RI: Small: Dynamic Invariants for Video Scenes Understanding

该项目旨在结合动态视觉、动力系统理论、最优化和半代数几何的元素，开发一个计算上易于处理、可扩展的框架，用于从多个潜在的不完整和损坏的数据流中自动理解动态场景。该项目的长期愿景是为合成能够在复杂动态场景中持续成功运行的可证明稳健的视觉系统奠定基础。该项目的核心是一个统一的愿景，以使用动态不变量作为信息封装器为中心，并强调稳健性和计算复杂性问题。在该方法中，观测数据被视为底层模型的输出，该模型通常是差分包含，该模型具有与坐标变换、初始条件、视点变化、同步等不变的某些量(例如阶数、嵌入流形、其轨迹所跨越的子空间)。这些不变量紧凑地从视频数据捕获时空信息，并导致用于自动视频场景理解的稳健的、计算高效的算法。例如，在该上下文中，可以通过检测这些动态不变量中的变化来有效地分割视频数据，或者根据适当的定义距离对视频数据进行聚类。受这项研究直接影响的一个应用领域是公共空间安全的感知环境，在那里，联合PI被提供了访问真实数据的机会，并为算法的实时测试提供了场所。

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.