Title: Accurate and Steady Inertial Pose Estimation through Sequence Structure Learning and Modulation
Venue: NeurIPS 2024
Accepted: yes
Keywords: Inertial Measurement Units (IMUs)

Pose Estimation

Transformer
Abstract: Transformer models excel at capturing long-range dependencies in sequential data, but lack explicit mechanisms to leverage structural patterns inherent in fixed-length input sequences. 
In this paper, we propose a novel sequence structure learning and modulation approach that endows Transformers with the ability to model and utilize such fixed-sequence structural properties for improved performance on inertial pose estimation tasks.
Specifically, our method introduces a Sequence Structure Module (SSM) that utilizes structural information of fixed-length inertial sensor readings to adjust the input features of transformers.
Such structural information can either be acquired by learning or specified based on users' prior knowledge.
To justify the prospect of our approach, we show that i) injecting spatial structural information of IMUs/joints learned from data improves accuracy, while ii) injecting temporal structural information based on smooth priors reduces jitter (i.e., improves steadiness), in a spatial-temporal transformer solution for inertial pose estimation.
Extensive experiments across multiple benchmark datasets demonstrate the superiority of our approach against state-of-the-art methods and has the potential to advance the design of the transformer architecture for fixed-length sequences.

Accurate and Steady Inertial Pose Estimation through Sequence Structure Learning and Modulation

Abstract

Transformer models excel at capturing long-range dependencies in sequential data, but lack explicit mechanisms to leverage structural patterns inherent in fixed-length input sequences. In this paper, we propose a novel sequence structure learning and modulation approach that endows Transformers with the ability to model and utilize such fixed-sequence structural properties for improved performance on inertial pose estimation tasks. Specifically, our method introduces a Sequence Structure Module (SSM) that utilizes structural information of fixed-length inertial sensor readings to adjust the input features of transformers. Such structural information can either be acquired by learning or specified based on users' prior knowledge. To justify the prospect of our approach, we show that i) injecting spatial structural information of IMUs/joints learned from data improves accuracy, while ii) injecting temporal structural information based on smooth priors reduces jitter (i.e., improves steadiness), in a spatial-temporal transformer solution for inertial pose estimation. Extensive experiments across multiple benchmark datasets demonstrate the superiority of our approach against state-of-the-art methods and has the potential to advance the design of the transformer architecture for fixed-length sequences.

1 Introduction

Estimating human pose is a long-standing and prominent task that underlies many computer vision and graphics applications, e.g., animation production, virtual reality. As an alternative to vision-based solutions, wearable device-based methods are gaining increasing interest as they are environmentfree, occlusion-unaware, privacy-friendly. For ensuring high accuracy and maintaining portability and usability, most prior works [18, 55, 56, 20, 60] abandon densely placed configurations, instead leveraging a sparse set of Inertial Measurement Units (IMUs) to reconstruct human motion. Since IMUs can provide continuous measurements of rotation and acceleration, we define pose estimation with sparse inertial sensors as a sequence learning task.

Recently, Transformer-based architectures have achieved tremendous success in various sequence learning tasks, and applying them to sparse inertial motion capture is a natural idea. However, empirically, we find that, directly using the native transformer to model IMU sequences results in unacceptable jitter and inaccurate postures. Through our analysis, we attribute this to the native Transformer architecture, whose self-attention mechanism was originally designed to flexibly handle variable-length sequence inputs, thus lacks inductive bias for modeling fixed-length sequences that have clear structures . For instance, for an IMUs reading sequence, the length is usually fixed (e.g., the number of observed past frames in a time window or the number of IMUs) and each token in the sequence has a specific meaning (e.g., each temporal token denotes a frame and each spatial token

represents an IMU). In other words, as a representative type of fixed-length sequences, IMU readings have clear structures both in spatial and temporal dimensions. However, such structural information is not explicitly modeled in native Transformers.

To bridge this gap, we present an innovative approach for learning and modulating sequence structure, which empowers transformers to effectively capture and leverage structural properties of fixed-length sequences, leading to enhanced performance in inertial pose estimation tasks. Specifically, our method introduces a novel Sequence Structure Module (SSM) designed to leverage the structural information of fixed-length sequences to adjust the input features of Transformers. For inertial pose estimation tasks, we devised two SSM variants: SSM-S and SSM-T, for injecting spatial and temporal structural information into spatial and temporal transformer features, respectively. Extensive experiments on four public benchmarks demonstrate that our method achieves superior performances than state-of-the-art methods, where the average errors of the whole-body angles decreased by 13% and 38%, together with the lowest jitter, on the DIP-IMU [18] and TotalCapture [46] datasets, respectively. In addition, we implemented a real-time pose estimation system to test the performance of our approach in real-world scenarios. In summary, our contributions include:

We identify a key limitation of the native transformer architecture: its lack of inductive biases for modeling fixed-length sequences with inherent structural properties. To address this shortcoming, we propose a novel Sequence Structure Module (SSM) that enables transformers to effectively capture and leverage the structural priors present in fixed-length sequential data.

For inertial motion capture tasks involving sequential IMU data, we propose two SSM variants: SSM-S and SSM-T, which incorporate structural inductive biases of the IMU sensor layout (spatial) and time frames (temporal), respectively, into transformer learning.

Extensive experiments demonstrate that our method outperforms state-of-the-art ones on the DIP-IMU and TotalCapture datasets by a large margin. To further demonstrate the superiority of our approach, we implemented a real-time motion capture system based on six IMUs to evaluate the performance of our model in complex real-world scenarios .

