Related papers: Fr\'echet Distance for Curves, Revisited
In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…
We study the minimum number of distinct distances between point sets on two curves in $R^3$. Assume that one curve contains $m$ points and the other $n$ points. Our main results: (a) When the curves are conic sections, we characterize all…
Imagine you are a dog behind a fence $Q$ and a hiker is passing by at constant speed along the hiking path $P$. In order to fulfil your duties as a watchdog, you desire to bark as long as possible at the human. However, your barks can only…
The ropelength of a space curve is usually defined as the quotient of its length by its thickness: the radius of the largest embedded tube around the knot. This idea was extended to space polygons by Eric Rawdon, who gave a definition of…
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…
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…
Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the…
We study the problem of polygonal curve simplification under uncertainty, where instead of a sequence of exact points, each uncertain point is represented by a region, which contains the (unknown) true location of the vertex. The regions we…
The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains…
In machine learning and particularly in topological data analysis, $\epsilon$-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Given a polygonal curve P, a pointset S, and an \epsilon > 0, we study the problem of finding a polygonal curve Q whose vertices are from S and has a Frechet distance less or equal to \epsilon to curve P. In this problem, Q must visit every…
The computation of the elastic registration of two simple curves in higher dimensions and therefore of the elastic shape distance between them has been investigated by Srivastava et al. Assuming the first curve has one or more starting…
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…
Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…
We show how to represent a simple polygon $P$ by a grid (pixel-based) polygon $Q$ that is simple and whose Hausdorff or Fr\'echet distance to $P$ is small. For any simple polygon $P$, a grid polygon exists with constant Hausdorff distance…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
We provide statistical analysis methods for samples of curves when the image but not the parametrisation of the curves is of interest. A parametrisation invariant analysis can be based on the elastic distance of the curves modulo warping,…