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Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems -- a…
Recent works in multiple object tracking use sequence model to calculate the similarity score between the detections and the previous tracklets. However, the forced exposure to ground-truth in the training stage leads to the…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like…
The accurate tracking of live cells using video microscopy recordings remains a challenging task for popular state-of-the-art image processing based object tracking methods. In recent years, several existing and new applications have…
In this paper, we propose a novel concept of path consistency to learn robust object matching without using manual object identity supervision. Our key idea is that, to track a object through frames, we can obtain multiple different…
Visual object tracking was generally tackled by reasoning independently on fast processing algorithms, accurate online adaptation methods, and fusion of trackers. In this paper, we unify such goals by proposing a novel tracking methodology…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
Accurately tracking and predicting behaviors of surrounding objects are key prerequisites for intelligent systems such as autonomous vehicles to achieve safe and high-quality decision making and motion planning. However, there still remain…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the category of tame functors. We show how this pseudo-metric can be…
Existing visual tracking methods usually localize a target object with a bounding box, in which the performance of the foreground object trackers or detectors is often affected by the inclusion of background clutter. To handle this problem,…
Multiple Object Tracking (MOT) has rapidly progressed in recent years. Existing works tend to design a single tracking algorithm to perform both detection and association. Though ensemble learning has been exploited in many tasks, i.e,…
High-resolution radar sensors are able to resolve multiple detections per object and therefore provide valuable information for vehicle environment perception. For instance, multiple detections allow to infer the size of an object or to…
A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination…
In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs.…
This paper assumes prior detections of multiple targets at each time instant, and uses a graph-based approach to connect those detections across time, based on their position and appearance estimates. In contrast to most earlier works in…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…