Symmetry-based Representation of 2D and 3D shapes and images for category-level recognition

该项目研究了2D和3D形状和图像表示的开发和使用，用于类别级识别，组织在四个密切相关的流中。首先，低失真嵌入的形状空间，捕捉其局部拓扑结构和其高阶结构将被调查的高效和实用的索引在数据库中的数万形状。查询搜索将被引导在嵌入空间通过层次结构的类别由认知科学的概念。其次，一种新的自由形式的可变形模板将通过构建一个参数空间，用于生成约束具有给定的冲击图拓扑结构的形状，并通过采样这个空间与低维密集和完整的近似。这将导致一个正式的完整的语言描述形状通过对称表示，并有基本的影响，在一些领域，包括分割，形状平均，和！形状设计第三，查看基于图像的表示主要作为联合表示的空间配置的功能对，一个正式的和完整的基于图像的表示将开发的基础上划分成补丁的图像称为“视觉片段”。视觉片段的建议的优点是，它们允许基于边界和区域属性的感知分组，并且还允许来自分组的部分识别部分的自上而下的反馈。第四，在平行于2D形状表示的研究的轨道中，将探索作为3D形状表示的图形结构的冲击支架的局部形式和过渡。两个图匹配技术，分级分配和编辑距离，将被研究用于索引到3D形状模型，并应用于一个大型的3D形状数据库。这项研究活动的更广泛的影响跨越了许多领域，如跟踪和识别车辆的监视，国土安全和国防应用，生成计算地图集和注册的数据集在医学成像，考古学中的多个范围数据集的片段组装和集成、视觉艺术中的虚拟雕刻、生物特征识别中的签名和指纹识别、通过形状内容索引到大型数据库中、娱乐应用中的关键帧动画等等。这里开发的概念也感兴趣的造型形状感知和皮层活动有关的形状识别。

This project investigates the development and use of 2D and 3D shape and image representations for category-level recognition, as organized in four closely related streams. First, low-distortion embeddings of the shape space that capture both its local topology and its high order structure will be investigated for efficient and practical indexing in a database of several tens of thousands of shapes. Query search will then be guided in the embedding space via hierarchically structured categories motivated by cognitive science notions. Second, a novel free-form deformable template will be developed by constructing a parametric space for generating shapes constrained to have a given shock-graph topology and by sampling this space with a low-dimensional dense and complete approximation. This will lead to a formal complete language for describing shape via symmetry representations and has fundamental implications in a number of areas including segmentation, shape averaging, and !shape design. Third, viewing symmetry-based representations primarily as the joint representation of the spatial configuration of pairs of features, a formal and complete symmetry-based representation of images will be developed based on a partitioning of the image into patches called "visual fragments". The proposed advantage of the visual fragments is that they allow for perceptual grouping based on both boundary and regional attributes, and also for top-down feedback from partially recognized portions of the grouping. Fourth, in a track parallel to investigations of 2D shape representations, the local form and transitions of the graph-structured shock scaffold as a representation of 3D shape will be explored. Two graph matching techniques, graduated assignment and edit distance, will be investigated for indexing into 3D shape models and applied to a large database of 3D shapes.The broader impact of this research activity spans a number of areas, such as tracking and recognition of vehicles for surveillance, homeland security, and defense applications, generation of computational atlases and registration of datasets in medical imaging, fragment assembly and integration of multiple range datasets in archaeology, virtual sculpting in visual arts, signature and fingerprint recognition in biometric identification, indexing into large databases by shape content, key frame animation for entertainment applications, among others. The concepts developed here are also of interest for both modeling shape perception and cortical activity as related to shape recognition.