Phase-Separated Complex Hilbert PCA on Markerless 3D Pose Estimation Data: A Global Phase Network and Its Extension to a Continuous Field on the Body Surface
Authors: Hiromitsu Goto, Tao Tao, Zheng-Lin Chia
Organizations: Faculty of Information Engineering, Kanazawa Gakuin University, Kanazawa, Japan
Abstract
Quantitative analysis of the kinematic chain in sports motion is essential for performance evaluation and injury prevention. Conventional methods such as the kinematic-sequence (KS) and continuous relative phase (CRP) are confined to adjacent joint pairs and lack a unified framework for whole-body coordination, while segmental power-flow analysis requires force plates and inertial parameters that restrict it to laboratory environments. We apply Complex Hilbert Principal Component Analysis (CHPCA) separately to each motion phase (backswing and downswing) on markerless 3D pose estimation data, extracting the dominant whole-body phase pattern as a single complex eigenvector. The pipeline further includes a fully automatic signal-based phase segmentation (no priors on strike count or rest location) and an extension to 1,079 body-surface mesh vertices, so that the kinematic chain is represented as a continuous phase field across the body. On 14 hammer-striking trials of a single subject, the framework reveals (i) a trunk-anchored global phase architecture, (ii) a functional asymmetry between preparation and execution phases quantified by Mode-1 contribution (45.5% vs. 70.5%) and inter-trial Spearman consistency (0.38 vs. 0.58), and (iii) a consistent reorganisation across both skeletal joints and mesh vertices (p<10−10 on 1,079 vertices). As a methodological consistency check, pairwise phase differences from the Mode-1 eigenvector are compared against CRP on all 190 joint pairs by a permutation test (ρ=0.473, p=0.0005). A correspondence analysis between Mode-1 amplitude and kinetic-energy mobilisation variance further shows a strong positive correlation in the downswing (ρ≈0.71 on both skeleton and mesh) and no correlation in the backswing, indicating that the proposed framework bridges kinematic and kinetic descriptions of coordination through phase structure.
arly identification of motor impairment in infancy relies on expert visual assessment of spontaneous movement, motivating the development of automated, objective alternatives. One promising approach is using computer vision, which benefits from high quality pose estimation from video. In this study, we systematically evaluated three state-of-the-art pose estimation frameworks (MeTRAbs-ACAE, SAM 3D Body, and Sapiens) on 100 videos over 13 sessions of 8 infants recorded with a multi-view markerless motion capture system. We quantified keypoint detection accuracy using reprojection error, geometric consistency, and Procrustes-aligned 3D position error, and demonstrated proof-of-concept for fitting an inverse kinematic framework to infant data. While Sapiens achieved the lowest reprojection error and highest geometric consistency of the methods evaluated (22.8 pixels and 0.82, respectively), SAM 3D Body provided the most comprehensive 3D information for kinematic reconstruction with Procrustes-aligned position errors of 19 to 28 mm. We demonstrate in a case comparison example that biomechanical models fit to SAM 3D estimates distinguish representative movement patterns in infants related to motor development, as identified by a clinical expert. Together, these findings highlight both the promise and current limitations of 3D pose estimation for infant biomechanics and establish preliminary groundwork for scalable, video-based assessment of early motor development.
We introduce HYPERPOSE, a novel 3D human pose estimation framework that performs spatio-temporal reasoning entirely within the Lorentz model of hyperbolic space Hd to natively preserve the hierarchical tree topology of the human skeleton. Current state-of-the-art pose estimators aim to capture complex joint dynamics by relying on transformers and graph convolutional networks. Since these architectures operate exclusively in Euclidean space which fundamentally mismatches the inherent tree structure of the human body, these methods inevitably suffer from exponential volume distortion and struggle to maintain structural coherence. To this end, we depart from flat spaces and aim to improve geometric fidelity with Hyperbolic Kinematic Phase-Space Attention (HKPSA), natively embedding complex joint relationships without distortion, alongside a multi-scale windowed hyperbolic attention mechanism that efficiently models temporal dynamics in O(TW) complexity. Furthermore, to overcome the well-known instability of training non-Euclidean manifolds, HYPERPOSE introduces a novel Riemannian loss suite and an uncertainty-weighted curriculum, enforcing physical geodesic constraints like bone length and velocity consistency. Extensive evaluations on the Human3.6M and MPI-INF-3DHP datasets demonstrate that HYPERPOSE achieves state-of-the-art structural and temporal coherence, significantly reducing both volume distortion and velocity error, while establishing new state-of-the-art benchmarks in overall positional accuracy.
Recent progress in 3D human pose estimation has made markerless recovery of skeletal motion increasingly accurate and scalable. However, most pose estimators remain optimized for geometric keypoint accuracy, while many real-world applications in rehabilitation, sports science, ergonomics, and clinical movement analysis require biomechanical quantities that describe how the body moves, loads, and activates. In this work, we propose BioModule, a lightweight plug-in temporal transformer that attaches downstream of any 3D pose estimator and predicts biomechanical attributes from standard 17-joint 3D skeletons. BioModule is estimator-agnostic and requires no modification of the upstream pose model, enabling existing pose estimators to be extended toward physically interpretable motion analysis. To train and evaluate BioModule, we construct a large-scale aligned dataset pairing Human3.6M video and 3D keypoints with the biomechanical label space of Human3.6Mplus. We establish and verify anatomical correspondence between coordinate systems of the two datasets, enabling frame-accurate cross-modal supervision. Using this aligned supervision, BioModule predicts biomechanical quantities. We further benchmark BioModule across seven state-of-the-art 3D pose estimators, providing the first systematic analysis of how upstream pose estimation quality propagates to downstream biomechanical prediction fidelity. The results position BioModule as a compact, modular bridge between vision-based pose estimation and biomechanically meaningful human motion analysis.