3D human motion prediction is a challenging task due to the highly non-linear nature of movements. Existing deep learning-based action prediction methods emphasize the design of sophisticated network architectures to achieve state-of-the-art performance on datasets. However, in real-life scenarios, changes in skeletal size lead to a shift in data distribution, which presents challenges for accurate motion prediction. Additionally, the presence of stretching artifacts in predicted bone sequences significantly impacts the quality of the predictions. To address these issues, we propose a framework that combines geometric encoding with neural networks to achieve size-invariant and high-quality motion prediction without stretching artifacts. We consider the constraint of bone length and construct a motion space using Riemannian manifold theory, which remains unaffected by changes in skeletal size and can fully represent human motion. Furthermore, we propose the trajectory transport square-root velocity function to encode motion sequences into a flattened space. This transformation simplifies the distance calculation and linearizes the optimization problem in non-flattened space. Experiments on the Human 3.6M and CMU MoCap datasets demonstrated that the proposed method has achieved competitive performance without any stretching artifacts and exhibits robustness to changes in skeletal size.

Abstract In this article, we propose a novel 3D face modeling method which constructs a new 3D face model from a low‐dimensional feature space consisted of a large set of blend shapes based on the discrete shape space theory. The details of original face features are completely retained during the modeling process and a large number of new natural faces are constructed by several face samples. The optimization process of our method is independently decoupled for different facial attributes (identity, expression, and head pose), which improves the application flexibility and reduces the probability of it falling into a local optimal situation. The new facial data with new attributes are constructed based on the geodesic path search in discrete shape space with sufficient freedom and accuracy. In experiments and applications based on public databases (Helen, LFW, and CUFS), the modeling results show our method can provide high‐quality 3D face model, with enough freedom for face expression editing and natural facial expression animation from a small facial sample set.

Abstract Team formation with realistic crowd simulation behavior is a challenge in computer graphics, multiagent control, and social simulation. In this study, we propose a framework of crowd formation via hierarchical planning, which includes cooperative‐task, coordinated‐behavior, and action‐control planning. In cooperative‐task planning, we improve the grid potential field to achieve global path planning for a team. In coordinated‐behavior planning, we propose a time–space table to arrange behavior scheduling for a movement. In action‐control planning, we combine the gaze‐movement angle model and fuzzy logic control to achieve agent action. Our method has several advantages. (1) The hierarchical architecture is guaranteed to match the human decision process from high to low intelligence. (2) The agent plans his behavior only with the local information of his neighbor; the global intelligence of the group emerges from these local interactions. (3) The time–space table fully utilizes three‐dimensional information. Our method is verified using crowds of various densities, from sparse to dense, employing quantitative performance measures. The approach is independent of the simulation model and can be extended to other crowd simulation tasks.