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

这个项目调查了用于类别级别识别的2D和3D形状和图像表示的开发和使用，这些表示被组织成四个密切相关的流。首先，将研究形状空间的低失真嵌入，该嵌入既能捕捉其局部拓扑结构，又能捕捉其高阶结构，以便在包含数万个形状的数据库中进行高效和实用的索引。然后，查询搜索将通过由认知科学概念驱动的分层结构的类别在嵌入空间中被引导。其次，通过构造一个参数空间来生成满足给定激波图拓扑结构的形状，并对该空间进行低维稠密和完全近似采样，从而开发出一种新的自由变形模板。这将导致一种形式完整的语言，用于通过对称表示来描述形状，并在许多领域具有基本意义，包括分割、形状平均和形状设计。第三，将基于对称性的表示主要视为特征对的空间构型的联合表示，将基于将图像分割成被称为“视觉碎片”的块来开发图像的形式和完整的基于对称性的表示。可视片段的拟议优势在于，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，在与2D形状表示研究平行的轨道中，将探索作为3D形状表示的图形结构冲击支架的局部形式和过渡。两种图形匹配技术，分级分配和编辑距离，将被用于索引到3D形状模型并应用于3D形状的大型数据库。这项研究活动的广泛影响跨越多个领域，例如用于监视、国土安全和国防应用的车辆的跟踪和识别、医学成像中的计算地图集的生成和数据集的注册、考古学中的多范围数据集的碎片组装和集成、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、按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。这里开发的概念对于形状感知和与形状识别相关的皮质活动的建模也是有意义的。

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.