Related papers: Minimum Opaque Covers for Polygonal Regions
An invisibility device should guide light around an object as if nothing were there, regardless where the light comes from. Ideal invisibility devices are impossible due to the wave nature of light. This paper develops a general recipe for…
Let $\cal R$ be a set of $n$ colored imprecise points, where each point is colored by one of $k$ colors. Each imprecise point is specified by a unit disk in which the point lies. We study the problem of computing the smallest and the…
A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of…
With the vigorous development of computer vision, oriented object detection has gradually been featured. In this paper, a novel differentiable angle coder named phase-shifting coder (PSC) is proposed to accurately predict the orientation of…
We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (\UDC) problem asks for a subset of disks of minimum total weight that covers all given points. \UDC\ is one of the…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
Many optical measurement techniques, such as light scattering from wavelength-scale particles or detecting motion from a surface with an optical lever, encode information in a complex radiation pattern. Extracting all available information…
Object detection remains as one of the most notorious open problems in computer vision. Despite large strides in accuracy in recent years, modern object detectors have started to saturate on popular benchmarks raising the question of how…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…
Given a set $P$ of $n$ points and a set $S$ of $m$ disks in the plane, the disk coverage problem asks for a smallest subset of disks that together cover all points of $P$. The problem is NP-hard. In this paper, we consider a line-separable…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
3D object detection using LiDAR point clouds is a fundamental task in the fields of computer vision, robotics, and autonomous driving. However, existing 3D detectors heavily rely on annotated datasets, which are both time-consuming and…
We revisit a natural variant of geometric set cover, called minimum-membership geometric set cover (MMGSC). In this problem, the input consists of a set $S$ of points and a set $\mathcal{R}$ of geometric objects, and the goal is to find a…
A spectrahedron is the feasible set of a semidefinite program, SDP, i.e., the intersection of an affine set with the positive semidefinite cone. While strict feasibility is a generic property for random problems, there are many classes of…
The development of robust, real-time optical methods for the detection and tracking of particles in complex multiple scattering media is a problem of practical importance in a number of fields, including environmental monitoring, air…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…
We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center…
Weakly supervised object detection aims at learning precise object detectors, given image category labels. In recent prevailing works, this problem is generally formulated as a multiple instance learning module guided by an image…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…