QuaMo: Quaternion Motions for Vision-based 3D Human Kinematics Capture
Authors: Cuong Le
Pavlo Melnyk
Urs Waldmann
Mårten Wadenbäck
Bastian Wandt
Venue: ICLR 2026 Poster (2026)
Keywords: human
kinematics
quaternion
motion
vision
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Vision-based 3D human motion capture from videos remains a challenge in computer vision.
Traditional 3D pose estimation approaches often ignore the temporal consistency between frames, causing implausible and jittery motion.
The emerging field of kinematics-based 3D motion capture addresses these issues by estimating the temporal transitioning between poses instead.
A major drawback in current kinematics approaches is their reliance on Euler angles.
Despite their simplicity, Euler angles suffer from discontinuity that leads to unstable motion reconstructions, especially in online settings where trajectory refinement is unavailable.
Contrarily, quaternions have no discontinuity and can produce continuous transitions between poses.
In this paper, we propose QuaMo, a novel Quaternion Motions method using quaternion differential equations (QDE) for human kinematics capture.
We utilize the state-space model, an effective system for describing real-time kinematics estimations, with quaternion state and the QDE describing quaternion velocity.
The corresponding angular acceleration are computed from a meta-PD controller with a novel acceleration enhancement that adaptively regulates the control signals as the human quickly change to new pose.
Unlike previous work, our QDE is solved under the quaternion geometric constraints that results in more accurate estimations.
Experimental results show that our novel formulation of the QDE with acceleration enhancement accurately estimates 3D human kinematics with no discontinuity and minimal implausible artifact.
QuaMo outperforms comparable state-of-the-art methods on multiple datasets, namely Human3.6M, Fit3D, SportsPose and a subset of AIST.
The code is available at https://github.com/cuongle1206/QuaMo

Published as a conference paper at ICLR 2026
QUAMo: QUATERNION MOTIONS FOR VISION-BASHD 3D HUMAN KINEMATICS CAPTURE
Cuong Le', Pavlo Melnyk', Urs Waldmann', Märten Wadenbäck', Bastian Wandt
1 Linköping University, Sweden 2 Independent researcher cuong. 1e@1l111 dil
Imput image
Figure 1: We present QuaMo, novel online 3D human kinematics capture approach based Quaternion Motions (pink), modeled via a meta-PD algorithm with acceleration enhancement. Given vision-based 3D pose estimation prior, QuaMo predicts plausible and accurate motions.
ABSTRACT
Vision-based 3D human motion capture from videos remains challenge in puter vision. Traditional 3D pose estimation approaches often ignore the tem- poral consistency between frames, causing implausible and jittery motion. The emerging field of kinematics- based 3D motion capture addresses these issues by estimating the temporal transitioning between poses instead. major drawback in current kinematics approaches is their reliance on Euler angles. Despite their simplicity, Euler angles suffer from discontinuity that leads to unstable motion re- constructions, especially in online settings where trajectory refinement is unavail- able. Contrarily, quaternions have no discontinuity and can produce continuous transitions between poses. In this paper, propose QuaMo. novel Quater- nion Motions method using quaternion differential equations (QDE) for human kinematies capture. We utilize the state-space model, effective system for de- scribing real-time kinematics estimations, with quaternion state and the QDE de- scribing quaternion velocity. The corresponding angular acceleration is computed from a meta-PD controller with a novel acceleration enhancement that adaptively regulates the control signals as the human quickly changes to new pose. Unlike previous work, our QDE is solved under the quaternion unit-sphere constraint that results in more accurate estimations. Experimental results show that our novel formulation of the QDE with acceleration enhancement accurately estimates 3D human kinematics with no discontinuity and minimal implausibilities. QuaMo outperforms comparable ofthe-ofth methods multiple datasets, namely Human3.6MG Fit3D, SportsPose and AIST. The code is available at ?
INTRODUCTION
Monocular 3D human motion capture is a challenging problem in computer vision due to the loss of depth information and the complexity of body articulation. Traditional 3D human pose estimation (HPE) approaches, which directly estimate 3D joint positions or angles, achieve high accuracy
bastance-based evaluation metrics (Pavllo et al., 2019 Zheng et al., 2021 Kocabas et al., 2020: Sun
et al. 2023 Goel et al. 2023). However, when considering captured trajectory consecutive

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frames from video, 3D HPE often results in implausible artifacts such jittery unnatural poses. Addressing these challenges by introducing physics models (i.e., state-space model with velocity and acceleration) to enforce temporal consistency between consecutive poses is an emerging research direction, fusing vision-based predictions with human kinematic chains (Shimada et al. 2020) or volumetric models (Loper et al. 2015). Our proposed method, QuaMo, falls into this category.
The foundation of all kinematics-bast approaches is the nonlinear state-space model, where human poses and their corresponding velocities are computed from either meta-PD controllers with learn- able PD gains (Shimada et al. [2021] Li et al., 2022a Le et al. 2024a), physics simulation engines Gärtner et al., 2022b a). or neural networks (Rempe et al., (02T). Using state-
Yuan et al., 20rtnGrrt space modeling. the process of predicting the next human poses is equivalent to solving a time-series ordinary differential equation (ODE) (Chen et al., 2018). Our proposed method, QuaMo, serves as the function that takes the current human pose as input and predicts the corresponding velocity, giving an estimate for the next pose. We develop QuaMo as an online approach, only relying on the single time step input, making QuaMo applicable to real-time applications (autonomous driving
(Prisalu et al. 2020 Wang et al. 2024), or biomechanics (Bogert et al. 2013 Uhlrich et al. 2023
Current modern temporal-based approaches often opt for Euler angles Yuan et al. 2021 Rempe jet al. 2021 Li et al., 2022a) as the main joint orientation representation for human kinematics estimation. Despite their simplicity and intuitive interpretation, Euler angles have two well-known issues: singularities ka. gimbal lock) and discontinuities (at angles 0 and 2x) (Shoemake) 1985).
