# A New Multi-Person Pose Estimation Method Using the Partitioned CenterPose Network
## 3 Partition Pose Representation  
In this section, we describe the proposed PPR in detail. Unlike traditional grouping methods, PPR is committed to generating connections between each body joint and instance of a person while simultaneously strengthening the correlations between different body joints. Let \(I\in R^{W\times H\times 3}\) denote an input image of width \(W\) and height \(H\) and \(p^{k}=\ \left\{p_{1}^{k},p_{2}^{k},\ldots,p_{N}^{k}\right\}\) denote \(N\) joint candidates from the \(k\)th persons in \(I\). \(\left(x_{n}^{k},y_{n}^{k}\right)\) is the spatial coordinate of \(p^{k}\), and \(\left(x_{lt}^{k},y_{lt}^{k},x_{rb}^{k},y_{rb}^{k}\right)\) is the bounding box of the \(k\)th instance of a person. Inspired by CenterNet [17], the body center is denoted by \(\left(\hat{x}_{0}^{k},\hat{y}_{0}^{k}\right)=\left(x_{lt}^{k}+x_{rb}^{k},y_{lt }^{k}+y_{rb}^{k}\right)/2\).  
PPR aims to aggregate the instance of a person and body pose with an offset to the body center. So, the coordinates of the \(n\)th joint of person \(k\) can be defined as:  
\[\left(x_{n}^{k},y_{n}^{k}\right)\ =\ \left(\hat{x}_{0}^{k}+\delta x_{n}^{k}, \hat{y}_{0}^{k}+\delta y_{n}^{k}\right) \tag{1}\]  
where \(\left(\delta x_{n}^{k},\delta y_{n}^{k}\right)\) is the offset of the \(n\)th joint to the body center.  
However, Equation (1) only considers unification of an instance of a person and body pose; it ignores the relationship between adjacent joints. Using additional information from correlated joints, the offset vector can be more accurately mapped to the position of the pose by the prediction model. Naturally, PPR divides the human body into five parts: (1) head, including nose, left eye, right eye, left ear, and right ear; (2) left arm, including left shoulder, left elbow, and left wrist; (3) right arm, including right shoulder, right elbow, and right wrist; (4) left leg, including left hip, left knee, and left ankle; and (5) right leg, including right hip, right knee, and right ankle. Then, we use the same approach as used in Equation (1) to represent the joints in each part. Here, the center points of each part \(p_{c}^{k}\) are no longer the body center, but the nose, left elbow, right elbow, left knee, and right knee are taken as the centers of the five respective body parts. Some complex environments may mean a part center is not visible; this will affect encoding by PPR. In this situation, we calculate the center of the remaining joints in this part to replace the part center; we call this point the illusion center. Thus, the complete PPR can be formulated as:  
\[\left(x_{n}^{k},y_{n}^{k}\right)\ =\ \begin{cases}\ \ \ \left(\hat{x}_{0}^{k}+ \delta x_{n}^{k},\hat{y}_{0}^{k}+\delta y_{n}^{k}\right)\ \text{if}p_{n}^{k}\in p_{c}^{k}\\ \ \ \left(\hat{x}_{m}^{k}+\delta\hat{x}_{n}^{k},\hat{y}_{m}^{k}+\delta\hat{y}_{n}^ {k}\right)\ \text{otherwise}\end{cases} \tag{2}\]  
when the part center is visible, \(\left(\hat{x}_{m}^{k},\hat{y}_{m}^{k}\right)\) is the coordinates of the center point of the \(m\)th part and \(\left(\delta\hat{x}_{n}^{k},\delta\hat{y}_{n}^{k}\right)\) is the offset of the \(n\)th joint from the corresponding part center. When the part center is not visible, \(\left(x_{m}^{k},y_{m}^{k}\right)\) is the coordinate of the illusion center of the \(m\)th part and \(\left(\delta\hat{x}_{n}^{k},\delta\hat{y}_{n}^{k}\right)\) is the offset of the \(n\)th joint from the corresponding illusion center.  
Using the offset from the part center to the body center, PPR establishes the connection between a body pose and the instance of a person. At the same time, PPR retains global information related to the limbs and generates correlations between body joints in one part through the offset of other joints to the part center.