Related papers: A metric for sets of trajectories that is practica…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…

With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…

Predicting human trajectories is a challenging task due to the complexity of pedestrian behavior, which is influenced by external factors such as the scene's topology and interactions with other pedestrians. A special challenge arises from…

This paper presents a generalization of the trajectory general optimal sub-pattern assignment (GOSPA) metric for evaluating multi-object tracking algorithms that provide trajectory estimates with track-level uncertainties. This metric…

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…

We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…

In this paper, we propose a new metric which measures the distance between two finite sets of tracks (a track is a path of either a real or estimated target). This metric is based on the same principle as the Optimal Subpattern Assignment…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…

Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…

This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches.…

We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…

Similarity search is the problem of finding in a collection of objects those that are similar to a given query object. It is a fundamental problem in modern applications and the objects considered may be as diverse as locations in space,…

Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…

The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining…

This paper proposes and evaluates a new metric. This metric will overcome a limitation of the Optimal Subpattern Assignment (OSPA) metric mentioned by Schuhmacher et al.: the OSPA distance between two sets of points is insensitive to the…

Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…

Trajectories represent the mobility of moving objects and thus is of great value in data mining applications. However, trajectory data is enormous in volume, so it is expensive to store and process the raw data directly. Trajectories are…