Related papers: Translation Invariant Fr\'echet Distance Queries
We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path…
Biological processes like growth, aging, and disease progression are generally studied with follow-up scans taken at different time points, i.e., with image time series (TS) based analysis. Comparison between TS representing a biological…
Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing,…
In this paper, we present an algorithm for evaluating lexical similarity between a given language and several reference language clusters. As an input, we have a list of concepts and the corresponding translations in all considered…
We consider a range-search variant of the closest-pair problem. Let $\varGamma$ be a fixed shape in the plane. We are interested in storing a given set of $n$ points in the plane in some data structure such that for any specified translate…
The Persistent Homology Transform (PHT) summarizes a shape in $\mathbb{R}^m$ by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathbb{S}^{m-1}$. It enjoys strong theoretical guarantees,…
The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit…
For a given a graph, a distance oracle is a data structure that answers distance queries between pairs of vertices. We introduce an $O(n^{5/3})$-space distance oracle which answers exact distance queries in $O(\log n)$ time for $n$-vertex…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…
We study the problem of finding the $k$ most similar trajectories to a given query trajectory. Our work is inspired by the work of Grossi et al. [6] that considers trajectories as walks in a graph. Each visited vertex is accompanied by a…
Evaluating the Quality of a Synthesized Motion with the Fr\'echet Motion Distance
Cosine similarity is a popular distance measure that measures the similarity between two vectors in the inner product space. It is widely used in many data classification algorithms like K-Nearest Neighbors, Clustering etc. This study…
Dictionary lookup methods are popular in dealing with ambiguous letters which were not recognized by Optical Character Readers. However, a robust dictionary lookup method can be complex as apriori probability calculation or a large…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…
Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the…
In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced\-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of…