中文摘要：

与传统的一阶马尔科夫随机场（Markov random field,MRF）相比,高阶马尔科夫随机场能够表达更加复杂的定性和统计性先验信息,在模型的表达能力上具有更大的优势。但高阶马尔科夫随机场对应的能量函数优化问题更为复杂。同时其模型参数数目的爆炸式增长使得选择合适的模型参数也成为了一个非常困难的问题。近年来,学术界在高阶马尔科夫随机场的能量模型的建模、优化和参数学习三个方面进行了深入的探索,取得了很多有意义的成果。本文首先从这三个方面总结和介绍了目前在高阶马尔科夫随机场研究上取得的主要成果,然后介绍了高阶马尔科夫随机场在图像理解和三维场景理解中的应用现状。

英文摘要：

Compared with traditional first-order Markov random fields （MRF）, higher-order Markov random fields could incorporate more sophisticated qualitative and statistical priors, thus have much more expressive power of modeling. However, it is even harder to minimize their corresponding energy functions. Besides, estimating the value of their parameters becomes much more complex due to the explosive growth of their number. Currently, numerous works have been devoted to solving the modeling, inference and parameter learning problems of higher-order random fields. This paper is a review of the related works as well as a short summary of the applications of higher-order Markov random fields to image understanding and 3D scene understanding.