2 Related Works

2.1 Human Pose Estimation

Human pose estimation (HPE) has been a long-standing research topic, with numerous researchers exploring it using various types of sensors. As our research lies on IMU sensors, we roughly categorize sensors into two types: non-IMU and IMU.

HPE with non-IMU Sensors . In non-IMU human motion capture solutions, vision-based methods still dominate the mainstream so far. Early methods [14, 23, 16, 42] used multiple cameras and marker points to capture human poses, which imposed significant constraints on the environment. With the popularity of deep learning, an increasing number of methods are using a single camera to capture human 2D/3D poses, such as CPN [8], HRNet [44] and others [62, 22, 54, 51, 61, 45, 39, 28, 67, 58, 25], achieving significant success. In addition, there are also other types of sensors used for tracking human motion, such as 6DOF trackers [43, 5, 13, 19, 63], flexible fabric sensors [7, 26, 68], wireless sensors [6, 53] and hybrid sensors [3, 35, 38]. Although each method has its own advantages, motion capture systems based on IMUs are emerging and gaining prominence, due to their wearability, portability, and ease of use.

HPE with IMU Sensors . The advantage of inertial motion capture systems compared to vision-based methods is their resistance to extreme conditions such as bright lights and occlusion. Commercial systems like Xsens [41] and Noitom [36] place multiple IMUs on the user's body, while achieving accurate pose estimation, also restricting the user's movements and requiring lots of time for IMU attachment. To enhance user comfort and usability, an increasing number of studies [48, 18, 56, 55, 20, 60] are shifting towards sparse inertial motion capture and predict human postures using only a few IMUs. As a pioneering work in sparse inertial pose prediction, SIP [48] demonstrates that recovering full-body motion using only 6 IMUs is feasible for the first time, but it is an optimizationbased approach which is computationally slow. Huang et al. [18], the first to introduce neural networks into this task, employ a bidirectional RNN to achieve real-time performance. After that, Transpose [56] proposes a multi-stage pose estimation framework, utilizing three sub-networks based on bidirectional RNN to predict pose, further enhancing accuracy. However, both of [18, 56] require future frames as input, which adds additional latency. PIP [55], introduces physical constraints, improving the physical plausibility of motion without the need for future frames. Another work, TIP [20], utilizes Transformer to predict human body poses while simultaneously generating terrain, achieving prediction of human motion in non-planar environments. Contemporaneous work, DynaIP [60], leverages pseudo-velocity learning to fully utilize acceleration and models the human body into three separate regions, each focusing on their unique characteristics. In addition, some studies [34, 69] have attempted to place IMUs in objects carried by the body for tracking human motion. For example, Zuo et al. [69] use a loose-wear jacket with 4 IMUs to capture the upper body motion, which provide the users with high comfort and freedom of movement.

However, existing methods only focus on modeling the temporal dimension (whether using RNNs or Transformers) while neglecting the spatial dimension. Unlike them, we utilize a two-stage Transformer-based spatial-temporal framework, independently capturing the dependencies of both space and time. Meanwhile, we have also designed two modules, SSM-S and SSM-T, enabling the Transformer to more effectively leverage structural information from fixed-length sequences.

2.2 Transformer Variants for Time Series

Transformer has seen a number of modifications to address the limitations of well-known works such as BERT [11] and ViT [12]. In the field of time-series data modeling, researchers have proposed various approaches, one common method being modifications in positional encoding [24, 59, 27, 64, 50, 65]. For example, Transformer-XL [10] introduced relative positional encoding, enabling the model to capture long-range dependencies, TCN-Transformer [2] combines the characteristics of convolutional networks with relative positional encoding. Self-attention module is the central part of Transformer. However, for many long-sequence based tasks, the time complexity of selfattention module is a computational bottleneck. Various works [31, 64, 65, 49, 4, 52] are proposed to address this issue. Longformer [4] employs a sparse attention mechanism, specifying local and global attention, allowing the model to handle long sequences while maintaining computational efficiency. Linformer [49] approximates the original high-dimensional attention matrix through low-rank projection, reducing both computational and memory requirements. Additionally, some researchers made structural modifications [52, 10, 64, 21] to Transformer for time series tasks. For example, Transformer-XL [10] incorporates a segment-level recurrence mechanism in the encoder to handle longer contextual information. Reformer [21] utilizes locality-sensitive hashing (LSH) and a reversible network structure, enabling the model to process extremely long sequences. Informer [64] introduces ProbSparse Self-Attention, reducing the computational complexity of self-attention.

Previous studies have modified the Transformer extensively, but they have largely overlooked its limitations in modeling fixed-length sequences and does not impose Transformer to explicitly utilize the inherent structural information within it. Our work bridges this gap.

3 Method

3.1 Why is Sequence Structure Modeling Missing in Native Transformer Architecture?

The Transformer architecture [47] was originally designed to accomplish machine translation tasks in natural language processing. To handle variable-length textual inputs with different syntaxes, the native Transformer architecture does not make any inductive bias on their structures, but instead focuses on the content of the input text. Specifically, let X ∈ R N × d be the embedded input sequence of length N and feature dimension d , the self-attention mechanism is defined as:

where Q = XW Q , K = XW K and V = XW V ∈ R N × d ; W Q , W K , and W V ∈ R d × d ; α ∈ R N × N . Among them, only the attention matrix α is modeling the relationships among the N input tokens. However, its element α ( i,j ) is calculated as the product between the i -th query ( Q ) and the j -th key ( K ) pair, thus representing the relationship between individual tokens rather than the structure of the input sequence as a whole. This enables it to handle sequences with different N that do not share a common structure (e.g., sentences).

