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Music-Driven Group Choreography (Part 3)

This is the final part of the series group dance choreography, In this part, we will provide detailed analyses of our proposed group dance generation method.


AIOZ-GDANCE Statistics

Figure 1. Distribution (%) of music genres (a) and dance styles (b) in our dataset.

In Figure 1, we show the distribution of music genres and dance styles in our dataset. As illustrated in Figure 1 (Left), Pop and Electronic are popular music genres while other music genres nearly share the same distribution. Meanwhile, on the right of Figure 1, Zumba, Aerobic, and Commercial are the dominant dance styles.

Figure 2. The correlation between dance styles and number of dancers (a); and between dance styles and music genres (b).

Figure 2 (Left) shows the number of dancers in each dance style. Naturally, we see that Zumba, Aerobic, and Commercial have more dancers. On the right of this figure, we illustrate the correlation between music genres and dance styles.

Evaluation Metrics

Similar to prior works on single-dance generation, we evaluate the generated motion quality by calculating the distribution distance between the generated and the ground-truth motions using Frechet Inception Distance (FID)[1, 2]. To evaluate how well the generated 3D motion correlates to the input music, we use the Motion-Music Consistency metric (MMC) [2,3]. We also evaluate our model's ability to generate diverse dance motions when given various input music by measuring Generation Diversity (GenDiv) [2,3].

To evaluate the group dancing quality, we propose three new metrics: Group Motion Realism (GMR), Group Motion Correlation (GMC), and Trajectory Intersection Frequency (TIF). Detailed calculations of these metrics are described as follows:

Group Motion Realism (GMR). To calculate the realism between generated and ground-truth group motion, we need to find a single unified representation for all dancers' motions in the scene. Based on the kinetic features of a single motion sequence [4], we propose to calculate Group Motion Realism (GMR), smaller is better. Specifically, for each entity, we compute the velocity of each element jj of the pose vector: vtn=yt+1nytnΔtv^n_t = \frac{y^n_{t+1} - y^n_t}{\Delta t} where Δt\Delta t is the time period between two consecutive frames. Note that the pose vector of each entity at each frame consists of the root orientation, root position and joint angles. The group kinetic features of a sequence is approximated by taking the logarithm of the total kinetic energy of all group entities as:

ej=log(1+1T1Nt=1Tn=1Nmj(vt,jn)2)e_j = \log \left(1 + \frac{1}{T}\frac{1}{N} \sum_{t=1}^T \sum_{n=1}^N m_j (v^n_{t,j})^2\right)

where mjm_j is the moment of inertia or mass of each joint. We assume that mjm_j is constant with respect to time and entity. Then, we split the sequence into smaller chunks and calculate the features of these chunks. This process is identical for both the generated and ground-truth sequences. Finally, we utilize these sets of features (from generated and ground-truth group dance) to calculate the GMR using the standard FID formulation as in [1].

Group Motion Correlation (GMC). We also evaluate the synchrony and the correlation between dancers within the generated group. We assume that the correlation of movements between individuals is likely to reflect their interaction in the choreography. For every pair of motions within a group, we first align the two motion sequences using Dynamic Time Warping algorithm based on the Euclidean distance in the joint position space (obtained by SMPL joint regressor). We then calculate the mean cross-correlations between the time-aligned motion pairs using the kinetic features [4]. The generated group motion correlation degree is then calculated as the average of all motion pairs.

Trajectory Intersection Frequency (TIF). For the generated group sequences, the intersection rate is calculated over all FF frames as:

TIR=Fi,j:ijI[intersect(M(yi),M(yj))]F,\text{TIR} = \frac{\sum_{F}\sum_{i,j : i\neq j} \mathbb{I}[\text{intersect}(M(y^i),M(y^j))]}{F},

where MM is the SMPL skinning function [5] which can output a 6890-vertices human mesh from the input pose parameters yy. intersect(x,y)\text{intersect}(x,y) is a function that returns 1 if the two meshes are intersect with each other and 0 otherwise. For TIF, smaller value is better and indicates less intersection of the generated group.

