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Video anomaly detection is a fundamental task in video surveillance, with broad applications in public safety and intelligent monitoring systems. Although previous methods leverage Euclidean representations in RGB or depth domains, such…
An additive Runge-Kutta method is used for the time stepping, which integrates the linear stiff terms by an explicit singly diagonally implicit Runge-Kutta (ESDIRK) method and the nonlinear terms by an explicit Runge-Kutta (ERK) method. In…
Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged…
We propose a new unsupervised and non-parametric method to detect change points in intricate quasi-periodic signals. The detection relies on optimal transport theory combined with topological analysis and the bootstrap procedure. The…
Current methods in multiple object tracking (MOT) rely on independent object trajectories undergoing predictable motion to effectively track large numbers of objects. Adversarial conditions such as volatile object motion and imperfect…
This paper presents a visual-inertial odometry-enhanced geometrically stable Iterative Closest Point (ICP) algorithm for accurate mapping using aerial robots. The proposed method employs a visual-inertial odometry framework in order to…
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that…
3D dynamic point cloud (DPC) compression relies on mining its temporal context, which faces significant challenges due to DPC's sparsity and non-uniform structure. Existing methods are limited in capturing sufficient temporal dependencies.…
We present the systemic Console, a new all-in-one, general-purpose software package for the analysis and combined multiparameter fitting of Doppler radial velocity (RV) and transit timing observations. We give an overview of the…
Dynamic obstacle avoidance is one crucial component for compliant navigation in crowded environments. In this paper we present a system for accurate and reliable detection and tracking of dynamic objects using noisy point cloud data…
We propose a useful method for mapping large-scale velocity fields in the solar photosphere. It is based on the local correlation tracking algorithm when tracing supergranules in full-disc dopplergrams. The method was developed using…
In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
Safety-critical perception for unmanned aerial vehicles and rotating machinery requires microsecond-latency tracking of fast, periodic motion under egomotion and strong distractors. Frame-based and event-based trackers drift or break on…
In this paper, we first study nonsmooth steepest descent method for nonsmooth functions defined on Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for…
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study…
Noisy observations coupled with nonlinear dynamics pose one of the biggest challenges in robot motion planning. By decomposing nonlinear dynamics into a discrete set of local dynamics models, hybrid dynamics provide a natural way to model…
This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…