相关论文: Planar Visibility: Testing and Counting

Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by…

Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…

Given a simple polygon $P$ with $n$ vertices, we consider the problem of constructing a data structure for visibility queries: for any query point $q \in P$, compute the visibility polygon of $q$ in $P$. To obtain $O(\log n + k)$ query…

Visual counting, a task that aims to estimate the number of objects from an image/video, is an open-set problem by nature, i.e., the number of population can vary in [0, inf) in theory. However, collected data and labeled instances are…

This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers, and comparing them to…

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic…

Consider two entities with constant but not necessarily equal velocities, moving on two given piece-wise linear trajectories inside a simple polygon $P$. The Trajectory Range Visibility problem deals with determining the sub-trajectories on…

Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of…

We study points in cut-and-project sets which are visible from the origin, continuing a direction of inquiry initiated in [6,14] where the asymptotic density of visible points was investigated. We establish an error bound for the density of…

Visual data, such as an image or a sequence of video frames, is often naturally represented as a point set. In this paper, we consider the fundamental problem of finding a nearest set from a collection of sets, to a query set. This problem…

This paper proposes the problem of point-and-count as a test case to break the what-and-where deadlock. Different from the traditional detection problem, the goal is to discover key salient points as a way to localize and count the number…

An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…

We propose a new method to count objects of specific categories that are significantly smaller than the ground sampling distance of a satellite image. This task is hard due to the cluttered nature of scenes where different object categories…

Point clouds are widely used representations of 3D data, but determining the visibility of points from a given viewpoint remains a challenging problem due to their sparse nature and lack of explicit connectivity. Traditional methods, such…

A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general (Garg and Tamassia, 2001), it is a long-standing open problem to establish a tight upper bound…

Let $P$ be a simple polygon with $n$ vertices, and let $q \in P$ be a point in $P$. Let $k \in \{0, \dots, n - 1\}$. A point $p \in P$ is $k$-visible from $q$ if and only if the line segment $pq$ crosses the boundary of $P$ at most $k$…

Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model…

One of the primary challenges faced by deep learning is the degree to which current methods exploit superficial statistics and dataset bias, rather than learning to generalise over the specific representations they have experienced. This is…

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…

Recent advances in 3D modeling provide us with real 3D datasets to answer queries, such as "What is the best position for a new billboard?" and "Which hotel room has the best view?" in the presence of obstacles. These applications require…