Discontinuities cause the joint incorrectly rotate backwards to the intended direction, resulting in highly unstable motion reconstructions. Quaternions are known to resolve the discontinuity problem by representing orientations with four-dimensional vector, but have not received proper studies within the field. To this end, we propose using quaternion joints for kinematics estimation, with their velocity computed from novel acceleration enhanced PD control. Unlike Euler angles, the quaternion derivative cannot be approximated by finite difference between respective elements due to rotational constraints (Kuipers) 1999) we use an operation based on the Hamilton product.
The underlying state-space model of QuaMo consists of joint orientation represented as a quater- nion and an angular velocity state, resulting two main parallel streams (Fig. 2 1) a quaternion first-order derivative calculation based on the Hamilton product between the current quaternion and the newly computed angular velocity, and 2) a meta-PD algorithm with newly developed accel- eration enhancement to estimate the rotational velocity derivative. Unlike prior work (Shimada ct al. |021| Le et al. 2024a), we apply the exact quaternion integration solution under unit sphere constraint, eliminating any approximation errors that arise when using the traditional Fuler integra- tion (a.k.a. first-order Runge-Kutta) method (Andrle & Crassidis) 2013). The novel acceleration enhancement term, computed based on the second-order quaternion difference between reference poses, adaptively compensates the signals of the PD algorithm for more accurate kinematics esti- mates. Specifically, the acceleration term increases the control signals when sudden pose changes occur (fast movement) and dampens the signals upon reaching the target poses. A demonstration of our proposed approach can be seen in Fig.
Our proposed approach is evaluated against current state-of thehe-r kinematics-basee methods on the Human3.66 6M (lonescu et al. 2014), Fit3D (Fieraru et al., (02T), SportsPose (Ingwersen et al., 2023). and a subset of AIST (Li et al.) 2021b) datasets. In summary, our main contributions are:
We propose a quaternion differential equation with quaternion as joint rotation for 3D human motion estimation, inherently overcoming the drawbacks of Euler angles.
We introduce a novel accelcration enhancement that adaptively regulates the angular accelcration based on quick movement changes for more accurate motion estimation.
We show that solving the QDE under the quaternion unit-sphere constraint 8 results in more plausible and accurate human poses in online real-time settings.
RELATED WORK
3D Human Pose Estimation. Traditionally, 3D human motion capture is addressed via 3D pose
estimations, either 1) lifting from 2D cues (Wang et al.
2019 Pavllo et al.
2019; Wandt & Rosen-
hahn 2019 Li et al. [2200] Xu et al. 22000] Wandt al. 2021
Zheng al.
2021 Zhao al. 2023
Peng et al. 2024: Cai et al. [2024] [Sn et al.) 20244) Lang & Chuah 2025 Huang et al. 2025 Kim
al. 2025)
2) directly estimating 31D human poses from input images (Pavlakos et al. 2017
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Kocabas et al. 2020 Li et al. 2021a 2022b You et al. 2023 Wang & Daniilide 2023 Kim al. 2023 Baradel et al. 2024; Dwivedi et al., 2024 Le et al., 2024b Patel & Black 2025 J. Despite the low average joint error. methods lifting from 2D do not consider the human body constraint, iee. bone-length consistency between consecutive 3D poses, thus cannot be compared to template- based approaches, and this argument has been raised by related work (Gärtner et al. 2022a Li al.) 2022a Zhang et al., (024). To impose natural body constraints, modern approaches utilize volu- metric human models such as SMPL (Loper et al. 2015) a prior and only estimate the angular poses for the models, fitting them to 2D and 3D observations (Pavlakos et al. (019)) Kanazawa et al., 2019 Mahmood et al., 2019 Zhu al., 2023). This line of research often overlooks the temporal consistency between consecutive estimated poses, leading to implausible artifacts such as jittery, foot-skating, and unnatural poses. In this work, we address these issues by employing a kinematics- based approach, taking into account the temporal consistency between consecutive 3D estimations.
3D Human Kinematics Capture Unlike 3D HPE, human kinematics approaches enforce temporal consistency to eliminate motion artifacts created by monocular estimation, either through pose pri- ors (Huang et al. 2022; Rempe et al.
202T). or physics laws and constraints (Shimada et al. 2020
Gärtner et al. 2022a Li al.
2022a Tripathi et al. 2023 Zhang et al. 2024).
Trajectory optimization is a popular approach for kinematics baaeed 3D human motion cap-
ture (Al Borno et al.) 2013 Shimada et al. 2020 Rempe et al. [220 Xie et al. 2021 Gärtner al.
2022b[a) a). These approaches commonly introduce kinematics constraints in the form of physics laws as their main optimization objective. This poses a challenge where the physical constraints are quired to be differentiable and the optimization is often done offline. Recent approaches extend the physics modeling with comprehensive contact estimations from modern physies engines Coumans & Bai (2016-2019) Todoroy et al. (2012). However, these contact models are non-differentiable motivating a subfield of motion imitation research that utilizes reinforcement learning with physics constraints in their reward designs (Yu et al. [202]] Yuan et al., 2021 Peng et al.) [2022] Yao et al.)
2022 Huang et al. 2022, Yuan et al., 2023 ) A major problem with trajectory optimization and
reinforcement learning is the limited adaptation to unseen motions.
