Related papers: Scenic Routes with Weighted Points in 2D

Consider a 2D coordinate space with a set of red and a set of blue points. We define a scenic point as a point that is equidistant to a red point and a blue point. The set of contiguous scenic points form a scenic path. The perpendicular…

In this work, we introduce the problem of scenic routes among points in Rd. The key development is the nature of the problem in terms of both defining the concept of scenic points and scenic routes and then coming up with algorithms that…

When users search for the routes between two places using map based services, these services compute and provide the top candidate routes based on shortest geometric distances or ideal time consuming. However, other real factors like…

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…

Every human likes choices. But today's fast route planning algorithms usually compute just a single route between source and target. There are beginnings to compute alternative routes, but this topic has not been studied thoroughly. Often,…

We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual…

For intelligent robots to interact in meaningful ways with their environment, they must understand both the geometric and semantic properties of the scene surrounding them. The majority of research to date has addressed these mapping…

This article proposes a new path planning method for addressing multi-level terrain situations. The proposed method includes innovations in three aspects: 1) the pre-processing of point cloud maps with a multi-level skip-list structure and…

Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…

An algorithm for 3D terrain-following area coverage path planning is presented. Multiple adjacent paths are generated that are (i) locally apart from each other by a distance equal to the working width of a machinery, while (ii)…

We outline an alternative approach to the geometric notion of a saddle point for real-valued functions of two variables. It is argued that this is more natural compared to the usual treatment of this topic in standard texts on Calculus.

We compute the distance-dependent two-point function of vertex-bicolored planar maps, i.e., maps whose vertices are colored in black and white so that no adjacent vertices have the same color. By distance-dependent two-point function, we…

Semantic 2D maps are commonly used by humans and machines for navigation purposes, whether it's walking or driving. However, these maps have limitations: they lack detail, often contain inaccuracies, and are difficult to create and…

A comprehensive semantic understanding of a scene is important for many applications - but in what space should diverse semantic information (e.g., objects, scene categories, material types, texture, etc.) be grounded and what should be its…

This paper introduces a new definition of multiscale neighborhoods in 3D point clouds. This definition, based on spherical neighborhoods and proportional subsampling, allows the computation of features with a consistent geometrical meaning,…

A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…

A set of points $S$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is called a 2-distance set if the set of pairwise distances between the points has cardinality two. The 2-distance set is called spherical if its points lie on the unit…

In the last decade, autonomous navigation for roboticshas been leveraged by deep learning and other approachesbased on machine learning. These approaches have demon-strated significant advantages in robotics performance. Butthey have the…

To autonomously navigate and plan interactions in real-world environments, robots require the ability to robustly perceive and map complex, unstructured surrounding scenes. Besides building an internal representation of the observed scene…

3D point cloud segmentation aims to assign semantic labels to individual points in a scene for fine-grained spatial understanding. Existing methods typically adopt data augmentation to alleviate the burden of large-scale annotation.…