Approches basées sur les variétés pour la reconnaissance des actions et des gestes

Human action recognition (HAR) has emerged as a critical research area due to its wide range of real-world applications, including human-computer interaction, intelligent healthcare, virtual reality, surveillance, UAV control, and autonomous systems. Over the past few decades, numerous approaches have been developed to recognize human actions from monocular RGB video sequences. More recently, the advent of depth sensors has fueled the growth of 3D activity analysis and 3D gesture recognition, leading to significant advancements in the field. Among the various techniques proposed, manifold-based approaches have gained prominence due to their ability to effectively model the temporal evolution of 3D skeletal data through manifold-invariant representations. These methods have demonstrated remarkable performance in addressing the challenging task of action recognition.In this work, we explore the properties of the Symmetric Positive Definite (SPD) manifold, one of the most widely used manifolds in action and gesture recognition. We propose a novel recognition framework that integrates both a detector and a classifier, leveraging an SPD-based neural network known as the SPD Siamese Neural Network. We validate its performance through extensive experiments on both segmented and continuous action sequences across multiple datasets. Our results demonstrate that this approach outperforms state-of-the-art methods in various scenarios.Despite these advancements, significant challenges persist, particularly in complex environments such as UAV-based human action recognition. To overcome these limitations, we introduce an improved model, SPDAGG-TransNet, which enhances the baseline SPD Siamese network by refining its temporal-spatial feature extraction and integrating a Transformer module. This enhancement strengthens the model's ability to capture long-range dependencies, enrich feature representations, and maintain the intrinsic geometric properties of SPD representations. By incorporating Transformer encoders, our approach further improves recognition accuracy by effectively modeling both local and global motion dynamics. Extensive evaluations on benchmark datasets, including DHG-14, UAV-Human, and UAV-Gesture, demonstrate that SPDAGG-TransNet achieves state-of-the-art performance.Beyond SPD-based approaches, we also explore hyperbolic space as an alternative geometric framework for motion recognition. Hyperbolic neural networks (HNNs) offer a promising direction for modeling hierarchical and structured relationships in motion data. Unlike conventional Euclidean-based deep learning models, hyperbolic architectures leverage Lorentz transformations and novel optimization techniques, such as the Riemannian Adam optimizer, to stabilize embeddings and enhance scalability. These advancements enable more effective hierarchical motion modeling, making hyperbolic learning particularly suitable for action recognition tasks.Extensive experiments conducted across multiple benchmarks—ranging from hand gesture recognition to full-body action recognition and UAV-based datasets demonstrate the effectiveness of both SPD-based and hyperbolic-based approaches in challenging scenarios. Our findings highlight the superiority of geometric learning frameworks in accurately modeling human motion, ensuring real-time adaptability, and overcoming the limitations of traditional Euclidean methods.