# Structured-Output Convolutional Neural Networks for Image Dependent Pairwise Relation

In this paper, we propose a novel model and its training strategy for the CRF.

## Model

We denote the input image by $$I$$, output by $$Y$$, set of parameters by $$\Theta$$.

Conditional Random Fields(CRF).

$$S(I,Y,\Theta)=\sum_{i\in V}{\Phi_{i}(I,Y_{i},\Theta)+\sum_{ij\in E}{\Psi_{ij}(I,Y_{i},Y_{j},\Theta)}}\\$$
$$\Psi_{ij}(I,Y_{i},Y_{j},\Theta)=\sum_{m=1}^{M}{w_{m}k_{m}(f(Y_{i}),f(Y_{j}))}\\$$
$$Y^{*}=\operatorname*{arg\,max}_{Y}{S(I,Y,\Theta)}\\$$