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

由于视觉（人类和机器）的目标是计算观察到的图像或图像序列的越来越抽象的解释的层次结构，因此了解每个解释层次使用的概念是至关重要的。在更通俗的语言中，什么是视觉的“笔画”、视觉的“字”、视觉的“词”？ 或者视觉上的“电子”、“原子”和“分子”是什么？ 建议的研究的目标是发现字典的各个层次的视觉概念，对应的基本拓扑，光度，几何和动态结构的图像和场景。 在数学语言中，这些结构是嵌入在非常高维的图像空间中的低维流形。更具体地说，我们建议构建自上而下的自然图像，三维表面，人脸，视频序列和二维形状轮廓生成模型。基本原子结构由生成模型中的参数定义，并且通过将模型拟合到训练数据来估计这些参数。这些结构是自然图像和视频的集合所固有的。我们提出了随机（马尔可夫链蒙特卡罗）学习算法，它能够计算全局最优解。

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.