However, in many other domains (e.g., pose estimation), the input sequences usually have fixed length (e.g., the number of observed past frames or body joints) and a clear structure (e.g., temporal continuity or spatial relationship), which implies that the structural information of input sequences can facilitate learning. Motivated by this key insight, we propose a novel Sequence Structure Module (SSM) to endow the Transformer architecture with the ability to model and utilize the structural information inherent in fixed-length input sequences.

3.2 Sequence Structure Module

Our Sequence Structure Module ( SSM ) aims to fully utilize the structured information of fixedlength sequence inputs to compensate for the lack of inductive bias in the transformer architecture. Specifically, as shown in Fig. 2 (d), given a sequence embedding X ∈ R N × d , before entering the transformer encoder, we multiply X with a structural matrix S ∈ R N × N , followed by a LayerNorm (LN) layer [1] and a MLP Block:

where ˜ X ∈ R N × d , LN( · ) is used to regularize the model and maintain gradient stability during training and MLP( · ) is used to increase the capacity of the module. The key distinction between the structural matrix S and the self-attention matrix α is that the elements of S are independent of the input X , making S universally applicable to all input sequences regardless of their content. This allows S to effectively capture structural information. Then, we feed the structure-enhanced ˜ X into the subsequent transformer encoder for modeling the long-range dependencies using Eq. (1). The structural matrix S can be obtained in various ways. For example, it can come from prior knowledge in the specific domains, be entirely data-driven through learning, or be a combination of the two. Here, we categorize the structure into the following three types: Explicit Structure S E , Implicit Structure S I , and Explicit-Implicit Hybrid Structure S EI .

Explicit Structure (ES) is particularly useful when each token in the input sequence of a fixed length N has a clear meaning (e.g., each token in a time sequence represents a frame), and the structural relationships between the N tokens can be precisely captured based on prior knowledge. That is, each element S E ( i, j ) in the structural matrix is provided by the user before training, allowing the user to impose prior knowledge of the sequence structure on learning. Notably, when S E is the identity matrix I , no modifications are made and the sequence structure module degenerates. We provide two examples of how to construct explicit structures S E in Sec. 3.4.

Implicit Structure (IS) becomes appropriate when the meaning of each token in the sequence and/or the structural relationships between tokens are unclear. Unlike ES , which are completely determined

IMU Measurement

Matrix

1. Explicit

Temporal Encoder

pose

Multiplication

MLP

2. Implicit

Spatial Encoder

TE

LayerNorm

3. Hybrid

SSM-T

pose

TE

SE

Nxd

pose

↑

NxN

Nxd

TE

SE

SSM-S

Input

Structural

Sequence

Matrix

X

S

(a)

(q)

(c)

(d)

by the user, the establishment of IS relies on a learnable matrix P , that is learned in a data-driven manner. We define the implicit structure matrix S I using the following equation:

where I, P ∈ R N × N and I denotes the identity matrix. Notably, another way to define S I is to solely use P without the identity matrix I , namely S I = P . But as pointed out in [17], in the extreme situation, it is easier to optimize P into a zero matrix rather than an identity matrix.

Explicit-Implicit Hybrid Structure (EIHS) aims to strike a balance between ES and IS by allowing the user to provide an initial structure matrix based on prior knowledge, while also using data-driven methods to modify it. It can also be referred to as a non-identity matrix initialization of Eq. (3):

where S E ∈ R N × N represents the explicit structure, and P ∈ R N × N is a learnable matrix. In the extreme case, when the user-designed explicit structure S E = I , EIHS degenerates into IS .

3.3 SSM for Transformer-based Sparse Inertial Pose Estimation

Problem Formulation . Our task is to accomplish real-time human pose estimation using data acquired from 6 inertial sensors positioned on the wrists of both hands, ankles of both feet, waist, and head (Fig. 1). Each IMU can provide sequential acceleration A and orientation R signals on the body part it is placed on, where A ∈ R 3 is the linear acceleration and R∈ R 3 × 3 is the rotation matrix. Our goal is to learn a mapping f which reconstructs the joints' rotations of the full body:

where T denotes the number of observed frames from the past, J denotes the number of predicted joints, N denotes the number of IMUs, and O ∈ SO (3) is the rotation of body joints, representing the human pose with a certain skeleton (e.g. SMPL [29]).

Spatial-Temporal Transformer with SSM . To accomplish this task, unlike previous works that only employed temporal encoders (Fig. 2 (a)), we utilize a spatial-temporal framework transformer network as our baseline model (Fig. 2 (b)), where the spatial transformer models the local motion correlations among N IMUs/joints within a frame, while the temporal transformer captures the global dependencies between T frames throughout the entire sequence. Since the values of N and T are typically fixed, (e.g. N = 6 and T = 30 ), we introduce two variants of Sequence Structure Module, SSM-S and SSM-T , to leverage the structural information of fixed sequences in spatial and temporal dimensions, respectively (Fig. 2 (c)). As previously mentioned, each SSM has three different choices for the structure matrix S . After thorough experimental comparisons in Sec 4.4, our final choice is that, the structural matrix of SSM-S is derived from EIHS , and the structure of SSM-T is ES . Due to page limitations, we have included more network details in Appendix Sec. 7.

3.4 Constructing Explicit Structures

The power of SSM lies in its large design space of explicit structures S E . Here, we take the sparse inertial pose estimation task as an example, to demonstrate how to construct S E in spatial and temporal dimensions based on prior knowledge.

