Division of Applied Mathematics, Brown University, Providence, RI 02912.
IEEE Trans Pattern Anal Mach Intell. 1984 Jun;6(6):721-41. doi: 10.1109/tpami.1984.4767596.
We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.
我们将图像和统计力学系统进行类比。像素的灰度级和边缘的存在和方向被视为晶格状物理系统中原子或分子的状态。物理系统中能量函数的分配决定了它的吉布斯分布。由于吉布斯分布和马尔可夫随机场（MRF）等价，这种分配也决定了 MRF 图像模型。能量函数是一种比 MRF 的局部特征更方便、更自然的体现图像属性的机制。对于一系列退化机制，包括模糊、非线性变形、乘性或加性噪声，后验分布是一个具有类似于图像模型的结构的 MRF。通过类比，后验分布定义了另一个（想象中的）物理系统。在物理系统中逐渐降低温度会隔离低能量状态（“退火”），或者说，在吉布斯分布下，是最可能的状态。在后验分布下进行类似的操作，会得到在退化观测下图像的最大后验（MAP）估计。其结果是一种高度并行的 MAP 估计“松弛”算法。我们建立了算法的收敛性质，并对一些简单的图片进行了实验，在低信噪比下获得了很好的恢复效果。