Cross-entity Attention Analysis

We compare our method with FACT [2]. FACT is a recent state-of-the-art method designed for single dance generation, thus giving our method an advantage. However, it is still the closest competing method as we propose a new group dance dataset that is not available for benchmarking before. We also analyse our method with and without using Cross-entity Attention. We train all methods with mini-batch containing all dancers within the group instead of sampling each dancer independently as in FACT’s original implementation.

Figure 3. Comparison between FACT and our GDanceR. Our method handles better the consistency and cross-body intersection problem between dancers.

Table 1 shows the method comparison between the baseline FACT[2] and our proposed GDanceR with and without Cross-entity Attention. The results show that GDanceR, especially with the Cross-entity Attention, outperforms the baseline by a large margin in all metrics. In Figure 3, we also visualize the example outputs of FACT and GDanceR. It is clear that FACT does not handle well the intersection problem. This is understandable as FACT is not designed for group dance generation, while our method with the Cross-entity Attention can deal with this problem better.

Table 1. Generation results comparison on AIOZ-GDANCE dataset. w/o CA denotes without using Cross-entity Attention.

Number of Dancers Analysis.

Table 2 demonstrates the generation results of our method when we want to generate different numbers of dancers. In general, the FID, GMR, and GMC metrics do not show much correlation with the numbers of generated dancers since the results are varied. On the other hand, MMC shows its stability among all setups (0.248\sim 0.248), which indicates that our network is robust in generating motion from given music regardless of the changing of initial positions. The generation diversity (GenDiv) decreases while the intersection frequency (TIF) increases when more dancers are generated. These results show that dealing with the collision during the group generation process is worth further investigation.

Table 2. Performance of our proposed method when increasing the number of generated dancers.

Dance Style Analysis

Figure 4. Examples of generated group motions from our method.

Different dance styles exhibit different challenges in group dance generation. As shown in Table 3, Aerobic and Zumba are quite similar for generating choreography as they usually focus on workout and sporty movements. Besides, while Commercial and Irish are easier for the model to reproduce the motions, Bollywood and Samba contain highly skilled movements that are challenging to capture and represent accurately. In Figure 4, we show the generated results of GDanceR with different dance styles. Our Supplementary Material and Demonstration Video also provide more examples.

Table 3. The results of different dance styles. These results are obtained by training the model on each dance style.

Ablation on Latent Motion Fusion.

We investigate different fusion strategies between the local motion hih^i and global-aware motion gig^i to obtain the final motion representation ziz^i. Specifically, we experiment with three settings: (i) No Fusion: the final motion is the global-aware motion obtained from our Cross-entity Attention (zi=giz^i = g^i); (ii) Concatenate: the final motion is the concatenation of the local and global-aware motion (zi=[hi;gi]z^i = [h^i; g^i]); (iii) Add: the final motion is the addition between local and global (zi=hi+giz^i = h^i + g^i). Table 4 summarizes the results. We find that fusing the motion by adding both the local and global motion features achieves the best results. In this strategy, the global information between entities is encoded to the local motion in an effective way so that the final motion retain the comprehensive information of their own past motion as well as the motion of every other entity. While in the concatenation, the model is prone to overfitting due to the redundant information of both the local and global representation. On the other hand, No Fusion can degrade the amount of information of the past motion, leading to insufficient input information and the Decoder may fail to generate the temporally-coherent motion aligned with the music.

Table 4. Ablation study on different fusion strategies for the latent motion representation.


In summary, we have introduced AIOZ-GDANCE, the largest dataset for audio-driven group dance generation. Our dataset contains in-the-wild videos and covers different dance styles and music genres. We then propose a strong baseline along with new evaluation metrics for group dance generation task. We also perform extensive experiments to validate our method on this interesting yet unexplored problem, using our new dataset and evaluation protocols. We hope that the release of our dataset will foster more research on audio-driven group choreography.


[1] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. NIPS 2017.

[2] Ruilong Li, Shan Yang, David A Ross, and Angjoo Kanazawa. Ai choreographer: Music-conditioned 3d dance generation with aist++. ICCV 2021

[3] Hsin-Ying Lee, Xiaodong Yang, Ming-Yu Liu, Ting-Chun Wang, Yu-Ding Lu, Ming-Hsuan Yang, and Jan Kautz. Dancing to music. NIPS 2019.