Recently, learning 3D human kinematics from data has received more attention, thanks to its strong generalization capability. Rempe et al. (202I) use a conditional variational autoencoder to gener- ate the next human pose, implicitly treating the latent variables as motion kinematics. While the latent kinematics is learned, [Rempe et al. (2021) still require test time optimization process to refine their estimation. In contrast, leveraging tff-the-shelf monocular 3D HPE (Kocabas et al.] 2020 Li al., 2022b) the targets for motion reconstruction can alleviate the offline optimization while retaining robust and physically plausible kinematics estimation. [Zhang et all (2024) utilize a cansformer-based autoencoder that takes the full sequence of monocular 31) poses as inputs, pre- dicts the corresponding sequence while enforcing physics constraints in the latent space. To maintain the explicit temporal consistency between frame-wise predictions, (Shimada et al. (202T) introduces the usage of meta-PD controller for predicting the motion dynamics based on the 2D pose cues estimated from video. While the 3D kinematics capture works online, [Shiaaaa al. (20TT) still require a pre-filtering of 2D cues to ensure plausible 3D estimations. Li et al. (2022a) apply the PD controller with temporal convolutions and an attentively refined target pose from the full sequence for robust motion estimation. The key similarity between these approaches is the access to future monocular cues, preventing them from real-time deployments. Le et al. (2024a) address the imper- fection of online PD-based simulation by re-integrating the input poses into the final prediction via a learnable Kalman filter. However, re-introducing noisy kinematics has the potential to break the temporal consistency enforced by the integration scheme. Furthermore, one source of error for poor simulations is the usage of Euler angles that are prone to representation changes when enforcing temporal consistency frame-wise (Allgeuer & Behnke 2018 Yang 2019).
Our work contributes towards the online 3D human kinematics capture, using a meta-PD algorithm with the robust quaternions as the joint orientation representation. The kinematics estimation follow the correct Lie-group constrained calculation for quaternions, while additionally dampened by a novel second-order control compensation that results in smoother and more accurate motions.
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B
Linear
Accelorstion,
4r
Next
Output
states
states
QDE,
9t
Control Net
Linear, fu
2--2ar
da
fa + Fmonsitoon
0le+at
dcear
SMPL Leyer
ODE.
Keypoint regressor
fzuier
dleeat
Pttde
Linear
Metai
6i2
Figure 2: QuaMo consists of two differentiable equations: ODE for angular velocity and QDE for quaternion pose q. The updated Wt+-tt is computed via data-driven meta-PD controller with the additional adaptive signals from our novel second-order acceleration enhancement and Euler integration. Given Wi+Ai, the next human pose Qt+Ar is updated by solving the QDE with the Hamilton quaternion product. The human body mesh M4+ and the corresponding keypoints Ar are retrieved by applying a linear transformation with the SMPL skinned model from Pavlakos et al. 2019), taking the pose +++A and shape parameter /3 as inputs.
METHODOLOGY
3.1 OVERALL PIPELINE
We model human motion via state-space system. Given N joints in the human body, let E Rx4 be the human pose tensor consisting of joint relative rotations represented as N quaternions q H (the Hamilton set). The corresponding angular velocities are denoted as E TR3. We use the SMPI. body model from Loper al.) (2015) with N 24 body joints with the root rotation at the first entry. The discrete-time state-space model of the system with a sampling rate of At
fEutte (we, We, At) [SHamitoon (ft, ét, At] dr
w
[u. we) ulqe, we, 4t) + a: wr+tt)
(I)
where ée and W are the first-order derivatives of and w at time step which can also be referred as the quaternion velocity and angular acceleration; qt+ and w are the pose and angular velocity the next time step + At. The function f estimates the next-step angular velocity via Fuler integration. The function fHamilton estimates the next-step quaternion pose using Hamilton opera- tions. The angular acceleration W; is modeled via three functions: predicts the acceleration given the current states de and wy; 2) an external control signal to based on the meta-PD algorithm given the reference pose q from an off-the-shelf 3D pose estimator; and 3) novel acceleration enhancement term a computed from the last three reference poses Q-221:1- The quaternion velocity dt rotates the current pose (: to Qt+ At along the unit sphere S group of quaternion multiplication (Andrle & Crassidis) 2013). Fig. shows how we build our pipeline with these functions. The predicted pose 4++2r is used to control an SMPL model together with shape parameter B Io resulting in human mesh m++Ar E 1680003 We apply joint regressor to 17x3 i.e. the 17 keypoints from lonescu et al. (201)), or the
data-driven fa that directly
obtain the keypoint pose Pt-At E COCO 17 keypoints from Lin et al. (014)).
3.2 QUATERNION DIFFERENTIAL EQUATION
quaternion E IH is represented by (7o, Q Q2, (3) E Rd,, also written as:
go + qıi + 92d + qzk.
(2)
The sum of two quaternions p and g is obtained by summing their respective scalar coefficients: p + g = (po + %o) + (q) + Pı)e + (g2 + Pa)j + (gs + k.)k. The (Hamilton) product & of two quaternions is defined as p 2 q = (Pogo p q, Po q + qo p +
where i, j. and & are imaginary units satisfying 12 = 12
q), with the crucial non-commutative property p q + q ② The non-commutativity of the Hamilton product is key to unit quaternions, i.e. quaternions normalized to unit length, || = 1, being broadly used to represent 3D rotations, with other representations, e-g., gimbal lock and discontinuity avoidance.
number of advantages For a unit quaternion E S3, 9o = (as(a/2) is the scalar part and (g), 92, qa) = esin(a/2) is the vector part representing rotation about axis R by angle a.
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Quaternion derivative over time, is important concept in various fields including roboties, physics, and engineering (e.g., in spacecraft modeling]
& Nikolakopoulos (2013);
Golabek et al. ). Given the angular velocity (W1, (y) E F., the corresponding quaternion velocity is defined via the following quaternion differential equation (QDE):
i ー 9(w)
1
[
w 0
g,
where [w]x
w3
0
W3
0
W2
W1
(3)
2
42
W1
0
In this work, the QDE effectively describes the quaternion transitioning between 3D human poses without any representation discontinuity. Assuming constant angular velocity we during At, the quaternion pose solution to Eq. 3 at time step + At can be written as
At 4++ = exp (2) s((wtaas)) qi = qw X 9t.
