Learning Fundamentals Atomic Image Structures From Natural Images, Video and Shapes

由于视觉（人类和机器）的目标是对观察到的图像或图像序列进行越来越抽象的解释，因此了解每个解释级别使用的概念是至关重要的。用更通俗的语言来说，什么是视觉“笔画”，什么是视觉“字”，什么是视觉“字”？或者什么是视觉上的“电子”、“原子”和“分子”？本研究的目标是发现不同层次的视觉概念字典，这些概念对应于图像和场景的基本拓扑、光度、几何和动态结构。用数学语言来说，这些结构是嵌入在高维图像空间中的低维流形。更具体地说，我们建议为自然图像、3D表面、人脸、视频序列和2D形状轮廓构建自上而下的生成模型。生成模型中的基本原子结构由参数定义，并通过将模型拟合到训练数据中来估计这些参数。这些结构是自然图像和视频集合所固有的。我们提出了能够计算全局最优解的随机（马尔可夫链蒙特卡罗）学习算法。

As the objective of vision (human and machine) is to compute a hierarchy of increasingly abstract interpretations of the observed images or image sequences, it is of fundamental importance to know what are the concepts used at each level of interpretation. In more plain language, what are the visual "strokes", visual "characters", and visual "words"? Or what are the visual "electrons", "atoms" and "molecules"? The goal of the proposed research is to discover dictionaries of various levels of visual concepts that correspond to fundamental topologic, photometric, geometric, and dynamic structures of the images and scenes. In a mathematical language, these structures are the low dimensional manifolds embedded in very high dimensional image space. More specifically, we propose to construct top-down generative models for natural images, 3D surfaces, human faces, video sequences, and 2D shape contours. The fundamental atomic structures are defined by parameters in the generative models, and these parameters are estimated by fitting the models to the training data. These structures are intrinsic to the ensemble of natural images and video. We propose stochastic (Markov chain Monte Carlo) learning algorithms which is capable of computing globally optimal solutions.