Related papers: Uncertain Curve Simplification
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…
A closed curve in the plane is weakly simple if it is the limit (in the Fr\'echet metric) of a sequence of simple closed curves. We describe an algorithm to determine whether a closed walk of length n in a simple plane graph is weakly…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
The article analyzes similarity of closed polygonal curves with respect to the Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that…
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…
The curvelet transform is a special type of wavelet transform, which is useful for estimating the locations and orientations of waves propagating in Euclidean space. We prove an uncertainty principle that lower-bounds the variance of these…
We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two…
Visibility graph of a simple polygon is a graph with the same vertex set in which there is an edge between a pair of vertices if and only if the segment through them lies completely inside the polygon. Each pair of adjacent vertices on the…
We present new approximation results on curve simplification and clustering under Fr\'echet distance. Let $T = \{\tau_i : i \in [n] \}$ be polygonal curves in $R^d$ of $m$ vertices each. Let $l$ be any integer from $[m]$. We study a…
Clustering trajectories is a central challenge when faced with large amounts of movement data such as GPS data. We study a clustering problem that can be stated as a geometric set cover problem: Given a polygonal curve of complexity $n$,…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…
Since its introduction to computational geometry by Alt and Godau in 1992, the Fr\'echet distance has been a mainstay of algorithmic research on curve similarity computations. The focus of the research has been on comparing polygonal…
The free space diagram is a popular tool to compute the well-known Fr\'echet distance. As the Fr\'echet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often,…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…