[4] Kensuke Onuma, Christos Faloutsos, and Jessica K Hodgins. Fmdistance: A fast and effective distance function for motion capture data. Eurographics 2008.

[5] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. SMPL: A skinned multi-person linear model. ACM Trans. Graphics, 2015

Music-Driven Group Choreography (Part 2)

In the previous post, we have introduced AIOZ-GDANCE, a new largescale in-the-wild dataset for music-driven group dance generation. On the basis of the new dataset, we introduce the first strong baseline for group dance generation that can jointly generate multiple dancing motions expressively and coherently.

Figure 1. The overall architecture of GDanceR. Our model takes in a music sequence and a set of initial positions, and then auto-regressively generates coherent group dance motions that are attuned to the input music.

Music-driven Group Dance Generation Method

Problem Formulation

Given an input music audio sequence {m1,m2,...,mT}\{m_1, m_2, ...,m_T\} with t={1,...,T}t = \{1,..., T\} indicates the index of music segments, and the initial 3D positions of NN dancers {τ01,τ02,...,τ0N}\{\tau^1_0, \tau^2_0, ..., \tau^N_0 \}, τ0iR3\tau^i_0 \in \mathbb{R}^{3}, our goal is to generate the group motion sequences {y11,...,yT1;...;y1n,...,yTn}\{y^1_1,..., y^1_T; ...;y^n_1,...,y^n_T\} where ytiy^i_t is the generated pose of ii-th dancer at time step tt. Specifically, we represent the human pose as a 72-dimensional vector y=[τ;θ]y = [\tau; \theta] where τ\tau, θ\theta represent the root translation and pose parameters of the SMPL model [1], respectively.

In general, the generated group dance motion should meet the two conditions: (i) consistency between the generated dancing motion and the input music in terms of style, rhythm, and beat; (ii) the motions and trajectories of dancers should be coherent without cross-body intersection between dancers. To that end, we propose the first baseline method, for group dance generation that can jointly generate multiple dancing motions expressively and coherently. Figure 1 shows the architecture of our proposed Music-driven 3D Group Dance generatoR (GDanceR), which consists of three main components:

  • Transformer Music Encoder.
  • Initial Pose Generator.
  • Group Motion Generator.

Transformer Music Encoder

From the raw audio signal of the input music, we first extract music features using the available audio processing library Librosa. Concretely, we extract the mel frequency cepstral coefficients (MFCC), MFCC delta, constant-Q chromagram, tempogram, onset strength and one-hot beat, which results in a 438-dimensional feature vector. We then encode the music sequence M={m1,m2,...,mT}M =\{m_1, m_2, ...,m_T\}, mtR438m_t \in \mathbb{R}^{438} into a sequence of hidden representation {a1,a2,...,aT}\{a_1, a_2,..., a_T\}, atRdaa_t \in \mathbb{R}^{d_a}. In practice, we utilize the self-attention mechanism of transformer [2] to effectively encode the multi-scale information and the long-term dependency between music frames. The hidden audio at each time step is expected to contain meaningful structural information to ensure that the generated dancing motion is coherent across the whole sequence.

Specifically, we first embed the music features mtm_t using a Linear layer followed by Positional Encoding to encode the time ordering of the sequence.

U=PE(MWau)U = \text{PE}({M} W^u_a)

where PE\text{PE} denotes the Positional Encoding, and WauR438×daW^u_a \in \mathbb{R}^{438 \times d_a} is the parameters of the linear projection layer. Then, the hidden audio information can be calculated using self-attention mechanism:

A=FF(softmax((UqUk)Tdk)Uv),Uq=UWaq,Uk=UWak,Uv=UWav\\ \mathbb{A} = \text{FF}(\text{softmax}\left(\frac{(U^q U^k)^T}{\sqrt{d_{k}}} \right) U^v ), \\ U^q = U W^q_a, \quad U^k = U W^k_a, \quad U^v = UW^v_a

where Waq,WakRda×dkW^q_a, W^k_a \in \mathbb{R}^{d_a \times d_k}, and WavRda×dvW^v_a \in \mathbb{R}^{d_a \times d_v} are the parameters that transform the linear embedding audio UU into a query UqU^q, a key UkU^k, and a value UvU^v respectively. dad_a is the dimension of the hidden audio representation while dkd_k is the dimension of the query and key, and dvd_v is the dimension of value. FF\text{FF} is a feed-forward neural network.