1.0

0

L_hand

1.0000

0.4920

0.04570.0528-0.02660.0503

0.8

R_hand

0.4920

1.00000.04220.0338-0.04430.0408

0.610

10

10

L_leg

0.04570.0422

1.0000

0.5437-0.0544-0.0473

0.4

R_leg

0.0528 0.0338

0.5437

1.0000-0.0194-0.0411

0.220

20

20

Head

0.0

Root

L_hand R_hand L_leg

SE-S

R_leg

Head

Root

0

SE-r(o = 30)

10

20

SE-r(o = 15)

10

20

SE-T(o =1)

10

20

Spatial Structure Construction . The motivation for constructing the spatial structure S E -S is to explore relevance and consistency between body joints when the human body moves. 'Relevance and consistency' refer to the tendency for certain joints to exhibit similar movement patterns across a large sample of human motions. For instance, when the left hand moves forward, the head, torso, and legs are likely to move in a certain coordinated manner.

We utilize a statistical approach to accomplish this task. Specifically, we utilize the AMASS [32] dataset to decompose the rotations of different joints in each frame into rotations along the x -axis, y -axis, and z -axis, representing the rotations in terms of Euler angles. By doing so, we obtain R x , R y , R z ∈ R J × f , where f denotes the number of observed frames and J denotes the number of joints. We select subsets ( sub ) of the rotations consisting of the N joints where IMUs are placed (e.g., N = 6 ) and have: R ( x,sub ) , R ( y,sub ) , R ( z,sub ) ∈ R N × f . We independently calculate the correlation matrix C k ∈ R N × N , k = x, y, z for each subset and sum up the results for average to obtain the spatial explicit structure S E -S ∈ R N × N :

where cov denotes the covariance between two variables, and var denotes the variance of a variable. The resulting S E -S is shown in Fig. 3. It can be observed that, the movements between the two hands and the two legs exhibit high correlation; but the movements of the head and the root (spine) are relatively independent; which aligns with our intuition.

Temporal Structure Construction . Unlike the use of statistical methods to calculate spatial explicit structures S E -S , the construction of temporal explicit structures S E -T is much more straightforward, which follows the 'distance' between two frames within a time sequence. That is, when two frames are 'close' enough, such as adjacent frames, their correlation is relatively high; when the frames are 'farther apart', such as the first and last frames in a sequence, their correlation tends to decrease as the 'distance' increases; akin to a smoothness prior. Mathematically, we define S E -T ∈ R T × T using a function that linearly decreases with increasing 'distance':

where σ is a hyperparameter, which represents the maximum 'distance' between two frames that are considered correlated. Specifically, when the 'distance' between i -th and j -th frame, namely | i -j | ≥ σ , we consider these two frames to be unrelated. Fig. 3 shows the visualization of S E -T

under different values of σ . In our experimental setup, T = 30 and σ = 10 . For details on how to determine σ , please refer to Sec. 4.4.

Notably, in addition to the two methods mentioned above, there are many ways to construct explicit structures. In fact, any matrix with a specific meaning can serve as an explicit structure. While we have presented two illustrative examples, the ongoing quest to design tailored SSM explicit structures for diverse tasks offers boundless opportunities for exploration and innovation.

4 Experiments

4.1 Datasets and Evaluation Metrics

Datasets. Weuse the following datasets in our experiments, which can be divided into three categories: 1) Synthetic dataset: AMASS [32]. 2) Real datasets with SMPL [29] skeleton: DIP-IMU [18] and TotalCapture [46]. 3) Real datasets with Xsens [41] skeleton: AnDy [33], CIP [37], and Emokine [9]. We use them to train and evaluate our methods as follows: 1) Following [56, 55, 20], we first pre-train our model on AMASS and fine-tune it on the training set of DIP-IMU, then test it on the test set of DIP-IMU and the entire TotalCapture dataset; 2) Following [60], we train our model on the training sets of AnDy, CIP, and Emokine datasets and test it on the test sets of AnDy and CIP datasets.

Evaluation Metrics. We use the following metrics to evaluate our method: 1) SIP error , measuring the mean global rotation error of upper arms and upper legs in degrees; 2) Angular error , measuring the mean global rotation error of all body joints in degrees; 3) Positional error , measuring the mean Euclidean distance error of all estimated joints in centimeters with the root joint (Spine) aligned; 4) Mesh error , measuring the mean Euclidean distance error of all vertices of the estimated body mesh with the root joint (Spine) aligned. The vertex coordinates are calculated by applying the pose parameters to the SMPL [29] body model; 5) Jitter , measuring the mean jerk (time derivative of acceleration) of all body joints in the global space, which reflects the smoothness of the motion [15].

4.2 Implementation Details

We implement our method using the PyTorch [40] framework on one NVIDIA GeForce RTX 4090 GPU. PyTorch version is 2.0.0, and CUDA version is 11.8. During the training stage, we use the AdamW [30] optimizer to train our model with a batch size of 4096. The learning rate is initialized to 0.0001 and decayed by 0.99 per epoch. We implement the live demo using a laptop equipped with an Intel® Core™ i9-13900HX Processor CPU and an NVIDIA GeForce RTX 4060 GPU.

4.3 Comparisons with SOTA

Quantitative Results. We compare our method with state-of-the-art ones, including TransPose [56], TIP [20], PIP [55], DynaIP [60], which also accomplish pose estimation from only 6 IMUs signals. All metrics are calculated in the real-time setting and the best and runner-up results in each column are marked in bold and underline respectively.

As shown in Table 1 and Table 2, the results indicate that our method has surpassed previous approaches by a significant margin on both four benchmark datasets, achieving more accurate and steadier pose estimation. Specifically, our SIP Err on four datasets is significantly ahead of other

methods, outperforming the runner-up by 44%, 44%, 49% and 29% respectively. We attribute this to our spatio-temporal framework and the spatial structure information in SSM-S, which help the model better capture the motion correlation between body joints. Besides, on the DIP-IMU and TotalCapture datasets, our predicted motion sequences exhibit the least jitter (i.e., smoothest motion sequence). We attribute this to the temporal sequence structure information in our SSM-T, which provides more temporal prior knowledge between frames and smooths the input features to generate more stable and consistent motion prediction results.

