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

该项目研究了2D和3D形状和图像表示在类别级识别中的发展和使用，组织在四个密切相关的流中。首先，将研究形状空间的低失真嵌入，同时捕获其局部拓扑和高阶结构，以便在数万个形状的数据库中进行有效和实用的索引。然后，查询搜索将通过由认知科学概念驱动的分层结构类别在嵌入空间中进行引导。其次，通过构造一个参数空间来生成受约束的具有给定激波图拓扑的形状，并通过对该空间进行低维密集和完全近似的采样，将开发一个新的自由形式可变形模板。这将导致一种通过对称表示来描述形状的正式完整的语言，并在许多领域具有基本的含义，包括分割，形状平均和！形状设计。第三，将基于对称的表示主要视为对特征对空间配置的联合表示，将基于图像划分为称为“视觉片段”的补丁的形式和完整的基于对称的图像表示。视觉片段的优点是，它们允许基于边界和区域属性的感知分组，也允许从分组部分可识别的部分进行自上而下的反馈。第四，在平行于研究二维形状表示的轨道上，将探索图形结构冲击支架作为三维形状表示的局部形式和过渡。两种图匹配技术，分级分配和编辑距离，将研究索引到三维形状模型和应用于大型三维形状数据库。这项研究活动的广泛影响跨越了许多领域，例如用于监视、国土安全和国防应用的车辆跟踪和识别，医学成像中计算地图集的生成和数据集的注册，考古学中碎片组装和多范围数据集的集成，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，关键帧动画的娱乐应用程序，等等。这里开发的概念对于形状感知建模和与形状识别相关的皮质活动也很有趣。

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.