RI: Small: Dynamic Invariants for Video Scenes Understanding

该项目旨在使用来自动态视觉，动力系统理论，优化和半代数几何的元素的组合来开发一个计算上易于处理的，可扩展的框架，用于从多个，可能不完整和损坏的数据流中自动理解动态场景。 长期愿景是为合成可证明的强大视觉系统奠定基础，能够在复杂的动态场景中持续成功运行。 是一个统一的愿景，集中在使用动态不变量作为信息分解器，并强调鲁棒性和计算复杂性的问题。 在这种方法中，观察到的数据被视为基础模型的输出，通常是差异包含，其具有关联的某些量（例如阶、嵌入流形、由其轨迹所跨越的子空间），这些不变量对于坐标变换、初始条件、视点变化、同步等是不变的。这些不变量从视频数据中复杂地捕获时空信息，并导致鲁棒的，计算有效算法 用于自动视频场景理解。 例如，在这种情况下，可以通过检测这些动态不变量的变化来有效地分割视频数据，或者根据合适的定义距离来聚类视频数据。 直接受本研究影响的一个应用领域是公共空间安全的感知环境，其中合作PI已被提供访问真实的数据，并提供了一个场地进行算法的真实的时间测试。

This project aims to use a combination of elements from dynamic vision, dynamical systems theory, optimization and semi-algebraic geometry to develop a computationally tractable, scalable framework for automatic dynamic scene understanding from multiple, potentially incomplete and corrupted data streams. The long-term vision is to lay the foundations for synthesizing provably robust vision systems, capable of sustained successful operation in complex dynamic scenarios.The core of the project is a unified vision, centered on the use of dynamical invariants as information encapsulators, and emphasizing robustness and computational complexity issues. In this approach, the observed data is treated as the output of an underlying model, typically a difference inclusion, which has associated certain quantities (for example order, embedding manifold, subspace spanned by its trajectories) that are invariant to coordinate transformations, initial conditions, viewpoint changes, synchronization, etc. These invariants compactly capture spatio-temporal information from video data and lead to robust, computationally efficient algorithms for automatic video scene understanding. For instance, in this context video data can be efficiently segmented by detecting changes in these dynamic invariants or clustered according to a suitable defined distance. An application domain directly impacted by this research is aware environments for public space safety, where the co-PIs have been provided access to real data and given a venue for real time testing of the algorithms.