(4)
A (())) is the rotation matrix, that rotates using wt. Equivalently, the next pose ft+ where exp( 2 can be obtained by the Hamilton product between 9.. the quaternion representation of the rotation matrix, and Compared to the integration approximation in prior work that violates the quaternion constraint of S (Supplementary E integration by Eq. and Eq. ensures an exact quaternion solution at all times, leading to more accurate estimations, as demonstrated via the ablation in Tab. 3
3.3 META-PD CONTROLLER WITH SECOND-ORDER ACCELERATION
The ordinary differential equation (ODE) that describes the motion acceleration Wi is written as Wh by + = @ (7- vec( @ T (5-22)))
Wi -Kp( (vee(cc @ 9i))
(5)
meta-PP algurithm
bias
acceleration cnhancement
where Kp R and KD R constitute the PD controller's proportional-derivativy gains, while RA E IR is the scaling factor of the newly introduced second-order acceleration. The control signals be, KP, KD. KA are predicted by a ControlNer via linear projections from the latent embedding. given We and q as inputs (Fig. ( Inspired by FFrsk & Nikolakopoulos (2013), the meta- PD controller is computed proportionally to the vector, i.e. imaginary, part of the quaternion error between ÿe and the complex conjugate of qt, qe. Due to the online setting considered in our work, the estimated ir is inherently noisy, especially when obtained from a direct regression method such as Sun et al. (2023). We suggest the derivative term KD Wi to dampen the predicted proportional control signal p vee & u/ ); effectively reducing overshooting and jittery. The data-driven be the estimation of fw approximated from the embedding of ControlNet, commonly referred as bias term in prior work (Shimada et al. 2020 Li ct al. 2022a).
The proposed acceleration enhancement term is the best guess of the person's 's intended target pose, computed from the second-orde -odder quaternion difference of the last three reference poses 4-22 re- sulting in the angular acceleration of the reference signal. This term, scaled by K.A. reacts adaptively to the rate of change in reference signals, i.e., it positively reinforces the controller when the refer- ence ; changes fast (quick movements to reach new target) and dampens the control signals the motion moves closer to the target. The adaptive nature of the acceleration enhancement helps the kinematics motion react quickly to the intended target, while maintaining minimal overshooting.
Global translation. We also compute the root translation F. with meta-PD and Euler integration (Li et al. 2022a). The calculation written as: rt+1r rt + (v2- + (xp(ft -rr) KDD 02 At) At. with i'; as the reference root position and 2 as the current root linear velocity. The global motion trajectory then obtained by adding the translation r, the body mesh m, or keypoints p; respectively. A stability analysis of global translation can be found in Supplementary
3.4 TRAINING OBJECTIVES
The total objective Lowil for capturing 3D human motion consists of three different loss terms, de- fined in Eq. 6 The first loss is the local reconstruction loss Liocat. which is the frame-wir wise LI distance between the predicted root-aligned 3D keypoint P; to the ground truth pf from the re- spective dataset. The same calculation applies the root translation rz- The second loss is the
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global consistency loss Cglobal, which is the average L1 distance between second-order finite differ- ences of the predicted motion P1:T and ground truth piT- The finite differences are computed as To:r = 20:r-2 2 2x1:T-1 + I2:T, with x being either or r. We additionally fine-tune the shape parameter B via a learnable fix- To prevent unrealistic body shapes, we introduce regularization Sax, ensuring the estimated body shapes do not deviate far from the average human shape (B = 0).
Liotal
Llocal + Gglabal + XLbeta
Lbeaa = 11
N Σ
Llocal
TN
1
GT POTT
Po:Tl +
T
1
D
GT o:
ro.T,,
(6)
T Σ
N
Lglohal
1 T
1 N
PO:T
Po.Tl
+
7
1
Σ
ICT io.T
4 EXPERIMENTS
4.1 DATASETS
We evaluate QuaMo on four established motion capture datasets. The main dataset in comparison with related methods is Human3.6M (Ionescu al. 2014). The dataset contains diverse human motion capture data from seven actors in a laboratory setup. Following prior work (Shimada et al., 2021 Yuan et al.) 2021, Le al. 2024a), data from the first five actors (S1, S5, S6, S7, S8) is used for training. while $9 and S11 are reserved for testing. For fair comparison,
suggested by Shimada al. (20TT), only actions that involve foot- foot-ground contacts are considered. To demonstrate the performance of our method on more diverse motions, we additionally evaluate on the Fit3D (Fieraru et al. (021) and SportsPose dataset (Ingwersen et al., 2023). The former contains complex exercise motions with laboratory setup similar to Human3.6M. 3... The latter comprises sport action videos taken with a mobile phone in different scene setups. We employ the training split from Le et al. (2024a) for evaluation. Lastly, following Gärtner al. (2022a), test QuaMo subset of AIST (Li et al. 2021b) (details in Supplementary consisting of dancing videos with pseudo ground-truths from 3D triangulation.
4.2 IMPLEMENTATION DETAILS
QuaMo is implemented as an online end-to-end approach as Fig. 2 At time step t, the system states qt, Wi and target pose q used inputs for the ControlNet, followed by heads for sp
and kp, one head for data-driven bias b, and one head for KA predictions of Eq. 5 The target
poses are initially extracted using TRACE (Sun al. 2023) and HMR2.0 (Goel al.) 2023). Following (Shimada et al., 2021 Gärtner et al.) 2022a
Le et al. 2024a), , the extracted motions
are down-sampled from 50Hz 25Hz, first frame prediction root-aligned to the world origin, and then split into sub-sequences of 100 frames for batch training. The estimated pose is in SMPL format and uses a mesh-based linear regression to obtain the keypoint predictions. In addition the NentrolNet, we create an InitNet for creating the initial states go. Wp and Bix. taking only the first two target poses タ0:1- I. and the first shape parameter 3n (from either TRACE or HMR2.0) as inputs. Please refer to Supplementary A for details about InitNet and ControlNet.