Initial Pose Generator

Figure 2.The Transformer Music Encoder encodes the acoustic and rhythmic information to generate the initial poses from the input positions.

Given the initial positions of all dancers, we generate the initial poses by combing the audio feature with the starting positions. We aggregate the audio representation by taking an average over the audio sequence. The aggregated audio is then concatenated with the input position and fed to a multilayer perceptron (MLP) to predict the initial pose for each dancer:

y0i=MLP([1Tt=1Tat;τ0i]),y^i_0 = \text{MLP}\left( \left[\frac{1}{T}\sum_{t=1}^T a_t ; \tau^i_0 \right] \right),

where [;][;] is the concatenation operator, τ0i\tau^i_0 is the initial position of the ii-th dancer.

Group Motion Generator

Figure 3. The Group Motion Generator auto-regressively generates coherent group dance motions based on the encoded acoustic information.

To generate the group dance motion, we aim to synthesize the coherent motion of each dancer such that it aligns well with the input music. Furthermore, we also need to maintain global consistency between all dancers. As shown in Figure 3, our Group Generator comprises a Group Encoder to encode the group sequence information and an MLP Decoder to decode the hidden representation back to the human pose space. To effectively extract both the local motion and global information of the group dance sequence through time, we design our Group Encoder based on two factors: Recurrent Neural Network [3] to capture the temporal motion dynamics of each dancer, and Attention mechanism [2] to encode the spatial relationship of all dancers.

Specifically, at each time step, the pose of each dancer in the previous frame yt1iy^i_{t-1} is sent to an LSTM unit to encode the hidden local motion representation htih^i_t:


To ensure the motions of all dancers have global coherency and discourage strange effects such as cross-body intersection, we introduce the Cross-entity Attention mechanism. In particular, each individual motion representation is first linearly projected into a key vector kik^i, a query vector qiq^i and a value vector viv^i as follows: \begin{equation} k^i = h^i W^{k}, \quad q^i = h^i W^{q}, \quad v^i = h^i W^{v}, \end{equation} where Wq,WkRdh×dkW^q, W^k \in \mathbb{R}^{d_h \times d_k}, and WvRdh×dvW^v \in \mathbb{R}^{d_h \times d_v} are parameters that transform the hidden motion hh into a query, a key, and a value, respectively. dkd_k is the dimension of the query and key while dvd_v is the dimension of the value vector. To encode the relationship between dancers in the scene, our Cross-entity Attention also utilizes the Scaled Dot-Product Attention as in the Transformer [3].

Figure 4. The Group Encoder learns to encode the relations among dancers through our proposed Cross-entity Attention mechanism.

In practice, we find that people having closer positions to each other tend to have higher correlation in their movement. Therefore, we adopt Spacial Encoding strategy to encode the spacial relationship between each pair of dancers. The Spacial Encoding between two entities based on their distance in the 3D space is defined as follows:

eij=exp(τiτj2dτ),e_{ij} = \exp\left(-\frac{\Vert \tau^i - \tau^j \Vert^2}{\sqrt{d_{\tau}}}\right),

where dτd_{\tau} is the dimension of the position vector τ\tau. Considering the query qiq^i, which represents the current entity information, and the key kjk^j, which represents other entity information, we inject the spatial relation information between these two entities onto their cross attention coefficient:

αij=softmax((qi)kjdk+eij).\alpha_{ij} = \text{softmax}\left(\frac{(q^i)^\top k^j}{\sqrt{d_k}} + e_{ij}\right).

To preserve the spatial relative information in the attentive representation, we also embed them into the hidden value vector and obtain the global-aware representation gig^i of the ii-th entity as follows:

gi=j=1Nαij(vj+eijγ),g^i = \sum_{j=1}^N\alpha_{ij}(v^j + e_{ij}\gamma),

where γRdv\gamma \in \mathbb{R}^{d_v} is the learnable bias and scaled by the Spacial Encoding. Intuitively, the Spacial Encoding acts as the bias in the attention weight, encouraging the interactivity and awareness to be higher between closer entities. Our attention mechanism can adaptively attend to each dancer and others in both temporal and spatial manner, thanks to the encoded motion as well as the spatial information.

