In recent years, there has been renewed interest in developing methods for skeleton-based human action recognition. A skeleton sequence can be naturally represented as a high-order tensor time series. In this paper, we model and analyze tensor time series with Linear Dynamical System (LDS) which is the most common for encoding spatio-temporal time-series data in various disciplines dut to its relative simplicity and efficiency. However, the traditional LDS treats the latent and observation state at each frame of video as a column vector. Such a vector representation fails to take into account the curse of dimensionality as well as valuable structural information with human action. Considering this fact, we propose generalized Linear Dynamical System (gLDS) for modeling tensor observation in the time series and employ Tucker decomposition to estimate the LDS parameters as action descriptors. Therefore, an action can be represented as a subspace corresponding to a point on a Grassmann manifold. Then we perform classification using dictionary learning and sparse coding over Grassmann manifold. Experiments on MSR Action3D Dataset, UCF Kinect Dataset and Northwestern-UCLA Multiview Action3D Dataset demonstrate that our proposed method achieves superior performance to the state-of-the-art algorithms.
@math The methods belonging to this category attempt to correlate joints locations. In order to add temporal information to this representation, Yang @cite_5 employed the differences of 3D joint position between the current frame and the preceding frame, and between the current frame and the initial one. Action classification was performed by using the Naive-Bayes nearest neighbor rule in a lower dimensional space constructed by using principal component analysis (PCA). Li @cite_12 employed a bag-of-3D-points graph approach to encode actions based on body silhouette points projected to the three orthogonal Cartesian planes. More complex representation is introduced in @cite_17 , where the relative 3D geometry between different rigid bodies is explicitly estimated. Their relative geometry between @math rigid body parts can be described as special Euclidean group @math using the rotation and translation. Therefore, the entire human skeleton in each frame can be described as a point in @math . A sequence of skeletons is a curve in the Lie group @math .
@cite_5 @cite_12 @cite_17
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Recently introduced cost-effective depth sensors coupled with the real-time skeleton estimation algorithm of [16] have generated a renewed interest in skeleton-based human action recognition. Most of the existing skeleton-based approaches use either the joint locations or the joint angles to represent a human skeleton. In this paper, we propose a new skelet al representation that explicitly models the 3D geometric relationships between various body parts using rotations and translations in 3D space. Since 3D rigid body motions are members of the special Euclidean group SE(3), the proposed skelet al representation lies in the Lie group SE(3)SE(3), which is a curved manifold. Using the proposed representation, human actions can be modeled as curves in this Lie group. Since classification of curves in this Lie group is not an easy task, we map the action curves from the Lie group to its Lie algebra, which is a vector space. We then perform classification using a combination of dynamic time warping, Fourier temporal pyramid representation and linear SVM. Experimental results on three action datasets show that the proposed representation performs better than many existing skelet al representations. The proposed approach also outperforms various state-of-the-art skeleton-based human action recognition approaches. Recently, skeleton-based human action recognition has been receiving significant attention from various research communities due to the availability of depth sensors and real-time depth-based 3D skeleton estimation algorithms. In this work, we use rolling maps for recognizing human actions from 3D skelet al data. The rolling map is a welldefined mathematical concept that has not been explored much by the vision community. First, we represent each skeleton using the relative 3D rotations between various body parts. Since 3D rotations are members of the special orthogonal group SO3, our skelet al representation becomes a point in the Lie group SO3    SO3, which is also a Riemannian manifold. Then, using this representation, we model human actions as curves in this Lie group. Since classification of curves in this non-Euclidean space is a difficult task, we unwrap the action curves onto the Lie algebra so3    so3 (which is a vector space) by combining the logarithm map with rolling maps, and perform classification in the Lie algebra. Experimental results on three action datasets show that the proposed approach performs equally well or better when compared to state-of-the-art. In this paper, we propose an effective method to recognize human actions from 3D positions of body joints. With the release of RGBD sensors and associated SDK, human body joints can be extracted in real time with reasonable accuracy. In our method, we propose a new type of features based on position differences of joints, EigenJoints, which combine action information including static posture, motion, and offset. We further employ the Naive-Bayes-Nearest-Neighbor (NBNN) classifier for multi-class action classification. The recognition results on the Microsoft Research (MSR) Action3D dataset demonstrate that our approach significantly outperforms the state-of-the-art methods. In addition, we investigate how many frames are necessary for our method to recognize actions on the MSR Action3D dataset. We observe 1520 frames are sufficient to achieve comparable results to that using the entire video sequences.