For all experiments, QuaMo is trained for a total 35 epochs with batch size of 64 and an initial learning rate of 5e with an exponential decay at epoch 20 and 30 by a factor of 10. The ControlNet consists of two fully connected layers with a hidden dimension of 512, followed by LayerNorm and LeakyReLU activation. To stabilize the training in the beginning, in the first epochs, the network parameters are updated per-frame with a learning rate of 1e while the global loss Lgtlbal is turned off. During training, the shape loss Leea is scaled by À 0.01. The time step Al = 0.04 corresponds to the down-sampled motion capture rate of 25Hz. All experiments are reported with error bars obtained by testing five different random seed values (0 4).
4.3 METRICS
We evaluate QuaMo on all of the datasets with two set of metrics: local and global. The local metrics consider the Mean Per Joint Position Error (MPJPE) (in mm) between root-aligned poses.

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Local metrics
Global metries
Method
Tmpl. Kin. Onl.
MPJPE
P-MPJPE Accel
G-MPJPE
GRE
G-Accel
FS
PoscAnchor
Kim
40.3
32.1
KTPFormer
Peng et dl.
2024
40.1
31.9
PoseMamba
[Tusnng
2025
37.1
31.5
Mambapose
Chuah
2025
36.5
28.6
HMMR
Kanuzawa
2019
79.4
55,0
231.1
VIBE
68.6
43.6
23.4
207.7
27.4
MAED
Wan of
2021
56.4
38.7
HMR Kanuzawa ot
2018
78.9
54.3
204.2
IPMAN-R Tripathi
2023
60.7
41.1
TRACE
2023
56.1
39,4
18.9
143.0
127.2
39.4
80.3
HybrIK
202
55.4
33.6
MeshPose et
2024b
35.4
HMR2.0
Cuel al
2023
46.7
30.7
9.1
97.2
86.8
16.8
11.5
PhysCap
Shimada at.
2020
/
65.1
182.6
TrajOpt
Garmerr et al
20226
84.0
56.0
143.0
4.0
DifiPhy
Güntner al.
2022
81.7
55.6
139.1
7.4
Xie al. 2021
V
68.1
85.1
PhysPT Zhang et
2024
52.7
36.7
335.7
DnD ai al 2022a)
52.5
35.5
525.3
NeurPhys Shimada et 2021
76.5
58.2
SimPoR Minnet
56.7
41.6
6.7
OSDCap at
54.8
39.8
8.4
132.8
119.1
16.0
15.2
QuaMo TRACE (Ours)
51.3++0.11
37.5 +0.05
4.7
116.2+1.4
101.4+127
7.8 6.64
QuaMo HMR2.0 (Ours)
46.04
30.6
5.3 +0,00
88.8
78.5+033
6.8 4.34
Table 1: Quantitative results the Human3.66 6M dataset (Ionescu al. 2014). Tmpl.: Template- based approach (i.e. SMPL-based). Kin.: kinematics-base approach. Onl.: online approach. Online methods work with only one future target pose at each time step. Bold highlights the best results within the kinematics category. The proposed QuaMo reaches state-of-the-ae performance on the MPJPE, P-MPJPE, G-MPJPE, and GRE with HMR2.0 the meta-PD controller target. On the motion plausibly metrics Accel, G-Accel, FS, we consistently record better results compared to other online kinematics- bassed approaches.
The MPJPE calculates the average frame-wise 1.2 distance between estimated human joint 3D co- ordinates and the ground truth data. The second metric, P-MPJPE, is MPJPE with rigid alignment between two poses. To evaluate the motion jitter, we consider the Accel metric (mm/ /fame") ) which measures the difference between the predicted joint acceleration and the ground truth. In addition, motion artifacts can only be observed a world coordinate with global translation (Gärtner et al., 2022a). The G-MPJPE computes MPJPE in global coordinates without root alignment. We also compute the Global Root Error (GRE), similar to MPJPE, but only on root translation. The global jitter G-Accel is computed similarly Accel without root alignment. Foot skating (FS) is measured as the percentage (%) of frames that contain foot movements more than 2cm during contact.
4.4 RESULTS
We report the quantitative evaluation results QuaMo in Tab. T with comparison five groups
of related study: 1) keypoint-baed approaches that lifted from 2D keypoints (Peng et al. 2024 Sun
al. 2024 Lang & Chuah, 2025) Huang al.] 2025 Kim et al. (025). 2) vision-based approaches
that utilize temporal information (Kanazawa et al.] | Kocabas et al. 2020 Wan et al. 2021 3)
single-or-two-framm prediction only (Kanazawa al. 2018 Tripathi et al. 2023 Li al. 202 la
Sun et al.] 2023 Goel et al.
large methods (Shimada 2022b Xie al. 202 and most related to work, 5) kinematies-
2023).
4) sisemattcc--based methods that base their prediction
window of frames (Li et al.
2022a Zhang et al. (2024) or
et al. 2020 Gärtner et al.
based online methods that only consider two frames as input (Shimada et al. 2021 Yuan et al,
2021 Le al. 2024a). The methods ranked with respect their performance on the MPJPF

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Data Method
MPJPE
P-MPJPE
Accel
G-MPJPE
GRE
G-Accel
FS
Fit3D
TRACE (Snn
2023
63.9
43.8
19.1
111.3
83.2
42.4
87.5
OSDCap [Le
58.7
42.6
8.2
73.8
47.2
12.8
25.9
QuaMo TRACE (Ours)
50.3
35.6:1004
3.8
68.8
45.2
5.61000
16.31022
Sports-
Pose
TRACE Sun et
2023
99.3
68.7
14.7
421.7
389.1
39.1
38.5
OSDCap Le al.
2024g
71.7
52.4
10.9
113.6
90.2
17.1
38.0
QuaMo _RACE (Ours)
71.4
48.7::021
1.3
1.2.2
82.3
13.7
24.1
TRACE (Sun et al.
2023
115.6
63.2
34.1
243.8
208.3
107.5
104.4
AIST
HUND Zandir et
2021
107.4
66.9
155.7
50.9
DitiPhy Gärtner
2022a
105.5
66.0
150.2
19.6
HMR2.0
GGol et al.
