Medial Axis Approximation and Regularization

Medial axis is a classical shape descriptor. Among many good properties, medial axis is thin, centered in the shape, and topology preserving. Therefore, it is constantly sought after by researchers and practitioners in their respective domains. However, two barriers remain that hinder wide adoption of medial axis. First, exact computation of medial axis is very difficult. Hence, in practice medial axis is approximated discretely. Though abundant approximation methods exist, they are either limited in scalability, insufficient in theoretical soundness, or susceptible to numerical issues. Second, medial axis is easily disturbed by small noises on its defining shape. A majority of current works define a significance measure to prune noises on medial axis. Among them, local measures are widely available due to their efficiency, but can be either too aggressive or conservative. While global measures outperform local ones in differentiating noises from features, they are rarely well-defined or efficient to compute. In this dissertation, we attempt to address these issues with sound, robust and efficient solutions. In Chapter 2, we propose a novel medial axis approximation called voxel core. We show voxel core is topologically and geometrically convergent to the true medial axis. We then describe a straightforward implementation as a result of our simple definition. In a variety of experiments, our method is shown to be efficient and robust in delivering topological promises on a wide range of shapes. In Chapter 3, we present Erosion Thickness (ET) to regularize instability. ET is the first global measure in 3D that is well-defined and efficient to compute. To demonstrate its usefulness, we utilize ET to generate a family of shape revealing and topology preserving skeletons. Finally, we point out future directions, and potential applications of our works in real world problems

Scouting algorithms for field robots using triangular mesh maps

Labor shortage has prompted researchers to develop robot platforms for agriculture field scouting tasks. Sensor-based automatic topographic mapping and scouting algorithms for rough and large unstructured environments were presented. It involves moving an image sensor to collect terrain and other information and concomitantly construct a terrain map in the working field. In this work, a triangular mesh map was first used to represent the rough field surface and plan exploring strategies. A 3D image sensor model was used to simulate collection of field elevation information.A two-stage exploring policy was used to plan the next best viewpoint by considering both the distance and elevation change in the cost function. A greedy exploration algorithm based on the energy cost function was developed; the energy cost function not only considers the traveling distance, but also includes energy required to change elevation and the rolling resistance of the terrain. An information-based exploration policy was developed to choose the next best viewpoint to maximise the information gain and minimize the energy consumption. In a partially known environment, the information gain was estimated by applying the ray tracing algorithm. The two-part scouting algorithm was developed to address the field sampling problem; the coverage algorithm identifies a reasonable coverage path to traverse sampling points, while the dynamic path planning algorithm determines an optimal path between two adjacent sampling points.The developed algorithms were validated in two agricultural fields and three virtual fields by simulation. Greedy exploration policy, based on energy consumption outperformed other pattern methods in energy, time, and travel distance in the first 80% of the exploration task. The exploration strategy, which incorporated the energy consumption and the information gain with a ray tracing algorithm using a coarse map, showed an advantage over other policies in terms of the total energy consumption and the path length by at least 6%. For scouting algorithms, line sweeping methods require less energy and a shorter distance than the potential function method

Network Survivability Analysis: Coarse-Graining And Graph-Theoretic Strategies

In this dissertation, the interplay between geographic information about the network and the principal properties and structure of the underlying graph are used to quantify the structural and functional survivability of the network. This work focuses on the local aspect of survivability by studying the propagation of loss in the network as a function of the distance of the fault from a given origin-destination node pair

An exploration of graph algorithms and graph databases

With data becoming larger in quantity, the need for complex, efficient algorithms to solve computationally complex problems has become greater. In this thesis we evaluate a selection of graph algorithms; we provide a novel algorithm for solving and approximating the Longest Simple Cycle problem, as well as providing novel implementations of other graph algorithms in graph database systems.The first area of exploration is finding the Longest Simple Cycle in a graph problem. We propose two methods of finding the longest simple cycle. The first method is an exact approach based on a flow-based Integer Linear Program. The second is a multi-start local search heuristic which uses a simple depth-first search as a basis for a cycle, and improves this with four perturbation operators.Secondly, we focus on implementing the Minimum Dominating Set problem into graph database systems. An unoptimised greedy heuristic solution to the Minimum Dominating Set problem is implemented into a client-server system using a declarative query language, an embedded database system using an imperative query language and a high level language as a direct comparison. The performance of the graph back-end on the database systems is evaluated. The language expressiveness of the query languages is also explored. We identify limitations of the query methods of the database system, and propose a function that increases the functionality of the queries

Surface parameterization over regular domains

Surface parameterization has been widely studied and it has been playing a critical role in many geometric processing tasks in graphics, computer-aided design, visualization, vision, physical simulation and etc. Regular domains, such as polycubes, are favored due to their structural regularity and geometric simplicity. This thesis focuses on studying the surface parameterization over regular domains, i.e. polycubes, and develops effective computation algorithms. Firstly, the motivation for surface parameterization and polycube mapping is introduced. Secondly, we briefly review existing surface parameterization techniques, especially for extensively studied parameterization algorithms for topological disk surfaces and parameterizations over regular domains for closed surfaces. Then we propose a polycube parameterization algorithm for closed surfaces with general topology. We develop an efficient optimization framework to minimize the angle and area distortion of the mapping. Its applications on surface meshing, inter-shape morphing and volumetric polycube mapping are also discussed