Statistical Modeling and Learning in Vision

寻找统计模型来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变异性，是理解视觉之谜的核心。继续由格勒南德首创并由芒福德倡导的模式理论方法，并在个人投资机构最近开发的主动基础模型的基础上，个人投资机构提出研究项目，以进一步开发统计模型以及相关的视觉学习和推理算法。主动基础模型是对象图案的可变形模板的数学表示。每个模板是被允许扰动其位置和方向的所选Gabor小波元素的稀疏组合。该模板可以通过共享草图算法从训练图像中学习。然后，可以使用学习的模板来识别来自测试图像的对象，该测试图像使用和-最大映射的皮质状体系结构。本研究发展了以主动基础模型为构件或部分模板的层次化组合模型。该研究从自然图像或多类别、多视点的物体图像出发，研究了主动基模板词典的无监督学习。该研究还研究了一种形状脚本模型，其中零件模板被设计为由活动基础模型表示的基本几何形状。此外，本研究以主动基础模式为例，比较了产生式和鉴别式两种学习方式。此外，通过将形状模式的小波稀疏编码和纹理模式的马尔可夫随机场相结合，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。人们可能会认为视觉皮质是一个极其复杂的统计模型，配备了极其高效和健壮的学习和推理算法。这个模型是什么样子，它是如何从视觉环境中学习的，仍然是一个深层次的谜。拟议的研究有可能有助于增进我们对这一问题的理解。它还产生了可用于学习和识别各种对象模式的具体模型和算法。

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.