近年來，由於RGB-D攝影機的發明，視頻不僅可以提供RGB信息，還可以提供深度信息。從深度影片中獲取關節，然後將關節連接形成骨架來代表人的身體，而基於骨架的人體行為辨識研究則越來越受到重視。在本文中，我們從深度影像中獲取骨架信息。除了使用20個關節連接得到的19個(局部)身體部位之外，我們將骨架分成多個大平面，稱為中級身體部位。然後將每個身體部位(局部以及中級身體部位)之間的3D幾何關係用旋轉和位移來代表，並在特殊歐幾里得SE(3)$的3D李群空間中表示為一個點。除了“姿態”信息之外，我們還從時間間隔中計算身體部位的3D幾何關係，以獲得“軌跡”信息，我們稱這特徵為時間間隔特徵。使用這種3D幾何關係特徵表示方法，人體行為可以被表示為李群SE(3)x...xSE(3)上的曲線，其中x表示李群之間的直接乘積，然後利用對數圖，將曲線從李群映射到李群的向量空間以進行後續時間處理及分類的部分。我們使用“Dynamic Time Warping”（DTW）處理不同人做相同動作的速率變化，以及“Fourier Temporal Pyramid”（FTP）處理時間上的偏差跟雜訊，最後使用線性支持向量機(SVM)建立模組來執行分類。 在MSRaction3D，UTKinect和Floerence3D數據集的實驗結果表明，我們提出的特徵表徵優於其他骨架表徵，並達到與各種最先進的基於骨架的人類動作識別方法相當的結果。

In recent years, skeleton-based human action recognition has been receiving significant attention. In this paper, we present a novel 3D geometric feature for skeleton-based action based on Lie group. First, we divide the skeleton into several parts called mid-level body parts. Then, the 3D geometric relationships between each pair of body parts are represented as a point in Lie group SE(3) through rotation and displacement operations. Having the 'posture' information, we also represent the 3D geometric relationships in time interval in order to obtain the temporal dynamical information, which can be regarded 'trajectory' information. Consequently, human actions can be modeled as curves in the Lie group SE(3)x...xSE(3), then mapping action curves from the Lie group to its Lie algebra by using the logarithm map. Finally, we can perform action classification by “dynamic time warping” (DTW), “Fourier temporal pyramid” (FTP) representation and linear SVM. Experimental results show the proposed feature representation outperforms state-of-the-art approaches on MSRaction3D, UTKinect and Floerence3D datasets.

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