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Navigation and guidance of autonomous vehicles is a fundamental problem in robotics, which has attracted intensive research in recent decades. This report is mainly concerned with provable collision avoidance of multiple autonomous vehicles…

In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Di\'osi,…

Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. SHREC'11 robust feature detection and description benchmark simulates…

While 3D object detection and pose estimation has been studied for a long time, its evaluation is not yet completely satisfactory. Indeed, existing datasets typically consist in numerous acquisitions of only a few scenes because of the…

Consider a system of N identical hard spherical particles moving in a d-dimensional box and undergoing elastic, possibly multi-particle, collisions. We develop a new algorithm that recovers the pre-collision state from the post-collision…

Discriminative correlation filters show excellent performance in object tracking. However, in complex scenes, the apparent characteristics of the tracked target are variable, which makes it easy to pollute the model and cause the model…

In this paper, we introduce a moving object detection algorithm for fisheye cameras used in autonomous driving. We reformulate the three commonly used constraints in rectilinear images (epipolar, positive depth and positive height…

Motion planning is a central challenge in robotics, with learning-based approaches gaining significant attention in recent years. Our work focuses on a specific aspect of these approaches: using machine-learning techniques, particularly…

We consider the motion of a finite though large number $N$ of hard spheres in the whole space $\mathbb{R}^n$. Particles move freely until they experience elastic collisions. We use our recent theory of Compensated Integrability in order to…

For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…

We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a…

Astronomical surveys and the growing involvement of amateur astronomers are producing more sky images than ever before, and this calls for automated processing methods that are accurate and robust. Detecting Deep Sky Objects -- such as…

The central collision between two solid spheres or the normal collision between a sphere and a plate are important to understand in detail before studying more complex particle interactions. Models exist to describe this basic problem but…

Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…

Point cloud models are a common shape representation for several reasons. Three-dimensional scanning devices are widely used nowadays and points are an attractive primitive for rendering complex geometry. Nevertheless, there is not much…

Simultaneous localisation and mapping (SLAM) is the problem of autonomous robots to construct or update a map of an undetermined unstructured environment while simultaneously estimate the pose in it. The current trend towards self-driving…