2023
101.9
60.2
24.4
154.3
110.5
40.7
56.0
QuaMo_ _MMR0 (Ours)
89.1
60.0
10.7=0.02
10.57
108.7=1.07
14.9=0.07
13.0=z0.46
Table 2: Quantitative results the Fit3D (Fieraru al. 202 (top), SportsPose (Ingwersen et al.
2023) (middle) and the AIST (Li et al. 202 (bottom) dataset. Compared to OSDCap (Le et al.,
2024a), QuaMo achieves a better performance on Fit3D and SportsPose, especially on the jittery metrics, using the same input TRACE. On AIST, with HMR2.0 as input, the proposed online QuaMo outperforms offline method, DiftPhy, both pose accuracy and motion jitter.
metric, within their respective category. Keypoint-based methods are only presented for referencing purposes and cannot be compared to template-basel methods.
The proposed Qua is evaluated using two different online approaches: TRACE (Sun et al. 2023)
and HMR2.0 (Goel et al. 2023) the references for the PD controller. TRACE (Sun et al. 2023
directly regresses the 3D SMPL pose from input images, resulting in noisy 3D estimation with an Accel of 18.9 and FS of 80.3%. Using QuaMo, we manage to improve not only Accel and FS, but also MPJPE by 8.6%, P-MPJPE by 5.1%, and G-MPJPE by 18.7%. While TRACE is used for a fair comparison competitors, we further improve the performance by using the newer HMR2.0 for the PD controller targets, which achieves state-of-the-at results on MPJPE, P-MPJPE, and G-MPJPE across all categories, while producing more plausible motions compared other online methods. The improvement compared to HMR2.0 on Accel is 41.8%, 59.5% on G-Accel, and 62.6% in FS.
Our direct competitor is OSDCap (Le al.) 2024a), which is also an online dynamics-based ap- proach. We outperform OSDCap on every metric. while using the same PD controller's s target as TRACE (Sun et al., 2023): notably, 6.3% on MPJPE, 32.1% on Accel, and 12.5% on G-MPJPE. OSDCap, despite achieving good state estimation through Kalman-filter approach, re-introduces implausibility from the inputs obtained by TRACE back to the final output. We, however, achieve much smoother and plausible motions by fully respecting the temporal relationship between con- secutive predictions from the integration scheme. DnD (Li et al. 2022a) and PhysPT (Zhang et al.) 2024]. despite having a competitive performance, take window of 16 frames input, while ours only takes one next frame as target. PhysPT (Zhang et al. 2024) achieves a smoother motion than our QuaMo; however, their motion is reconstructed from seq2seq transformer model (Vaswani et al., 2017]. without having an integration scheme to ensure temporal dependency between consecutive frame predictions. TrajOpt (Gärtner et al. (022b) has a better FS measurement due to their offline trajectory optimization approach with a global refinement, whereas QuaMo is fully online and still maintains competitive FS of 4.3% (compared to 4.0% of TrajOpt) with much lower MPJPE.
While the Human3.6N dataset serves as a baseline for benchmarking human pose estimation ap- proaches, the variability of motions in the dataset is limited. Therefore, we also conduct an evalua- tion on the Fit3D (Fieraru et al. (02T) and SportsPose (Ingwersen et al. 2023) datasets with more complex and more challenging sports movements, presented in Tab. 2 Similar to the results in Tab. [ we improve upon the input TRACE by a large margin and outperform OSDCap on all met- rics. Additionally, we follow DiffPhy (Gärtner et al. 2022a) and evaluate QuaMo on the same subset of the AIST database (Li et al. 2021b), shown in Tab. 2 Because the implementation of HUND (Zanfir et al. 2021), the target input of DiffPhy, is not publicly available, we use HMR2.0 as our PD target instead. QuaMo achieves better results on all accuracy and plausibility metrics. Some qual- itative results showing the advantage of QuaMo are presented in Fig. 3 Additional visualizations can be found in Supplementary B and videos our supplemental webpage.
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Agasm
procng
Figure 3: Qualitative results on three datasets: Fit3D (left), SportsPose (middle), AIST (right). QuaMo's predictions shown in blue, the input (from TRACE HMR2.0) in green, and ground truth keypoints red for reference. The start frame has lower transparency. The reconstructed motions from QuaMo have significantly lower jitter and higher accuracy along the optical axis.
Method
Rotation
fw S
MPJPE
P-MPJPE
Accel
G-MPJPE
G-Accel
FS
TRACE
Axis-angle
56.3
39.3
19.3
146.4
44,5
80.3
PD only
Euler XYZ
24.4
39.7.084
13.7
148.7 13371
15.4
17.3
PD only
Buler ZXY
71.2:12.17
41.1
7.6
143.9
9.3
19.7
PD only
Axis-angle
60.6=1.4m
39.0=m.14
6.4
137.8
8.2
17.2#t0.8
PD only
Quaternion
53.8
38.8=0.15
5.7:0007
132.6=3.22
7.9=0.94
19.5
QuaMo
Quaternion
53. 10.05
38.620.04
5.3
115.9:20.0
8.6=2.12
13.9
QuaMo Quaternion
52.0=0.07
38, 10005
5.2 +0.02
114.8 #
7.8 #0.09
10.6
QuaMo
Quaternion
51.0
3..4
5.940.02
114.7#1.01
8.4
10.0
Table 3: Ablation studies. The baseline uses only a PD controller (PD only), taking TRACE as targets. The fw: using the data-driven bias in Eq. 5 3 using the integration method from Eq. 3 and Eq. | a: using the acceleration enhancement term in Eq. [ The model configurations are ranked based on their MPJPE score, and the lowest MPJPE with a reasonable Accel is most desired.
