An Elastic Shape Variational Autoencoder for Skeleton Pose Trajectories
Authors: Arafat Rahman, Shashwat Kumar, Laura E. Barnes, Anuj Srivastava
Organizations: Systems and Information Engineering, University of Virginia, Charlottesville, VA, USA · Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA · Dept. of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA
Abstract
Deep generative models provide flexible frameworks for modeling complex, structured data such as images, videos, 3D objects, and texts. However, when applied to sequences of human skeletons, standard variational autoencoders (VAEs) often allocate substantial capacity to nuisance factors-such as camera orientation, subject scale, viewpoint, and execution speed-rather than the intrinsic geometry of shapes and their motion. We propose the Elastic Shape - Variational Autoencoder (ES-VAE), a geometry-aware generative model for skeletal trajectories that leverages the transported square-root velocity field (TSRVF) representation on Kendall's shape manifold. This representation inherently removes rigid translations, rotations, and global scaling of shapes, and temporal rate variability of sequences, isolating the underlying shape dynamics. The ES-VAE encoder maps skeletal sequences to a low-dimensional latent space incorporating the Riemannian logarithm map, while the decoder reconstructs sequences using the corresponding exponential map. We demonstrate the effectiveness of ES-VAE on two datasets. First, we analyze skeletal gait cycles to predict clinical mobility scores and classify subjects into healthy and post-stroke groups. Second, we evaluate action recognition on the NTU RGB+D dataset. Across both settings, ES-VAE consistently outperforms standard VAEs and a range of sequence modeling baselines, including temporal convolutional networks, transformers, and graph convolutional networks. More broadly, ES-VAE provides a principled framework for learning generative models of longitudinal data on pose shape manifolds, offering improved latent representation and downstream performance compared to existing deep learning approaches.
Visual AutoRegressive Modeling (VAR) has excelled in natural image generation via next-scale prediction, but its use on topology-structured data like human skeletons is still unexplored. VARPose is proposed to adaptively densify 2D sparse poses, thereby enriching the anatomical information available for 3D lifting models. Our core contributions are twofold. First, we introduce a Granularity-agnostic Pose Tokenizer (GPT), which employs a single hybrid codebook and a residual quantization strategy to encode poses of varying densities into a unified, multi-scale discrete representation. Our results demonstrate the strong generalizability of this representation. By decoupling the representation from the projection, we can successfully decode novel pose granularities using a frozen codebook with a retrained decoder. Second, we propose UniSkelar, a unified autoregressive model that treats "joint density" as "scale". UniSkelar learns to predict the token sequence for the next density level in a coarse-to-fine manner, conditioned on the sparsest pose. VARPose not only outperforms state-of-the-art methods and generalizes to unseen granularities, but also confers tangible performance gains on downstream tasks, such as 3D Pose Estimation and Human Mesh Recovery, through 2D pose densification. Our code and model are available at https://github.com/BRL-SYSU/VARPose.git.
Despite their ubiquity, variational autoencoders (VAEs) inherently suffer from posterior collapse, a failure mode in which latent variables are effectively ignored. This failure arises because explicit prior imposition drives optimization toward loss landscape regions corresponding to uninformative latent representations. Here, we introduce Entropic Autoencoders (EAEs), a framework in which reconstruction loss is the only explicit objective, and entropy generates the latent variables' prior implicitly through a free energy-minimizing ensemble of encoders. This ensemble biases learning toward high-volume regions of near-optimal solutions, while decoder updates direct the search trajectories toward informative latent representations. We demonstrate that EAEs mitigate posterior collapse by learning non-Gaussian, multimodal latent distributions that yield diverse, data-consistent generations and preserve different forms of underlying structure in the data. As a proof-of-concept, we show that an EAE captures a superposition of the known low-dimensional dynamics of a reaction-diffusion process. Then, we show that an EAE identifies implicit categorical distinctions in MNIST latent representations, and displays a hierarchical understanding of facial structure on the CelebA dataset, from an "all-human" face to individual-dependent features.
Learning natural body motion remains challenging due to the strong coupling between spatial geometry and temporal dynamics. Embedding motion in phase manifolds, latent spaces that capture local periodicity, has proven effective for motion prediction; however, existing approaches are tied to fixed skeletons and narrow motion distributions, limiting their applicability across diverse settings. We introduce FunPhase, a functional periodic autoencoder that learns a phase manifold for motion and replaces discrete temporal decoding with a function-space formulation, enabling smooth trajectories that can be sampled at arbitrary temporal resolutions. FunPhase unifies motion prediction and generation within a single interpretable phase manifold, enabling motion generation via latent diffusion, generalizes across skeletons and datasets, and supports downstream tasks such as motion super-resolution and partial-body completion. Our model achieves substantially lower reconstruction error than prior periodic autoencoder baselines, achieving uniform improvements of at least 45% across all metrics, while enabling a broader range of applications and performing on par with state-of-the-art motion generation methods.