hidden state space without deviating too far the current motion. [sent-157, score-0.292]

71 Applying this “noisy” sampling approach, we see that the generated motion occasionally transitions between learned styles. [sent-158, score-0.46]

72 4 Filling in missing data Due to the nature of the motion capture process, which can be adversely affected by lighting and environmental effects, as well as noise during recording, motion capture data often contains missing or unusable data. [sent-161, score-1.164]

73 The majority of motion editing software packages contain interpolation methods to ﬁll in missing data, but this leaves the data unnaturally smooth. [sent-163, score-0.639]

74 These methods also rely on the starting and end points of the missing data, so if a marker goes missing until the end of a sequence, na¨ve interpolation will not work. [sent-164, score-0.396]

75 Such methods often only use the past and future ı data from the single missing marker to ﬁll in that marker’s missing values, but since joint angles are highly correlated, substantial information about the placement of one marker could be gained from the others. [sent-165, score-0.719]

76 Our trained model has the ability to easily ﬁll in such missing data, regardless of where the dropouts occur in a sequence. [sent-166, score-0.241]

77 Due to its approximate inference method which does not rely on a backward pass through the sequence, it also has the ability to ﬁll in such missing data on-line. [sent-167, score-0.278]

78 Filling in missing data with our model is very similar to generation. [sent-168, score-0.229]

79 We simply clamp the known data to the visible units, initialize the missing data to something reasonable (for example, the value at the previous frame), and alternate between stochastically updating the hidden and visible units, with the known visible states held ﬁxed. [sent-169, score-1.872]

80 1 except that one walking and one running sequence were left out of the training data to be used as test data. [sent-172, score-0.371]

81 For each of these walking and running test sequences, we erased two different sets of joint angles, starting halfway through the test sequence. [sent-173, score-0.324]

82 For the missing leg, mean squared reconstruction error per joint using our model was 8. [sent-180, score-0.338]

83 78, measured in normalized joint angle space, and summed over the 62 frames of interest. [sent-181, score-0.249]

84 For the missing upper body, mean squared reconstruction error per joint using our model was 20. [sent-184, score-0.338]

85 5 20 40 60 80 Frame 100 120 140 −2 0 20 40 60 80 100 120 140 Frame Figure 4: The model successfully ﬁlls in missing data using only the previous values of the joint angles (through the temporal connections) and the current angles of other joints (through the RBM connections). [sent-196, score-0.715]

86 Shown are two of the three angles of rotation for the left hip joint (the plot of the third is similar to the ﬁrst). [sent-197, score-0.269]

87 The original data is shown on a solid line, the model’s prediction is shown on a dashed line, and the results of nearest neighbor interpolation are shown on a dotted line (see a video on the website). [sent-198, score-0.225]

88 The previous layer CRBM is kept, and the sequence of hidden state vectors, while driven by the data, is treated as a new kind of “fully observed” data. [sent-200, score-0.352]

89 If we i keep only the visible layer, and its n-th order directed connections, we have a standard AR(n) model with Gaussian noise. [sent-206, score-0.584]

90 6 Discussion We have introduced a generative model for human motion based on the idea that local constraints and global dynamics can be learned efﬁciently by a conditional Restricted Boltzmann Machine. [sent-208, score-0.497]

91 The model has been designed with human motion in mind, but should lend itself well to other high-dimensional time series. [sent-210, score-0.45]

92 It would be possible to preserve the global phase information by using a much higher order model, but for higher dimensional data such as full body motion capture this is unnecessary because the whole conﬁguration of joint angles and angular velocities never has any phase ambiguity. [sent-212, score-0.685]

93 Models with more hidden layers are able to implicitly model longer-term temporal information, and thus will mitigate this effect. [sent-214, score-0.376]

94 We have demonstrated that our model can effectively learn different styles of motion, as well as the transitions between these styles. [sent-215, score-0.258]

95 The ability of the model to transition smoothly, however, is dependent on having sufﬁcient examples of such transitions in the training data. [sent-217, score-0.216]

96 We plan to train on larger datasets encompassing such transitions between various styles of motion. [sent-218, score-0.204]

97 If we augment the data with some static skeletal and identity parameters (in essence mapping a person’s unique identity to a set of features), we should be able to use the same generative model for many different people, and generalize individual characteristics from one type of motion to another. [sent-219, score-0.522]

98 For Matlab playback of motion and generation of videos, we have used Neil Lawrence’s motion capture toolbox (http://www. [sent-231, score-0.807]

99 Popovic, “Learning physics-based motion style with nonlinear inverse optimization,” ACM Trans. [sent-247, score-0.404]

100 Shum, “Motion texture: a two-level statistical model for character motion synthesis,” in Proc. [sent-270, score-0.408]

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