Related papers: An Efficient Solution to the 2D Visibility Problem…
This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The…
In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an $xy$-monotone grid path connects the two endpoints without hitting an…
Optimizing robot poses and the map simultaneously has been shown to provide more accurate SLAM results. However, for non-feature based SLAM approaches, directly optimizing all the robot poses and the whole map will greatly increase the…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form…
In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…
Implicit neural representations have shown promising potential for the 3D scene reconstruction. Recent work applies it to autonomous 3D reconstruction by learning information gain for view path planning. Effective as it is, the computation…
This paper investigates the usefulness of reasoning about the uncertain presence of obstacles during path planning, which typically stems from the usage of probabilistic occupancy grid maps for representing the environment when mapping via…
We study hyperplane covering problems for finite grid-like structures in $\mathbb{R}^d$. We call a set $\mathcal{C}$ of points in $\mathbb{R}^2$ a conical grid if the line $y = a_i$ intersects $\mathcal{C}$ in exactly $i$ points, for some…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel…
Heuristic search algorithms, e.g. A*, are the commonly used tools for pathfinding on grids, i.e. graphs of regular structure that are widely employed to represent environments in robotics, video games etc. Instance-independent heuristics…
We describe a general method of detecting valid chains or links of pieces on a two-dimensional grid. Specifically, using the example of the chess variant known as Switch-Side Chain-Chess (SSCC). Presently, no foolproof method of detecting…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent…
A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…
Given a grid terrain T and a viewpoint v, the viewshed of v is the set of grid points of T that are visible from v. To decide whether a point p is visible one needs to interpolate the elevation of the terrain along the line-of-sight vp.…