Related papers: Near-Delaunay Metrics

Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…

Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…

Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…

Finding best architectures of learning machines, such as deep neural networks, is a well-known technical and theoretical challenge. Recent work by Mellor et al (2021) showed that there may exist correlations between the accuracies of…

Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperbolic surface of genus $g$ has a simplicial Delaunay…

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as $\delta$-quasi-self-similar sets, and some other geometric notions in Euclidean…

In the study of depth functions it is important to decide whether we want such a function to be sensitive to multimodality or not. In this paper we analyze the Delaunay depth function, which is sensitive to multimodality and compare this…

The local angle property of the (order-$1$) Delaunay triangulations of a generic set in $\mathbb{R}^2$ asserts that the sum of two angles opposite a common edge is less than $\pi$. This paper extends this property to higher order and uses…

We propose a novel measure for template matching named Deformable Diversity Similarity -- based on the diversity of feature matches between a target image window and the template. We rely on both local appearance and geometric information…

Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…

Artificial neural networks (NN) are instrumental in realizing highly-automated driving functionality. An overarching challenge is to identify best safety engineering practices for NN and other learning-enabled components. In particular,…

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…

Human similarity judgments are inconsistent with Euclidean, Hamming, Mahalanobis, and the majority of measures used in the extensive literatures on similarity and dissimilarity. From intrinsic properties of brain circuitry, we derive…

This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…

We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a…

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…

With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish…

In this article, recent works on 2D Constrained Delaunay triangulation(CDT) algorithms have been reported. Since the review of CDT algorithms presented by de Floriani(Issues on Machine Vision, Springer Vienna, pg. 95--104, 1989), different…

A new interactive approach to navigate on approximations of in general non-convex but connected Pareto fronts is introduced. Given a finite number of precalculated representative Pareto-efficient solutions, an adapted Delaunay triangulation…

This paper aims to theoretically analyze the complexity of feature transformations encoded in piecewise linear DNNs with ReLU layers. We propose metrics to measure three types of complexities of transformations based on the information…