4.5 ABLATION STUDIES
We conduct ablations in Tab. B verify the usage of our proposals: using the quaternion as joint representation, and using the quaternion S constraint for integration and the acceleration enhancement. To reduce computational load, all ablations are conducted on subset of Human3.6M taken from camera 60457274. Methods with lower MPJPE are more desirable. TRACE is chosen as the baseline and presented in the first row Tab. for comparisons.
Joint rotation. We first compare the common joint representations: Axis-angle, Euler ZXY, Euler XYZ, and quaternion (ours), in row 2 to 5 in Tab. 3 As described Sec. [ axis-angle and Euler angles suffer from discontinuities over all three angles, causing instability during integration. An example shown Fig 4 when the temporally consistent human reconstruction has to make a full 180-degree rotation when the root joint encounters discontinuity. This situation be easily avoided by using quaternions. The experimental result Euler angles in Tab. 3 shows that while having reasonable MPJPE, the Accel is significantly larger, due the constant compensation that the model has to produce to overcome the angle discontinuity. The axis-angle representation is more robust the discontinuity; however, the error between two axis-angles for the PD controller cannot be defined in physically meaningful way. We instead apply finite differences between each of the three components of the axis-angles separately as the error. As demonstrated with relevant metrics in Tab. it is more difficult to correctly capture the motions with axis-angles than with quaternions.
QuaMo's components. We gradually add the proposed solution the baseline with quaternion ro- tation. The data-driven fa, helps address the database-spedd specific offsets that ensure accurate estimation, especially the global translation with G-MPJPE decreases from 132.6 to 115.9 mm. The quaternion integration with the spherical constraint S reduces the error of the QDE solving process, leading to a decrement from 53.1 to 52.0 mm in MPJPE. The proposed acceleration enhancement term with its adaptive ability further improves the estimation accuracy, with an MPJPE decrease from 52.0 to 51.3 mm. A trade-off of the acceleration term is the motion jitter (Accel increases from 5.2 to 5.9) due to the noise amplification from the second-order differences of the input TRACE. Despite the jittery

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Published as a conference paper at ICLR 2026
Quaternion
Axis angle
Euler XYZ
Figure 4: An example of motion reconstruction when discontinuity occurs in the root joint rotation for different rotation representations. Blue means low and orange high MPJPE. The transparency corresponds to the time steps in the sequence. The model attempts to compensate for the disconti- nuity by rotating along the different rotation axes for representations, except our quaternions.
trade-off, our proposed method enables accurate estimations for real-time downstream applications.
The computational complexity of QuaMo is presented in Supplementary D
(2024a) such as the same batch size 64, learning rate 5e 4, hidden dimension 512, and the usage of LayerNorm
Besides the training hyper-parameter taken from previous work OSDCap Le al.
and LeakyReLU activations; we additionally provide an ablation study on the choice of shape loss scaling factor À in Tab Because the Accel between different À are similar, we choose À = 0.01 as our final selection due to the good trade-off off between the local MPJPE and the global G-MPJPE.
A
MPJPE
G-MPIPE
Accel
1.0
52.8
120.2
5.8
0.1
51.8
118.6
5.8
0.01
51.2
116.2
5.7
0.001
51.0
116.9
5.7
0.0
51.1
117.1
5.7
Table Ablation study on the shape loss scaling X. choose 0.01 as our final selection due to the good performance trade-off between the local MPJPE and the global G-MPIPE.
CONCLUSION
In this paper, we introduce QuaMo, novel online vision- based human kinematics capture method for recovering plausible human motions from cameras. Prior works often make use of Euler angles as the joint representation, which creates inaccurate solutions due to discontinuity during temporal integration. We propose the usage of the quaternion differential equation together with unit-sphere constrained solutions and acceleration enhancements for accurate and plausible 3D kinematics cap- ture. We evaluate QuaMo in comparison with related work and achieve state-of-the-an results on four datasets: Human3.6M 6M, Fit3D, SportsPose and AIST.
Limitation and future work. While human kinematics can be accurately estimated with QuaMo, the influence of the surrounding environment the velocity predictions has the potential to fur- ther improve the plausibility of the reconstructed motions. As natural extension, contacts and interactions of humans with external scenes will be investigated in future work.
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ACKNOWLEDGMENTS AND DISCLOSURE OF FUNDING
This research is supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by Knut and Alice Wallenberg Foundation. The computa- tional resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) C3SE, and by the Berzelius resource, provided by the Knut and Alice Wal- lenberg Foundation at the National Supercomputer Centre. U.W. acknowledges funding from the Connected Minds Program, supported by Canada First Research Excellence Fund, Grant #CFREF. 2022-00010.
