Related papers: Weighted distance transforms generalized to module…

This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…

The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted…

We discuss two versions of the Fr\'echet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance…

In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…

Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…

The computation of the geometric transformation between a reference and a target image, known as registration or alignment, corresponds to the projection of the target image onto the transformation manifold of the reference image (the set…

We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…

This paper considers the problem of estimating a matrix that encodes pairwise distances in a finite metric space (or, more generally, the edge weight matrix of a network) under the barycentric coding model (BCM) with respect to the…

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…

Chamfer Distance (CD) is widely used as a metric to quantify difference between two point clouds. In point cloud completion, Chamfer Distance (CD) is typically used as a loss function in deep learning frameworks. However, it is generally…

We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations).…

High calorie intake in the human body on the one hand, has proved harmful in numerous occasions leading to several diseases and on the other hand, a standard amount of calorie intake has been deemed essential by dieticians to maintain the…

One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

We consider the problem of choosing Euclidean points to maximize the sum of their weighted pairwise distances, when each point is constrained to a ball centered at the origin. We derive a dual minimization problem and show strong duality…

The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the…