Qualitative Results. We also provide a visual comparison between the estimated pose and the ground truth on the TotalCapture dataset. Compared with state-of-the-art methods, our method achieves more precise predictions as shown in Fig. 4. The comparison of the two actions (leaning forward and bending over) indicates that, our method can estimate the positions of arms and legs more accurately than previous methods. Additionally, the comparison of the two ambiguous actions (raising a leg and raising both hands) in the second row shows that our model better identifies these ambiguous actions.

TIP

PIP

DynaIP

Ours

Ground Truth

ARTRR

Analysis for Error of Joints . As shown in Fig. 5, we also compare the angular errors of individual joints on the DIP-IMU and TotalCapture datasets. It can be observed that, the errors of previous methods are mostly concentrated in the joints of the hands (L/R elbows and shoulders) and legs (L/R hips and knees), which are the main sources of SIP Err . We believe this is because they only capture the inter-frames dependencies in the temporal dimension, while neglecting to model the motion correlations between body joints in the spatial dimension. Unlike them, we utilize a two-stage spatial-temporal framework, where the spatial encoder independently models the motion consistency of IMUs/joints within a frame, and SSM-S injects spatial structural information into the features. Their combined effect allows for more accurate estimation of each joint rotation.

4.4 Ablation Study

We conduct ablation experiments on the TotalCapture dataset, reporting two metrics: Ang Err and Jitter . Additionally, we observe a trade-off between Ang Err and Jitter , challenging the simultaneous achievement of the lowest values for both. For convenience, we introduce a temporary metric τ = ( Ang Err ) ∗ Exp ( Jitter ) as a reference for selecting the optimal model, where a lower τ represents the balance between accuracy and stability, with Exp ( · ) denoting exponential operation.

Error ofDifferent Joints onDIP-IMU

Error ofDifferentJointsonTotalCapture

20.0

Ours

Ours

16

PIP

PIP

17.5

TIP

14

TIP

15.0

12

AugularError

AugularError

12.5

10

10.0

8

7.5

6

5.0

4

2.5

2

0.0

llar

N

R

Collar

Head

Elbow

R

Elbow

R

Collar

Head

LElbow

RElbow

Design of Sequence Structure for SSM-S and SSM-T . We first explore the designs of sequence structure in SSM-S and SSM-T. As previously mentioned, each SSM can have three different choices, resulting in a total of 3 × 3 = 9 combinations for the two SSMs. To simplify this, we first fix the type of SSM-S as IS and explore the best structure type for SSM-T. As shown in Tab. 4, comparing Settings 1, 2, and 3 demonstrates that ES is the best structure choice for SSM-T, as the other two structures result in unacceptable jitter. Based on this, we conduct experiments with Settings 4 and 6. By comparing Settings 2, 4, and 6, we find that EIHS is the best choice for SSM-S, as it significantly reduces angular error without substantially increasing jitter (i.e., with lower τ ). Thus, we conclude that, EIHS + ES is the best combination for SSM-S and SSM-T.

Further Exploration for S E -T . Fig. 3 shows the visualization of S E -T under different choices of σ , and Tab. 5 shows their performance on TotalCapture dataset. It can be observed that the model achieves the best performance when σ = 10 . We hypothesize that this means the information from the adjacent 10 frames should be given more emphasis for IMU measurements in our case.

Contribution of Each Component . We conduct a thorough ablation study when σ = 10 , to investigate the respective contributions of SSM-S and SSM-T. We use the most basic spatial-temporal framework (Fig. 2 (b)) as the baseline model and sequentially add SSM-S and SSM-T. The results are shown in Tab. 3. It can be observed that the primary function of SSM-S is to reduce joint angle error to improve the accuracy of human pose prediction, while the role of SSM-T is to reduce jitter to enhance the coherence of the posture and generate steadier motion sequence.

In-depth analysis of SSM-S . To look deeper into SSM-S, we visualized the spatial structure matrix S E -S (before training), the learnable matrix P S and the final spatial structure matrix S EI -S as shown in Fig. 6. It can be observed that:

The overall pattern of the structure matrix remain the same before and after training ( S E -S and S EI -S ), i.e., the movements between the two hands and the two legs still exhibit high correlation; and the movements of the head and the root (spine) are still negatively correlated. This demonstrates the effectiveness of our S E -S as initialization/prior.

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L_leg

0.0457

0.0422

1.0000

0.5437

-0.0544-0.0473

L_leg

-0.0166-0.0152-0.0666-0.2017

0.0057

0.0196

L_leg

0.0291

0.0270

0.9334

0.3420

-0.0487-0.0277

0.4

0.4

0.4

R_leg

0.0528 0.0338

0.5437

1.0000

-0.0194-0.0411

R_leg

0.0203-0.0124-0.1986-0.0694-0.0040 0.0189

R_leg

0.0326

0.0214

0.3451

0.9306

-0.0234-0.0222

0.2

0.2

0.2

Head

-0.0266-0.0443-0.0544-0.0194

1.0000

-0.1919

Head

0.0089

0.01490.0041 -0.0034 0.0313

0.0598

Head

-0.0177 -0.0294-0.0503-0.0228

1.0313

-0.1321

0.0

0.0

0.0

Root

0.0503 0.0408-0.0473-0.0411-0.1919

1.0000

Root

0.0115 -0.0088 0.0277 0.0312 0.0543

0.0437

Root

0.0387 0.0320 -0.0196 -0.0098-0.1376

1.0437

R_ieg

Head

Root

L_hand R_hand Lieg

R_ieg

Head

Root

L_hand R_hand Lieg

R_ieg

Head

Root

SE-s (Before Training)

