Related papers: Can we Compute the Similarity Between Surfaces?
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…
We present simple and practical $(1+\eps)$-approximation algorithm for the Frechet distance between curves. To analyze this algorithm we introduce a new realistic family of curves, $c$-packed curves, that is closed under simplification. We…
Let $P$ be a polygon with $k$ vertices. Let $R$ and $B$ be two simple, interior disjoint curves on the boundary of $P$, with $n$ and $m$ vertices. We show how to compute the Fr\'echet distance between $R$ and $B$ using the geodesic…
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…
The Fr\'{e}chet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently…
The classical and extensively-studied Fr\'echet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this…
A pseudo-polynomial time $(1 + \varepsilon)$-approximation algorithm is presented for computing the integral and average Fr\'{e}chet distance between two given polygonal curves $T_1$ and $T_2$. In particular, the running time is…
We study the $c$-approximate near neighbor problem under the continuous Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the curves into a…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…
We give algorithms to compute the Fr\'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…
We study the problem of constructing a data structure that can store a two-dimensional polygonal curve $P$, such that for any query segment $\overline{ab}$ one can efficiently compute the Fr\'{e}chet distance between $P$ and…
Let $\tau$ and $\sigma$ be two polygonal curves in $\mathbb{R}^d$ for any fixed $d$. Suppose that $\tau$ and $\sigma$ have $n$ and $m$ vertices, respectively, and $m\le n$. While conditional lower bounds prevent approximating the Fr\'echet…
The fine-grained complexity of computing the Fr\'echet distance has been a topic of much recent work, starting with the quadratic SETH-based conditional lower bound by Bringmann from 2014. Subsequent work established largely the same…
In 2012 Driemel et al. \cite{DBLP:journals/dcg/DriemelHW12} introduced the concept of $c$-packed curves as a realistic input model. In the case when $c$ is a constant they gave a near linear time $(1+\varepsilon)$-approximation algorithm…
Given two polygonal curves, there are many ways to define a notion of similarity between them. One popular measure is the Fr\'echet distance which has many desirable properties but is notoriously expensive to calculate, especially for…
This paper studies the $r$-range search problem for curves under the continuous Fr\'echet distance: given a dataset $S$ of $n$ polygonal curves and a threshold $r>0$, construct a data structure that, for any query curve $q$, efficiently…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…