To incorporate spatial (neighborhood) and bidirectional hierarchical
relationships as well as features and priors of the samples into their
classification, we formulated the classification problem on three variants of
multiresolution neighborhood graphs and the graph of a hierarchical conditional
random field. Each of these graphs was weighted and undirected and could thus
incorporate the spatial or hierarchical relationships in all directions. In
addition, each variant of the proposed neighborhood graphs was composed of a
spatial feature-based subgraph and an aspatial prior-based subgraph. It
expanded on a random walker graph by using novel mechanisms to derive the edge
weights of its spatial feature-based subgraph. These mechanisms included
implicit and explicit edge detection to enhance detection of weak boundaries
between different classes in spatial domain. The implicit edge detection relied
on the outlier detection capability of the Tukey's function and the
classification reliabilities of the samples estimated by a hierarchical random
forest classifier. Similar mechanism was used to derive the edge weights and
thus the energy function of the hierarchical conditional random field. This
way, the classification problem boiled down to a system of linear equations and
a minimization of the energy function which could be done via fast and
efficient techniques.

为了将空间（邻域）和双向分层关系以及样本的特征和先验信息纳入他们的分类中，我们针对三种变型的多分辨率邻域图以及分层条件随机场图制定了分类问题。