We then fuse both the local and global motion representation by adding hih^i and gig^i to obtain the final latent motion ziz^i. Our final global-local representation of each entity is expected to carry the comprehensive information of their own past motion as well as the motion of every other entity, enabling the MLP Decoder to generate coherent group dancing sequences. Finally, we generate the next movement yti{y}^i_t based on the final motion representation ztiz^i_t as well as the hidden audio representation ata_t, and thus can capture the fine-grained correspondence between music feature sequence and dance movement sequence:

yti=MLP([zti;at]).y^i_t = \text{MLP}([z^i_t; a_t]).

Built upon these components, our model can effectively learn and generate coherent group dance animation given several pieces of music. In the next part, we will go through the experiments and detailed studies of the method.


[1] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. SMPL: A skinned multiperson linear model. ACM Trans. Graphics, 2015

[2] Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser Ł, Polosukhin I. Attention is all you need. NIPS 2017.

[3] Hochreiter S, Schmidhuber J. Long short-term memory. Neural computation. 1997 Nov 15;9(8):1735-80.

Music-Driven Group Choreography (Part 1)

Dancing is an important part of human culture and remains one of the most expressive physical art and communication forms. With the rapid development of digital social media platforms, creating dancing videos has gained significant attention from social communities. As a result, millions of dancing videos are created and watched daily on online platforms. Recently, studies of how to create natural dancing motion from music have attracted great attention in the research community.

Figure 1. We demonstrate the AIOZ-GDANCE dataset with in-the-wild videos, music audio, and 3D group dance motion.

Nevertheless, generating dance motion for a group of dancers remains an open problem and have not been well-investigated by the community yet. Motivated by these shortcomings and to foster research on group choreography, we establish AIOZ-GDANCE, a new largescale in-the-wild dataset for music-driven group dance generation. Unlike existing datasets that only support single dance, our new dataset contains group dance videos as shown in Figure 1, hence supporting the study of group choreography. On the basis of the new dataset, we propose the first strong baseline for group dance generation that can jointly generate multiple dancing motions expressively and coherently.

Dataset Construction

Figure 2. The pipeline of making our AIOZ-GDANCE dataset.

In this section, we will elaborate and describe the process to build our dataset from a large variety of videos available on the internet. Because our main goal is to develop a large-scale dataset with in-the-wild videos, setting up a MoCap system as in many classical approaches is not feasible. However, manually creating 3D groundtruth for millions of frames from dancing videos is also an extremely costly and tedious job. To that end, we propose a semi-automatic labeling method with humans in the loop to obtain the 3D ground truth for our dataset. The process to construct the data includes the five following key steps:

  1. Video collection
  2. Human Tracking
  3. Human Pose Estimation
  4. Local Fitting for Invidual Motions
  5. Global Scene Optimization

Data Collection and Preprocessing

Figure 3. Human Tracking.

Video Collection. We collect the in-the-wild, public domain group dancing videos along with the music from Youtube, Tiktok, and Facebook. All group dance videos are processed at 1920 × 1080 resolution and 30FPS.

Human Tracking. We perform tracking for all humans in the videos using the state-of-the-art multi-object tracker [1] to obtain the tracking bounding boxes. Note that although the tracker can produce reasonable results, there are failure cases in some frames. Therefore, we manually correct the bounding box of the incorrect cases. This tracking correction is crucial since we want the trajectory of each person to be accurately tracked in order to reconstruct their motion in latter stages.

Pose Estimation. Given the bounding boxes of each person in the video, we leverage a state-of-the-art 2D pose estimation method [2] to generate the initial 2D poses for each person. In practice, there exist some inaccurately detected keypoints due to motion blur and partial occlusion. We manually fix the incorrect cases to obtain the 2D keypoints of each human bounding box.

Local Mesh Fitting

Figure 4. Local Mesh Fitting.

To construct 3D group dance motion, we first reconstruct the full body motion for each dancer by fitting the 3D mesh. We then jointly optimize all dancer motions to construct the globally-coherent group motion. Finally, we post-process and remove wrong cases from the optimization results.

