Statistical Modeling and Learning in Vision

寻找统计模型，捕捉自然场景中令人眼花缭乱的各种视觉模式的规律性和可变性，是理解视觉之谜的核心。延续Grenander开创并由Mumford倡导的模式理论方法，并以pi最近开发的主动基础模型为基础，pi提出了进一步开发视觉统计模型以及相关学习和推理算法的研究项目。活动基模型是对象模式的可变形模板的数学表示。每个模板是选定的Gabor小波元素的稀疏组合，允许扰动它们的位置和方向。模板可以通过共享草图算法从训练图像中学习。然后，可以使用学习到的模板来识别来自测试图像的对象，使用类似于皮质的和最大值地图架构。提出了一种以活动基模型作为构建块或部分模板的分层组合模型。本研究从自然图像或多类别、多视点的物体图像中研究主动基模板字典的无监督学习。本研究还研究了一种形状脚本模型，其中零件模板设计为基本几何形状，由活动基模型表示。此外，本研究还以主动基模型为例，对生成式学习和判别式学习进行了比较。此外，通过对形状模式进行小波稀疏编码，对纹理模式进行马尔可夫随机场耦合，扩展了主动基模型。生物视觉皮层可以毫不费力地学习和识别其环境中的大量视觉模式。人们可以把视觉皮层看作是一个极其复杂的统计模型，配备了极其高效和强大的学习和推理算法。这个模型是什么样子的，以及它如何从视觉环境中学习，仍然是一个深谜。拟议的研究有可能有助于促进我们对这一问题的理解。它还导致具体的模型和算法，可用于学习和识别各种各样的对象模式。

Finding statistical models that capture the regularities and variabilities of the bewildering varieties of visual patterns in natural scenes is at the heart of understanding the mystery of vision. Continuing the pattern-theoretical approach pioneered by Grenander and advocated by Mumford, and building on the active basis model that the PIs have recently developed, the PIs propose research projects to further develop statistical models as well as associated learning and inference algorithms for vision. The active basis model is a mathematical representation of deformable templates of object patterns. Each template is a sparse composition of selected Gabor wavelet elements that are allowed to perturb their locations and orientations. The template can be learned from training images by a shared sketch algorithm. The learned template can then be used to recognize objects from testing images using a cortex-like architecture of sum-max maps. The proposed research develops hierarchical compositional models with active basis models as building blocks or part-templates. The proposed research studies unsupervised learning of dictionaries of active basis templates from natural images or images of objects from multiple categories and viewpoints. The proposed research also studies a shape script model where the part-templates are designed elementary geometric shapes that are represented by the active basis models. Moreover, the proposed research compares generative and discriminative approaches to learning, using active basis model as an example of generative model. In addition, the proposed research extends the active basis model by coupling wavelet sparse coding for shape patterns and Markov random fields for texture patterns.Biological visual cortex can learn and recognize huge number of visual patterns in its environment effortlessly. One may consider the visual cortex as an extremely sophisticated statistical model equipped with extremely efficient and robust learning and inference algorithms. What this model looks like and how it learns from its visual environment is still a deep mystery. The proposed research has the potential to contribute to advancing our understanding of this issue. It also leads to concrete models and algorithms that can be used for learning and recognizing a wide variety of object patterns.