Ps (Learnable Matrix)

The learnable matrix P S adds small offsets to the spatial structure matrix, i.e., slightly suppresses the correlation between two hands, two legs and head vs. root. We attribute this to the different motion distributions among datasets: i) in AMASS, daily actions (e.g., walking, jogging, running, sitting and stretching) are dominant, and the movements of both hands and legs show extremely high consistency; ii) in the DIP-IMU, although daily actions are also the majority, there are a large number of single-hand and single-leg movements, such as single-hand raising, grasping and swinging; single-leg lifting, etc., which weaken the movement consistency of both hands and legs; iii) in the Andy and CIP, there are numerous industry-oriented activities, which are very different from daily movements, resulting in a relatively large adjustment range of the learnable matrix P S . This demonstrates the effectiveness of our P S in adapting the structure matrix to different datasets, and maintains a high generalization ability.

4.5 Live Demo

We have implemented a real-time pose estimation visualization system using Python and Unity. We select a variety of actions to evaluate the performance of our model in real-world scenarios. These include everyday actions like walking, sitting, kicking, stretching, sports and more. Additionally, we choose some challenging movements such as single-leg standing, rolling, Chinese Kung Fu and dance movements to assess the generalization ability of our model. Through the live demo, it can be observed that even under intense physical activity, our approach still maintains long-term stability and shows robust generalization capability. Please refer to the supplementary video for our demo.

5 Conclusion

In this paper, we propose a novel sequence structure learning and modulation approach that empowers Transformers with the ability to model and utilize fixed-length sequence structural information. We present a simple yet effective Sequence Structure Module (SSM) to accomplish this, achieving impressive performance in sparse inertial pose estimation tasks. This showcases the powerful potential of the SSM to generalize to other Transformer-based fixed-length sequence tasks.

6 Acknowledgments

This work is supported by National Natural Science Foundation of China (62072383, 61702433), the Public Technology Service Platform Project of Xiamen City (No.3502Z20231043), Xiaomi Young Talents Program/Xiaomi Foundation, the Fundamental Research Funds for the Central Universities. This work is also partially supported by Royal Society (IEC\NSFC \211022).

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Appendix

7 Detailed Network Architecture

IMU

LinearEmbedding

Joint

Measurement

Rotation

RegressionHead

Spatial

Temporal

Position

Tokens

Tokens

Embedding

Temporal Transformer Encoder x L

2

TemporalPosition

pose

Embedding

SSM-T

TE

SpatialTransformerEncoder

XL

SSM-T

InDetail

1

SE

Spatial Position

SSM-S

Embedding

1

SSM-S

(c)

As shown in Fig. 7, our network mainly consists of Linear Embedding, SSM-S, Spatial Transformer Encoder, SSM-T, Temporal Transformer Encoder and Regression Head Module. In the main text, we introduce SSM-S and SSM-T. Here, we provide an introduction to the remaining parts.

Linear Embedding . Our network takes M∈ R T × N × 12 , the measurements from N IMUs over the past T frames as input. Firstly, we linearly map each IMU measurement m ( i,j ) ∈ R 12 into an embedding vector z ( i,j ) ∈ R D by means of a learnable matrix E ∈ R 12 × D :

After that, the input M∈ R T × N × 12 becomes F s ∈ R T × N × D . The spatial feature F s is fed into SSM-S to inject spatial structure, and the resulting ˜ F s is then send into the Spatial Transformer Encoder to model the motion correlation between body joints.

Spatial Transformer Encoder . Given ˜ F s , we first add a learnable spatial position embedding P s ∈ R N × D to each token for maintaining spatial position information. The resulting joint sequence of features z s are fed into a spatial encoder consisting of a sequence of L transformer layers. Each layer ℓ comprises of Multi-Head Self-Attention [47], LayerNorm [1], and MLP blocks:

The output of the last transformer layer is z L s ∈ R T × N × D , which is sent into SSM-T where temporal structural information is incorporated.

Temporal Transformer Encoder . We treat the output of SSM-T, ˜ F t ∈ R T × N × D , as the input of temporal transformer encoder, to further extract the global dependencies across frames in the entire sequence. We first reshape ˜ F t into ˜ F t ∈ R T × ( N · D ) . Before the temporal transformer encoder, we add a learnable temporal positional embedding P t ∈ R T × ( N · D ) to retain frame position information. The resulting frame sequence of features z t are fed into a temporal encoder, which has the same architecture as the spatial transformer encoder. The procedure can be formulated as:

The output of the last transformer layer is z L t ∈ R T × ( N · D ) , a compact spatial-temporal feature representation, which is sent into regression head module.

Regression Head Module. We map z L t into the whole body joint rotations ˆ O ∈ R T × J × 6 using Layer Normalization [1] and MLP block:

where J denotes the number of joints and 6 denotes 6D rotation representation [66]. The whole network is optimized by minimizing the Mean Squared Error (MSE) between ˆ O and the ground-truth O as:

During the training stage, we compute the loss using the predictions ˆ O and ground-truth O of T frames. During the inference stage, we only utilize the last frame as the output.

8 Additional Experiments

Result of Another Definition for S E -T .

