http://cvrc.ece.utexas.edu/Publications/Xia_HAU3D12.pdf
View Invariant Human Action Recognition Using Histograms of 3D Joints
The HOJ3D computed from the action depth sequences are reprojected using LDA and then clustered into k posture visual words, which represent the prototypical poses of actions. The temporal evolutions of those visual words are modeled by discrete hidden Markov models (HMMs).
特征定义
In this representation, the 3D space is partitioned into n bins using a modified spherical coordinate system. We manually select 12 informative joints to build a compact representation of human posture. To make our representation robust against minor posture variation, votes of 3D skeletal joints are cast into neighboring bins using a Gaussian weight function.
we acquire the 3D locations of 20 skeletal joints which comprise hip center, spine, shoulder center, head, L/ R shoulder, L/ R elbow, L/ R wrist, L/ R hand, L/ R hip, L/ R knee, L/ R angle and L/ R foot.
we compute our histogram based representation of postures from 12 of the 20 joints, including head, L/ R elbow, L/ R hands, L/ R knee, L/ R feet, hip center and L/ R hip. We take the hip center as the center of the reference coordinate system, and define the x-direction according to L/ R hip. The rest 9 joints are used to compute the 3D spatial histogram.
要达到视不变（不同视角下相同姿态正确归类）：We achieve this by aligning our spherical coordinates with the person’s specific direction。We define the center of the spherical coordinates as the hip center joint.Define the horizontal reference vector α to be the vector from the left hip center to the right hip center projected on the horizontal plane (parallel to the ground), and the zenith reference vector θ as the vector that is perpendicular to the ground plane and passes through the coordinate center.
partition the 3D space into n bins
The inclination angle is divided into 7 bins from the zenith vector θ: [0, 15], [15, 45], [45, 75], [105, 135], [165, 180]
Our HOJ3D descriptor is computed by casting the rest 9 joints into the corresponding spatial histogram bins.
To make the representation robust against minor errors of joint locations, we vote the 3D bins using a Gaussian weight function:
For each joint, we only vote over the bin it is in and the 8 neighboring bins. We calculate the probabilistic voting on θ and α separately since they are independent (see Fig. 4). The probabilistic voting for each of the 9 bins is the product of the probability on α direction and θ direction. Let the joint
location be 
The vote of a joint location to bin 
is 
The vote of a joint location to bin is 输入为20*3（20个关节点，xyz3维空间坐标），输出为84位HOJ3D特征
特征为84维向量，水平方向12，垂直方向7
1，12个关节点局部坐标的计算：1，根据L_HIP和R_HIP的连线方向计算转换后的坐标 ； 2，计算相对于HIP_CENTER的坐标
2，之后计算两个偏转角 vector α 和 vector θ
3，在每个关节所属的bin中的8个邻域内，按双方向的单高斯分布乘积投票
特征降维
Linear discriminant analysis (LDA) is performed to extract the dominant features.
降维的目的是得到区分度更大的9个维度信息
输入为84维HOJ3D特征，输出为9维降维特征
特征聚类
We cluster the vectors into K clusters (a K-word vocabulary) using K-means. Then each posture is represented as a single number of a visual word.
聚类是为了减少观察特征表示，训练阶段需要把所有观测数据（所有动作，每一个动作包含若干帧，每帧的20个骨骼节点经过LDA降维成9）在9维空间中聚类，可以得到25个聚类中心的坐标（9维），依次标号
在识别阶段，将LDA之后的特征，分配到最近邻的聚类中心，记录其标号，作为HMM的输入参数
训练阶段，输入为所有动作的9维特征，输出为25个聚类中心
识别阶段，输入为每一帧的动作特征（9维），输出为距其最近的聚类中心的标号
动作识别
the HMM gives a state based representation for each action. After forming the models for each activity, we take an action sequence 
and calculate its probability of a model
for the observation sequence, 
for every model, which can be solved using the forward algorithm. Then we classify the
and calculate its probability of a modelfor the observation sequence, for every model, which can be solved using the forward algorithm. Then we classify the action as the one which has the largest posterior probability.
训练阶段，输入为每一类动作的时序标号，输出为HMM模型参数
识别阶段，输入为某一动作的时序标号，输出为前向概率即模型匹配度最大的动作模型 —— 识别结束