We use SMPL model [3] to represent the 3D human. The SMPL model is a differentiable function that maps the pose parameters θ\mathbf{\theta}, the shape parameters β\mathbf{\beta}, and the root translation τ\mathbf{\tau} into a set of 3D human body mesh vertices VR6890×3\mathbf{V}\in \mathbb{R}^{6890\times3} and 3D joints XRJ×3\mathbf{X}\in \mathbb{R}^{J\times3}, where JJ is the number of body joints.

Our optimizing motion variables for each individual dancer consist of a sequence of SMPL joint angles {θt}t=1T\{\mathbf{\theta}_t\}_{t=1}^T, a sequence of the root translation {τt}t=1T\{\mathbf{\tau}_t\}_{t=1}^T, and a single SMPL shape parameter β\mathbf{\beta}. We fit the sequence of SMPL motion variables to the tracked 2D keypoints by extending SMPLify-X framework [4] across the whole video sequence:

Elocal=EJ+λθEθ+λβEβ+λSES+λFEFE_{\rm local} = E_{\rm J} + \lambda_{\theta}E_{\theta} + \lambda_{\beta} E_{\beta} + \lambda_{\rm S}E_{\rm S} + \lambda_{\rm F}E_{\rm F}


  • EJE_{\rm J} is the 2D reprojection term between the 2D keypoints and the 2D projection of the corresponding 3D poses.
  • EθE_{\theta} is the pose prior term from the latent space of the VPoser model [4] to encourage plausible human pose.
  • EβE_{\beta} is the shape prior term to regularize the body shape towards the mean shape of the SMPL body model.
  • ES=t=1T1θt+1θt2+j=1Jt=1T1Xj,t+1Xj,t2E_{\rm S} = \sum_{t=1}^{T-1}\Vert \mathbf{\theta}_{t+1} - \mathbf{\theta}_{t} \Vert^2 + \sum_{j=1}^J\sum_{t=1}^{T-1}\Vert \mathbf{X}_{j,t+1} - \mathbf{X}_{j,t} \Vert^2 is the smoothness term to encourage the temporal smoothness of the motion.
  • EF=t=1T1jFcj,tXj,t+1Xj,t2E_{\rm F} = \sum_{t=1}^{T-1} \sum_{j \in \mathcal{F}} c_{j,t}\Vert \mathbf{X}_{j,t+1} - \mathbf{X}_{j,t} \Vert^2 is to ensure feet joints to stay stationary when in contact (zero velocity). Where F\mathcal{F} is the set of feet joint indexes, cj,tc_{j,t} is the feet contact of joint jj at time tt.

Global Optimization

Figure 5. Global Optimization.

Given the 3D motion sequence of each dancer pp: {θtp,τtp}\{\mathbf{\theta}^p_t, \mathbf{\tau}^p_t\}, we further resolve the motion trajectory problems in group dance by solving the following objective:

Eglobal=EJ+λpenEpen+λregpEreg(p)+λdepp,p,tEdep(p,p,t)+λgcpEgc(p)E_{\rm global} = E_{\rm J} + \lambda_{\rm pen}E_{\rm pen} + \lambda_{\rm reg}\sum_{p}E_{\rm reg}(p) + \lambda_{\rm dep}\sum_{p,p',t}E_{\rm dep}(p,p',t) + \lambda_{\rm gc}\sum_{p}E_{\rm gc}(p)

EpenE_{\rm pen} is the Signed Distance Function penetration term to prevent the overlapping of reconstructed motions between dancers.

Ereg(p)=t=1Tθtpθ^tp2{E_{\rm reg}(p) =\sum_{t=1}^T\Vert \mathbf{\theta}^p_t - \hat{\mathbf{\theta}}^p_t\Vert^2} is the regularization term that prevents the motion from deviating too much from the prior optimized individual motion {θ^tp}\{\hat{\mathbf{\theta}}^p_t\} obtained by optimizing the local mesh for dancer pp.

