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

 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

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