A Sweep-Plane Algorithm for Calculating the Isolation of Mountains

One established metric to classify the significance of a mountain peak is its isolation. It specifies the distance between a peak and the closest point of higher elevation. Peaks with high isolation dominate their surroundings and provide a nice view from the top. With the availability of worldwide Digital Elevation Models (DEMs), the isolation of all mountain peaks can be computed automatically. Previous algorithms run in worst case time that is quadratic in the input size. We present a novel sweep-plane algorithm that runs in time ?(nlog n+pT_NN) where n is the input size, p the number of considered peaks and T_NN the time for a 2D nearest-neighbor query in an appropriate geometric search tree. We refine this to a two-level approach that has high locality and good parallel scalability. Our implementation reduces the time for calculating the isolation of every peak on Earth from hours to minutes while improving precision

Algorithms for Triangles, Cones & Peaks

Three different geometric objects are at the center of this dissertation: triangles, cones and peaks. In computational geometry, triangles are the most basic shape for planar subdivisions. Particularly, Delaunay triangulations are a widely used for manifold applications in engineering, geographic information systems, telecommunication networks, etc. We present two novel parallel algorithms to construct the Delaunay triangulation of a given point set. Yao graphs are geometric spanners that connect each point of a given set to its nearest neighbor in each of $k$ cones drawn around it. They are used to aid the construction of Euclidean minimum spanning trees or in wireless networks for topology control and routing. We present the first implementation of an optimal $\mathcal{O}(n \log n)$-time sweepline algorithm to construct Yao graphs. One metric to quantify the importance of a mountain peak is its isolation. Isolation measures the distance between a peak and the closest point of higher elevation. Computing this metric from high-resolution digital elevation models (DEMs) requires efficient algorithms. We present a novel sweep-plane algorithm that can calculate the isolation of all peaks on Earth in mere minutes

Architectures for online simulation-based inference applied to robot motion planning

Robotic systems have enjoyed significant adoption in industrial and field applications in structured environments, where clear specifications of the task and observations are available. Deploying robots in unstructured and dynamic environments remains a challenge, being addressed through emerging advances in machine learning. The key open issues in this area include the difficulty of achieving coverage of all factors of variation in the domain of interest, satisfying safety constraints, etc. One tool that has played a crucial role in addressing these issues is simulation - which is used to generate data, and sometimes as a world representation within the decision-making loop. When physical simulation modules are used in this way, a number of computational problems arise. Firstly, a suitable simulation representation and fidelity is required for the specific task of interest. Secondly, we need to perform parameter inference of physical variables being used in the simulation models. Thirdly, there is the need for data assimilation, which must be achieved in real-time if the resulting model is to be used within the online decision-making loop. These are the motivating problems for this thesis. In the first section of the thesis, we tackle the inference problem with respect to a fluid simulation model, where a sensorised UAV performs path planning with the objective of acquiring data including gas concentration/identity and IMU-based wind estimation readings. The task for the UAV is to localise the source of a gas leak, while accommodating the subsequent dispersion of the gas in windy conditions. We present a formulation of this problem that allows us to perform online and real-time active inference efficiently through problem-specific simplifications. In the second section of the thesis, we explore the problem of robot motion planning when the true state is not fully observable, and actions influence how much of the state is subsequently observed. This is motivated by the practical problem of a robot performing suction in the surgical automation setting. The objective is the efficient removal of liquid while respecting a safety constraint - to not touch the underlying tissue if possible. If the problem were represented in full generality, as one of planning under uncertainty and hidden state, it could be hard to find computationally efficient solutions. Once again, we make problem-specific simplifications. Crucially, instead of reasoning in general about fluid flows and arbitrary surfaces, we exploit the observations that the decision can be informed by the contour tree skeleton of the volume, and the configurations in which the fluid would come to rest if unperturbed. This allows us to address the problem as one of iterative shortest path computation, whose costs are informed by a model estimating the shape of the underlying surface. In the third and final section of the thesis, we propose a model for real-time parameter estimation directly from raw pixel observations. Through the use of a Variational Recurrent Neural Network model, where the latent space is further structured by penalising for fit to data from a physical simulation, we devise an efficient online inference scheme. This is first shown in the context of a representative dynamic manipulation task for a robot. This task involves reasoning about a bouncing ball that it must catch – using as input the raw video from an environment-mounted camera and accommodating noise and variations in the object and environmental conditions. We then show that the same architecture lends itself to solving inference problems involving more complex dynamics, by applying this to measurement inversion of ultrafast X-Ray scattering data to infer molecular geometry

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum