RI: Small: Dynamic Invariants for Video Scenes Understanding

该项目旨在结合动态视觉、动态系统理论、优化和半代数几何的元素，开发一个计算可处理、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动态场景理解。长期愿景是为合成可证明的鲁棒视觉系统奠定基础，能够在复杂的动态场景中持续成功地运行。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，并强调鲁棒性和计算复杂性问题。在这种方法中，观察到的数据被视为底层模型的输出，通常是一个差异包含，它与某些数量（例如顺序，嵌入流形，由其轨迹跨越的子空间）相关联，这些数量对坐标变换，初始条件，视点变化，同步等是不变的。这些不变量紧凑地从视频数据中捕获时空信息，并导致鲁棒，计算效率高的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进行聚类。受本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，在这些环境中，合作伙伴可以访问真实数据，并为算法提供实时测试的场所。

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.