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Reviews:
[{"review_id": "zd8ov1DWEj", "reviewer": "Reviewer_6eiP", "summary": "The paper targets the challenging problem of 3D human motion capture based on visual input. To address the problem of implausible and jittery motion due to the representation of Euler angles, the paper propose to use Quaternion motions instead and an effective system based on QDE  is utilized. The experiments on several benchmarks like Human3.6M, Fit3D, SportsPose and AIST validate the effectiveness of the proposed algorithm.", "questions": "Please address the questions raised in the weakness section. More specifically, please provide more comparisons in Table 1 to validate the effectiveness of the proposed algorithm against the state-of-the-art algorithms.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The paper targets the challenging problem of 3D human motion capture based on visual input, which is of great importance to the industry applications. \n\n* The idea of using quaternion differential equations for human kinematics capture is intersting. \n\n* It reports reasonable results on several benchmarks like Human3.6M, Fit3D, SportsPose and AIST.", "weaknesses": "* It should include the recent references published in the recent two years. Currently, there is no reference published in 2025.\n\n* For the experiments, there are several releated works which are not compared. For example, [R1] is referenced in the paper but not compared in Table 1. By checking the results report in [R1], it would have obviously better results compared with the prposed algorithm. Please involve more papers published in the recent two years (2024-2025) for comparisons. \n\n[R1] Jihua Peng, Yanghong Zhou, and PY Mok. Ktpformer: Kinematics and trajectory prior knowledge-\nenhanced transformer for 3d human pose estimation. In CVPR, pp. 1123–1132, 2024\n\n* In Section 4.2, there are several implementation details reported in the paper. As there are many hyper-parameters defined in the paper, is there possible to provide more ablations on the setting of these hyper-parameters?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4d0pHGq7qj", "reviewer": "Reviewer_BjYh", "summary": "The paper presents QuaMo, an online 3D human kinematics capture framework from monocular video. The method replaces Euler angles with a quaternion differential equation (QDE) under a unit-sphere constraint to avoid discontinuity and gimbal lock. It further combines a meta-PD controller with a second-order acceleration term to better handle fast motion changes. Experiments on four benchmarks (Human3.6M, Fit3D, SportsPose, AIST) indicate improved accuracy and smoother motion over several online kinematics baselines, with ablation results supporting each component.", "questions": "1. What is the training/inference time cost relative to Euler or axis-angle versions? Does the quaternion formulation require higher compute/latency?\n\n2. How does the method perform when reference poses are distorted or noisy? Any filtering or noise-robust adaptation tested?\n\n3. Could the approach be extended to longer-horizon online settings (multiple future poses) without sacrificing latency?\n\n4. Would the method benefit from incorporating environment contacts (as mentioned in future work) into the controller?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "Clear articulation of the discontinuity/gimbal lock problem and why Euler angles are problematic in online capture.\n\nCorrect quaternion-based formulation with integration respecting the unit-sphere constraint.\n\nAdaptive acceleration term adds responsiveness to the PD controller, helping in fast motion regimes.\n\nSolid empirical evaluation across multiple datasets, and thorough ablation on rotation representations and pipeline components.", "weaknesses": "Novelty: Quaternions for rotation representation are standard in robotics, graphics, and physics simulation. The specific QDE formulation and its integration here are sound, but not a fundamentally new concept.\n\nNo cost analysis: The paper doesn’t compare training/inference speed, memory usage, or computational overhead with Euler/axis-angle setups. The practical trade-off is unclear.\n\nInput dependency: Performance varies greatly depending on upstream reference pose quality (TRACE vs HMR2.0). There is no robustness study under noisy or degraded inputs.\n\nEvaluation scope: Benchmarks target relatively clean, single-person motions. Multi-person, occlusion-heavy, or contact-rich scenarios are not tested.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jYjsvk1Szf", "reviewer": "Reviewer_qvAF", "summary": "This paper proposes QuaMo, an online kinematics module that replaces Euler-angle dynamics with a quaternion differential equation (QDE) solved exactly on the unit sphere $S^3$, coupled with a meta-PD controller augmented by a second-order acceleration enhancement term. Given per-frame vision priors (e.g., TRACE, HMR2.0), QuaMo predicts angular velocities and integrates quaternions via the Hamilton product to reduce the motion jitter and produce temporally consistent motion from the monocular videos.", "questions": "- Given that the input $\\hat{q}_t$ is noisy and the acceleration enhancement term uses a second-order difference, it can inherently amplify high-frequency noise. How is noise propagation controlled? Is it handled by ControlNet by assigning an appropriate $\\kappa_A$ depending on the level of noise present in $\\hat{q}_t$?\n- Can the QuaMo method be applied to per-frame approaches that estimate MANO parameters, such as HaMeR [1]? If so, what modifications would be required to adapt the quaternion-based kinematic formulation to hand-specific articulations?\n\n[1] Pavlakos, Georgios, Dandan Shan, Ilija Radosavovic, Angjoo Kanazawa, David Fouhey, and Jitendra Malik. \"Reconstructing hands in 3d with transformers.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9826-9836. 2024.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- A key strength of QuaMo is its fully online state-space formulation, which does not rely on future observations, enabling real-time refinement of off-the-shelf 3D pose estimators through iterative updates of angular velocity and quaternion states.\n- Unlike integration approximation methods, which risk moving the estimated quaternion outside the unit sphere $S^3$ and therefore require normalization to mitigate this issue, this work uses the Hamilton product between the quaternion representation of the rotation matrix and the current $q_t$. This leads to more accurate estimations, since normalization in previous approaches turns the quaternion into a direction that does not correspond to the true rotation and distorts the trajectory.\n- The proposed acceleration enhancement $\\alpha$ is computed from the second-order quaternion difference of the last three reference poses. It boosts control only when the reference is changing quickly (i.e., during true fast movement) and dampens as the target is reached. This allows QuaMo to treat fast, intended motion and jitter differently.\n- For evaluation, the work reports both local and global metrics (MPJPE, P-MPJPE, Accel, global MPJPE/GRE, global jitter, and foot-skating) and provides error bars across random seeds. Evaluating the proposed QuaMo using TRACE and HMR2.0 as baselines, the results show that incorporating QuaMo significantly reduces acceleration errors. While the improvements in joint-based errors for HMR2.0 in camera coordinates are marginal, the method substantially decreases errors in the world coordinate system.", "weaknesses": "- As shown in table 3, although the proposed acceleration term $\\alpha$ enhances the joint-based errors, it increases the acceleration error. It would be useful to clarify when to disable/attenuate the term to prevent the rise of acceleration error.\n- Although the addition of Euler integration for root translation shows an improvement in GRE, it is a first-order numerical integration method, and I suspect that small errors could accumulate over time. A figure or analysis of translation error versus time would be useful.\n-  There are minor ambiguities in the writing. First, $f_\\omega$ is introduced as a function of $q_t$ and $\\omega_t$. Then, at line~240, the term $b_t$ is introduced as an approximation of $f_\\omega$, but $b_t$ is the output of the ControlNet, which receives additional inputs.\n- Minor writing issues:\n  - line 240 misses close parenthesis\n  - line 236 has redundant comma after imaginary\n  - line 290 mentions $\\kappa_I$ of Eq. 5 that does not exist.\n  - In table 1 and 2, Foot skating is mentioned as FS while in table 3 FK is used.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)