Related papers: An Algorithm for Illuminating $n$ Nonoverlapping C…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
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…
With the advent of autonomous vehicles, LiDAR and cameras have become an indispensable combination of sensors. They both provide rich and complementary data which can be used by various algorithms and machine learning to sense and make…
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…
We describe a numerical algorithm which simulates the propagation of light in inhomogeneous universes, using the multiple lens-plane method. The deformation and deflection of light beams as they interact with each lens plane are computed…
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
The Delaunay triangulation (DT) is one of the most common and useful triangulations of point sets $P$ in the plane. DT is not unique when $P$ is degenerate, specifically when it contains quadruples of co-circular points. One way to achieve…
We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental…
Non-line-of-sight (NLOS) imaging is based on capturing the multi-bounce indirect reflections from the hidden objects. Active NLOS imaging systems rely on the capture of the time of flight of light through the scene, and have shown great…
In this paper, it is proposed to solve the problem of triangulation for calibrated omnidirectional cameras through the optimisation of ray-pairs on the projective sphere. The proposed solution boils down to finding the roots of a quadratic…
This paper introduces path triangulation of points in a bounded, simply connected surface region, replacing ordinary triangles in a Delaunay triangulation with path triangles from homotopy theory. A {\bf path triangle} has a border that is…
In the efforts for safer roads, ensuring adequate vertical clearance above roadways is of great importance. Frequently, trees or other vegetation is growing above the roads, blocking the sight of traffic signs and lights and posing danger…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Accurate environment maps are a key component for rendering photorealistic outdoor scenes with coherent illumination. They enable captivating visual arts, immersive virtual reality, and a wide range of engineering and scientific…
Circumstellar disks play a key role in the understanding of stellar systems. Direct imaging of such extended structures is a challenging task. Current post-processing techniques, first tailored for exoplanets imaging, tend to produce…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
We propose a novel filter for segmenting the regions of interest from LiDAR 3D point cloud for multirotor aerial vehicles. It is specially targeted for real-time applications and works on sparse LiDAR point clouds without preliminary…
Cameras are a crucial exteroceptive sensor for self-driving cars as they are low-cost and small, provide appearance information about the environment, and work in various weather conditions. They can be used for multiple purposes such as…
We report on a novel detection system for collinear laser spectroscopy which provides an almost $4\pi$ solid angle for fluorescence photon detection by employing curved surface mirrors. Additional parabolic angular filters offer passive…
Navigating unmanned aerial vehicles (UAVs) through cluttered and dynamic environments remains a significant challenge, particularly when dealing with fast-moving or sudden-appearing obstacles. This paper introduces a complete LiDAR-based…