10

10

10

10

20

20

20

20

10

20

10

20

10

20

10

20

( = 10)

(α = 10)*

(α = 20)

( = 20)*

We further explore an alternative definition of S E -T :

Differing from Eq. (8), in Eq. (18), σ has been replaced by T . We compare the cases with σ = 10 and σ = 20 to the previous scenario, denoted as ∗ . The visualization for S E -T are shown in Fig. 8 and the performance on TotalCapture dataset is shown in Tab. 6. It is easily discernible that the definition of Eq. (8) is significantly superior to that of Eq. (18), both in terms of accuracy and stability.

Ablation Study of the Order of SE/TE .

We provide the results of switching the order from "SE-TE" to "TE-SE" as Tab. 7. The results show that our "SE-TE" order outperforms its "TE-SE" variant by a large margin, which is consistent with the common practice in many spatio-temporal frameworks.

Generalization of Module under More Sensors .

Although we focused on the more challenging "sparse" settings (6 IMUs) in our paper, showing additional results of applying our modules to more sensors could further demonstrate their generalization ability. Specifically, we increase the number of IMUs from 6 to 10 (with the additional 4 IMUs placed on the left and right shoulders and thighs), and conduct experiments and ablation studies on the DIP-IMU dataset.

As shown in Tab. 8, after adding 4 IMUs, our proposed method still works effectively (higher accuracy and lower jitter). Additionally, the ablation study results show that the roles of SSM-S and SSM-T remain consistent with their performance when using 6 IMUs. That is, SSM-S improves the accuracy of motion prediction, while SSM-T reduces jitter to enhance the coherence of the posture. Based on the above experimental results, it can be concluded that our proposed method maintains strong generalization ability as the number of sensors increases.

Performance on Different Users with Different Physiques . To study the performance on different users with different physiques, we conduct experiments on DIP-IMU dataset. To demonstrate this more clearly, we computed the BMI values (BMI = Mass(kg) / Height 2 (m)) for each individual, categorize them into three groups, and report our model's performance across these three categories as Tab. 10:

The experimental results demonstrate that our method is robust and performs well across users with different physiques. For reference, we also include the results for each individual as Tab. 10.

More Comparisons with Other NN Structures . As shown in Tab. 11, we construct a spatio-temporal framework using GCN layers as the spatial encoder and Conv1d layers as the temporal encoder. The results show that our method significantly outperforms the GCN + Conv1d implementation.

9 Discussion

The Design of τ . In our experiments, we observed that it is difficult for Ang Err and Jitter to simultaneously reach their minima, forming a trade-off in-between. For example, in Tab. 6, with

σ = 20 , Ang Err is 7.76 and Jitter is 0.07; with σ = 10 , Ang Err decreases to 6.82 while Jitter increases to 0.09. To strike a balance in this trade-off, we introduce τ = ( AngErr ) ∗ Exp( Jitter ) to combine Ang Err and Jitter into a single measure. The reason for using Exp is that we have observed that the impact of the Jitter on viewing experience is non-linear:

When Jitter is relatively high (e.g., jitter > 0 . 3 ), the visual quality is unacceptable.

When Jitter is relatively low (e.g., 0 < jitter < 0 . 2 ), the visual experience is good and insensitive to changes in Jitter .

Therefore, we use Exp to measure the impact of Jitter on the viewing experience.

10 Limitation

Lack of Global Translation . Although our method has made significant progress in predicting human pose from sparse inertial sensor data, it lacks global tracking of human motion trajectories. We believe that relying solely on IMU for accurate global translation prediction is challenging, as IMUs may drift, resulting in unreliable measurements of acceleration. Combining other types of sensors with IMUs is a promising solution.

