# sum product algorithm and Convolution Neural Network

I'm trying to understand the sum-product algorithm implemented using Convolution Neural Network by the paper [1,2] to solve the problem of human pose estimation.

Human pose estimation is formulated using a graph G=(V, E) where V specify the body part position. E indicate spatial relationship between parts.

The sum-product algorithm is expressed below

$m_{ij}(x_i) \leftarrow \sum{_{x_i}}(u_i(x_i) + \psi(x_i,x_j))$ (1)

$u_i(x_i) \leftarrow \phi(x_i) + \sum_{k \in N(i)}m_{ki}(x_i,x_j))$ (2)

In above equations

$u_i(x_i)$ is the belief of part i.

$\phi(x_i)$ is the appearance term obtained from CNN

$m_{ij}(x_i)$ is the message from part i to part j

The $m_{ij}(x_i)$ in equation (1) is implemented by passing $u_i(x_i)$ to conv and relu layer as shown in the figure .

I didn't understand how conv and relu can function like this.

Reference

[1] X. Chu, W. Ouyang, H. Li, and X. Wang, “Structured feature learning for pose estimation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, pp. 4715–4723

[2] End-to-end learning of deformable mix- ture of parts and deep convolutionl neural networks for human pose estimation