解读Towards Unified Depth and Semantic Prediction from a Single Image（4）
那就接着分析Section 2 Formulation
对这个图已经熟悉不过了，
our HCRF is composed of two layers of nodes and edges
先来看一下bottom layer的叙述，
1, In the bottom layer, the nodes are the pixels in the image I
2, For each pixel i belongs to I (i # I), we would like to predict its depth value d_i and
semantic label I_i
3, We use x_i = {d_i, I_i} to denote the inference output at pixel i
然后再来看upper layer的叙述，
1, In the upper layer, we decompose image I to local segments, and use the segments to
represent the node
2, Similarly, we would like to infer the depth and semantic labels y_s = {d_s, l_s} for each segment
s # S where S denotes the set of segments after decomposition
3, We use R_s to denote all the pixels inside inside segment s
We use X_s to denote the predicted labels of R_s
作者然后定义了三种edges，
Apparently there are three kinds of edges in the HCRF ,
1, the pair-wise edges between neighboring pixels
2, the edges between neighboring segments
3, the edges connecting R_s and s
对上面的edge还是一脸懵B...
然后，作者给出了能量函数，
图 1
图 2
图1和图2是对作者对能量函数的解释，似乎有一些复杂，
先阅读公式（1），可以了解一些知识(希腊字母实在是不想打，凑合看呗，哈哈)，
1，变量i和s分别指像素（pixel）和块块（segment），在之前已经叙述
2，u_i(x_i)指bottom layer的单个像素的能量函数
3，u_i_j(x_i, x_j)指bottom layer的像素与像素间的能量函数
4，u_s_t(y_s, y_t)指upper layer的块块与块块间的能量函数
5，u_s(X_s, y_s)的具体展开是公式（2），即块块和对应的像素之间的能量函数以及单个块块的能量函数之和
虽然能量函数看上去比较复杂，但是它的物理含义还是比较明显的，
论文经常出现Unary potentials这个词，查一下，可以译为“一元势函数”，目前为止，只知道能量函数的结构
但是不知道能量函数中各个函数的具体表达式，
没关系，可以一一说明，
1, 函数u_i(x_i)
provided by a CNN trained globally on the whole image, which jointly predicts pixel-wise depth
values and probabilities of semantic labels
which would be introduced in Section 3
2, 函数o_s(y_s)
the segment-level potential is generated by a CNN-based regressor trained on local regions
which details described in Section 4
下次再讨论剩下的