The Construction for Explicit Structure . As mentioned earlier, any matrix can serve as an explicit structure S E . Weprovide two examples demonstrating how to construct an explicit structure solely for illustrative purposes. Constructing S E more effectively for specific tasks requires further exploration.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the human pose estimation task with signals of 6 IMUs on the body. Because there are spatial correspondence in multiple IMUs across the body and temporal correspondence in the signal, this paper proposes to model the spatial relation of the 6 devices and the temporal relation in the signal by using learnable weight matrix. The weight matrix is initialized by distribution in the dataset and the transformer model first model the spatial info and then the temporal info. The proposed model achieves the SOTA accuracy compared to previous methods.\n\nSTRENGTHS:\n* This paper identifies a key character of IMU signals, the structural relation in the spatial and temporal dimensions, especially between devices.\n* The experiment accuracy is clearly better than previous methods.\n* This paper is well written and the structure is clear.\n\nWEAKNESSES:\n1. The authors attribute the performance increment to 1) spatio-temporal framework 2) SSM-S 3) SSM-T, but they only conduct ablation studies for 2) and 3). From table 3, we can see that the 1) as the baseline already outperforms all the previous methods significantly. The readers may expect more analysis and ablation experiments on the reason why 1) already achieves the SOTA accuracy.\n\n2. Figure 3 shows that there is an obvious relationship between the left and right hands and the left and right legs. This data distribution is specific to particular datasets. Although good results have been achieved with the current datasets, if such a distribution pattern does not exist in a new dataset, using the same parameters to model multiple devices may not yield good results.\n\nQUESTIONS:\nFigure 3 and 7 show the explicitly-set weight matrix which show obvious patterns in spatial and temporal dimensions. Do you observe any explainable patterns in the learned weight matrix (EIHS)?\n\nLIMITATIONS:\nThis paper has listed some limitations and there is no obvious negative societal impact of their work.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-06-26"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors study the inertial pose estimation problem and propose to add Sequence Structure Modules (SSM) to the spatial-temporal transformer architecture. The proposed SSM carries prior structural information of both spatial and temporal domain, and is shown to outperform multiple baselines and a plain spatial-temporal transformer.\n\nSTRENGTHS:\n1. The proposed method achieves significant improvement compared to the baselines across multiple datasets.\n\nWEAKNESSES:\n1. Though the proposed method achieves great performance, it is unclear why the proposed SSM structure works. The proposed SSM modules are essentially heuristically designed attention modules. Self-attention modules should be able to learn those structural patterns as well.\n\n2. The motivation for this approach is to add inductive bias to the original transformer structure. However, this paper lacks comparisons with other NN structures that contain such inductive bias by their design. For example, one could use GNNs as the spatial encoder and CNNs as the temporal encoder.\n\n3. The novelty of this paper is somewhat limited.\n\nQUESTIONS:\n1. It is not clear whether the spatial structural information calculated by (6) and (7) really works. According to setting 4 in Table 4, using ES for SSM-S does not show significant improvement. The best performance is achieved with EIHS for SSM-S (setting 5). However, since it contains learnable parameters, the final attention matrix might look very different from the pre-computed $E_{E-S}$ shown in Figure 3. Maybe it is better to show the learned spatial matrix in the paper as well.\n\n2. It is also not clear how the SSM-T module works. The authors mention that the aim of the SSM-T module is to enforce a high correlation between adjacent frames. However, since SSM-T is only applied to the inputs of the temporal encoder, it is not guaranteed that such constraint still exists within the temporal encoder. It would be great if the authors could provide some more explanations.\n\nLIMITATIONS:\nTthe authors have addressed the limitations", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nExisting transformers have shown great promise in modeling temporal data. However, in the field of inertial pose estimation from inertial measurement units (IMUs),\nthe lengths of time series are often fixed. This is a property that transformers can take advantage of. Thus, this paper proposes a Sequence Structure Module \nthat explicitly accounts for fixed-length input but also factors in the spatial dependencies of the IMUs worn at various body placements. \n\nThis paper deals with an emerging paradigm for inertial pose estimation that relies on IMUs instead of video. The experiments showed \nthat the proposed architecture can improve the task performance on several metrics including rotation errors, distance errors and motion smoothness.\n\nSTRENGTHS:\n1. This paper improves IMU-based inertial pose estimation with fewer sensors, which is preferable in their real world applications \n2. The Sequence Structure Module trick is well-motivated. The authors identified the unique aspects of inertial post estimation: (1) fix-length input sequence (2) spatially rich. The proposed module can incorporate the spatial and temporal structure within the data with different priors and optimisation techniques. \n3. The demo provided was much appreciated. The pose estimation seems to be realistic and better than other benchmark techniques.\n\nWEAKNESSES:\n1. Given that the proposed sequence structure module could work with data of fixed lengths with rich spatial information, I am curious how this module could also be applied with more or sensors that either make the structural correlation stronger or weaker. It will help to understand the generasibility of the proposed module.\n2. In your evaluations, how did you tune other models?\n3. Your SSM-T for temporal dependency modelling seems to be very effective in bringing down the jitter from 0.48->0.09 with pre-defined structure. Are there cases where SSM-T will benefit from training at all? If not, maybe there is no need for SSM-T after all but some sort weighted averaging with neighbouring timestamps?\n\nQUESTIONS:\n1. Can you show a few examples of what your structure matrices look like before and after training? It will help understand what has changed.\n2. How will your model perform on different users with different physiques? In your demo, most users have similar body shapes?\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel sequence structure learning and modulation approach that endows Transformers with the ability to model and utilize such fixed-sequence structural properties for improved performance on inertial pose estimation tasks. Specifically, this paper introduces a Sequence Structure Module (SSM) that utilizes structural information of fixed-length inertial sensor readings to adjust the input features of transformers. Further, this paper proposes two SSM variants: SSM-S and SSM-T. These variants incorporate the structural inductive biases of the IMU sensor layout (spatial) and time frames (temporal) into transformer learning.\nExtensive experiments across multiple benchmark datasets demonstrate the superiority of the approach against state-of-the-art methods and has the potential to advance the design of the transformer architecture for fixed-length sequences.\n\nI have read the responses of the authors and the comments of other reviewers, I would keep my original score.\n\nSTRENGTHS:\n1. This paper identifies a key limitation of the native transformer architecture: its lack of inductivebiases for modeling fixed-length sequences with inherent structural properties. To address this shortcoming, we propose a novel Sequence Structure Module (SSM) that enables transformers to effectively capture and leverage the structural priors present in fixed-length  sequential data.\n2. For inertial motion capture tasks involving sequential IMU data, we propose two SSM variants: SSM-S and SSM-T, which incorporate structural inductive biases of the IMU sensor layout (spatial) and time frames (temporal), respectively, into transformer learning.\n3. Extensive experiments demonstrate that the method outperforms state-of-the-art ones on the DIP-IMU and TotalCapture datasets by a large margin. To further demonstrate the superiority of the approach, this paper implemented a real-time motion capture system based on six IMUs to evaluate the performance of the model in complex real-world scenarios.\n\nWEAKNESSES:\n1. In the field of pose estimation, integrating spatio-temporal information is not new. Please explain the innovation and difference of the method in this paper compared with previous methods. \n2. The claim regarding the limitations of the Transformer architecture in handling fixed-length input sequences and the extent of these limitations is not sufficiently supported by evidence or theory.\n3. The number of comparison methods in the experiments is insufficient.\n\nQUESTIONS:\n1. In the field of pose estimation, integrating spatio-temporal information is not new. Please explain the innovation and difference of the method in this paper compared with previous methods. \n2. In the model structure design, whether the order of encoders such as SE\\TE will affect the model performance.\n\nLIMITATIONS:\nThis paper has no obvious negative social impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-11"}