In practice, we find that the relative depth ordering of dancers in the scene can be inconsistent due to the ambiguity of the 2D projection. To ensure the group motion quality, we watch the videos and manually provide the ordinal depth relation information of all dancers in the scene at each frame tt as follows:

rt(p,p)={1,if dancer p is closer than p1,if dancer p is farther than p0,if their depths are roughly equalr_t(p,p') = \begin{cases} 1, &\text{if dancer } p \text{ is closer than } p' \\ -1, &\text{if dancer } p \text{ is farther than } p' \\ 0, &\text{if their depths are roughly equal} \end{cases}

Given the relative depth information, we derive the depth relation term EdepE_{\rm dep}. This term encourages consistent ordinal depth relation between the motion trajectories of multiple dancers, especially when dancers partially occlude each other:

Edep(p,p,t)={log(1+exp(ztpztp)),rt(p,p)=1log(1+exp(ztp+ztp)),rt(p,p)=1(ztpztp)2,rt(p,p)=0E_{\rm dep}(p,p',t) = \begin{cases} \log(1+\exp(z^p_t - z^{p'}_t)), &r_t(p,p')=1 \\ \log(1+\exp(-z^p_t + z^{p'}_t)), &r_t(p,p')=-1 \\ (z^p_t - z^{p'}_t)^2, &r_t(p,p')=0 \\ \end{cases}

where ztpz^p_t is the depth component of the root translation τtp\mathbf{\tau}^p_t of the person pp at frame tt. Intuitively, for r(p,p)=1r(p,p')=1, zpz_p should be smaller than zpz_{p'} and otherwise.

Finally, we apply the global ground contact constraint EgcE_{\rm gc} to further ensure consistency between the motion of every person and the environment based on the ground contact information. This contact term is also needed to reduce the artifacts such as foot-skating, jittering, and penetration under the ground.

Egc(p)=t=1T1jFcj,tpXj,t+1pXj,tp2+cj,tp(Xj,tpf)n2E_{\rm gc}(p) = \sum_{t=1}^{T-1} \sum_{j \in \mathcal{F}} c^p_{j,t}\Vert \mathbf{X}^p_{j,t+1} - \mathbf{X}^p_{j,t} \Vert^2 + c^p_{j,t} \Vert (\mathbf{X}^p_{j,t} - \mathbf{f})^\top \mathbf{n}^* \Vert^2

where F\mathcal{F} is the set of feet joint indexes, n\mathbf{n}^* is the estimated plane normal and f\mathbf{f} is a 3D fixed point on the ground plane. The first term in Equation~\ref{eq_Egc} is the zero velocity constraint when the feet are in contact with the ground, while the second term encourages the feet position to stay near the ground when in contact. To obtain the ground plane parameters, we initialize the plane point f\mathbf{f} as the weighted median of all contact feet positions. The plane normal n\mathbf{n}^* is obtained by optimizing a robust Huber objective:

n=argminnXfeetH((Xfeetf)nn)+nn12,\mathbf{n}^* = \arg\min_{\mathbf{n}} \sum_{\mathbf{X}_{\rm feet}} \mathcal{H}\left((\mathbf{X}_{\rm feet} - \mathbf{f})^\top \frac{\mathbf{n}}{\Vert\mathbf{n}\Vert}\right) + \Vert \mathbf{n}^\top\mathbf{n} - 1 \Vert^2,

where H\mathcal{H} is the Huber loss function, Xfeet\mathbf{X}_{\rm feet} is the 3D feet positions of all dancers across the whole sequence that are labelled as in contact (i.e., cj,tp=1c^p_{j,t} = 1) .

How will AIOZ-GDANCE be useful to the community?

We bring up some interesting research directions that can be benefited from our dataset:

  • Group Dance Generation
  • Human Pose Tracking
  • Dance Education
  • Dance style transfer
  • Human behavior analysis

While single-person choreography is a hot research topic recently, group dance generation has not yet well investigated. We hope that the release of our dataset will foster more this research direction.


[1] Peize Sun, Jinkun Cao, Yi Jiang, Zehuan Yuan, Song Bai, Kris Kitani, and Ping Luo. Dancetrack: Multi-object tracking in uniform appearance and diverse motion. In CVPR, 2022

[2] Hao-Shu Fang, Shuqin Xie, Yu-Wing Tai, and Cewu Lu. RMPE: Regional multi-person pose estimation. In ICCV, 2017.

[3] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J. Black. SMPL: A skinned multiperson linear model. ACM Trans. Graphics, 2015

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