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Deep Learning architectures, albeit successful in most computer vision tasks, were designed for data with an underlying Euclidean structure, which is not usually fulfilled since pre-processed data may lie on a non-linear space. In this paper, we propose a geometry aware deep learning approach using rigid and non rigid transformation optimization for skeleton-based action recognition. Skeleton sequences are first modeled as trajectories on Kendall's shape space and then mapped to the linear tangent space. The resulting structured data are then fed to a deep learning architecture, which includes a layer that optimizes over rigid and non rigid transformations of the 3D skeletons, followed by a CNN-LSTM network. The assessment on two large scale skeleton datasets, namely NTU-RGB+D and NTU-RGB+D 120, has proven that the proposed approach outperforms existing geometric deep learning methods and exceeds recently published approaches with respect to the majority of configurations.

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