相关论文: Planar Visibility: Testing and Counting

Sequence to Sequence models struggle at compositionality and systematic generalisation even while they excel at many other tasks. We attribute this limitation to their failure to internalise constructions conventionalised form meaning…

Linearizability of concurrent data structures is usually proved by monolithic simulation arguments relying on the identification of the so-called linearization points. Regrettably, such proofs, whether manual or automatic, are often…

Counting the number of items in a visual scene remains a fundamental yet challenging task in computer vision. Traditional approaches to solving this problem rely on domain-specific counting architectures, which are trained using datasets…

We analyze the observability of motion estimates from the fusion of visual and inertial sensors. Because the model contains unknown parameters, such as sensor biases, the problem is usually cast as a mixed identification/filtering, and the…

Handling visual complexity is a challenging problem in visualization owing to the subjectiveness of its definition and the difficulty in devising generalizable quantitative metrics. In this paper we address this challenge by measuring the…

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general…

Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…

In agile software development, test code can considerably contribute to the overall source code size. Being a valuable asset both in terms of verification and documentation, the composition of a test suite needs to be well understood in…

In this paper, we consider the problem of determining in polynomial time whether a given planar point set $P$ of $n$ points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing $P$, and present…

Recognizing and reasoning about occluded (partially or fully hidden) objects is vital to understanding visual scenes, as occlusions frequently occur in real-world environments and act as obstacles for spatial comprehension. To test models'…

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural…

Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…

An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigate the problem of computing an obstacle…

This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze…

The ability to discriminate between large and small quantities is a core aspect of basic numerical competence in both humans and animals. In this work, we examine the extent to which the state-of-the-art neural networks designed for vision…

A graph $G$ with vertex set $\{v_1,v_2,\ldots,v_n\}$ is an intersection graph of segments if there are segments $s_1,\ldots,s_n$ in the plane such that $s_i$ and $s_j$ have a common point if and only if $\{v_i,v_j\}$ is an edge of~$G$. In…

Programming based approaches to reasoning tasks have substantially expanded the types of questions models can answer about visual scenes. Yet on benchmark visual reasoning data, when models answer correctly, they produce incorrect programs…

Mechanistic interpretability seeks to uncover how internal components of neural networks give rise to predictions. A persistent challenge, however, is disentangling two often conflated notions: decodability--the recoverability of…

Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is…

Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$, respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ and $B$ are linearly separable. Our algorithm exploits the…