Load-Balancing for Parallel Delaunay Triangulations

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Comment: Short version submitted to EuroPar 201

Fast multipole networks

Two prerequisites for robotic multiagent systems are mobility and communication. Fast multipole networks (FMNs) enable both ends within a unified framework. FMNs can be organized very efficiently in a distributed way from local information and are ideally suited for motion planning using artificial potentials. We compare FMNs to conventional communication topologies, and find that FMNs offer competitive communication performance (including higher network efficiency per edge at marginal energy cost) in addition to advantages for mobility

Geometry Processing of Conventionally Produced Mouse Brain Slice Images

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as an application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data.Comment: 14 pages, 11 figure

Efficient Generating And Processing Of Large-Scale Unstructured Meshes

Unstructured meshes are used in a variety of disciplines to represent simulations and experimental data. Scientists who want to increase accuracy of simulations by increasing resolution must also increase the size of the resulting dataset. However, generating and processing a extremely large unstructured meshes remains a barrier. Researchers have published many parallel Delaunay triangulation (DT) algorithms, often focusing on partitioning the initial mesh domain, so that each rectangular partition can be triangulated in parallel. However, the comproblems for this method is how to merge all triangulated partitions into a single domain-wide mesh or the significant cost for communication the sub-region borders. We devised a novel algorithm --Triangulation of Independent Partitions in Parallel (TIPP) to deal with very large DT problems without requiring inter-processor communication while still guaranteeing the Delaunay criteria. The core of the algorithm is to find a set of independent} partitions such that the circumcircles of triangles in one partition do not enclose any vertex in other partitions. For this reason, this set of independent partitions can be triangulated in parallel without affecting each other. The results of mesh generation is the large unstructured meshes including vertex index and vertex coordinate files which introduce a new challenge \-- locality. Partitioning unstructured meshes to improve locality is a key part of our own approach. Elements that were widely scattered in the original dataset are grouped together, speeding data access. For further improve unstructured mesh partitioning, we also described our new approach. Direct Load which mitigates the challenges of unstructured meshes by maximizing the proportion of useful data retrieved during each read from disk, which in turn reduces the total number of read operations, boosting performance

The projector algorithm: a simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs

The Voronoi diagram is a certain geometric data structure which has numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that no essentially new algorithms have entered the game. In addition, most of the known algorithms are serial in nature and hence cast inherent difficulties on the possibility to compute the diagram in parallel. In this paper we present the projector algorithm: a new and simple algorithm which enables the (combinatorial) computation of 2D Voronoi diagrams. The algorithm is significantly different from previous ones and some of the involved concepts in it are in the spirit of linear programming and optics. Parallel implementation is naturally supported since each Voronoi cell can be computed independently of the other cells. A new combinatorial structure for representing the cells (and any convex polytope) is described along the way and the computation of the induced Delaunay graph is obtained almost automatically.Comment: This is a major revision; re-organization and better presentation of some parts; correction of several inaccuracies; improvement of some proofs and figures; added references; modification of the title; the paper is long but more than half of it is composed of proofs and references: it is sufficient to look at pages 5, 7--11 in order to understand the algorith

MRSL: AUTONOMOUS NEURAL NETWORK-BASED SELF-STABILIZING SYSTEM

Stabilizing and localizing the positioning systems autonomously in the areas without GPS accessibility is a difficult task. In this thesis we describe a methodology called Most Reliable Straight Line (MRSL) for stabilizing and positioning camera-based objects in 3-D space. The camera-captured images are used to identify easy-to-track points “interesting points� and track them on two consecutive images. The distance between each of interesting points on the two consecutive images are compared and one with the maximum length is assigned to MRSL, which is used to indicate the deviation from the original position. To correct this our trained algorithm is deployed to reduce the deviation by issuing relevant commands, this action is repeated until MRSL converges to zero. To test the accuracy and robustness, the algorithm was deployed to control positioning of a Quadcopter. It was demonstrated that the Quadcopter (a) was highly robust to any external forces, (b) can fly even if the Quadcopter experiences loss of engine, (c) can fly smoothly and positions itself on a desired location

A new methods of mobile object measurement by using radio frequency identification

In this study, the mobile robot conducts tag of RFID and the antennas’ reader was scattered at the indoor-outdoor environment, which represents the novelty of the study, as this has not been done in the previous studies. This protects the mobile robot from weight increase reduces the consumption of the battery. Moreover, mobile object increase demands an increase in cheap passive Radio Frequency Identification tags in the system of navigation. Techniques of Signal processing utilize both accompanied by the theories of electromagnetics in locating the robot’s position. Numerous antennas usage provides a breadth of comparisons. In this work, have been provide a new RFID tracking approach that can also be used for interior positioning. This technique employs RSS to gather the signal intensity of reference tags before they are used. The next step is to send a signal. Setting up Power Level ranges via reference tags uses strength as a setting parameter. Then, based on the intensity of the signal, you can determine how far away you are. Reference tags are used to match the signal intensity of track tags. Finally, when track tags are installed in indoor locations, they can be used to monitor the movement of people. It will use the arithmetic mean of the positions of surrounding reference tags to determine the location. Values. According to preliminary results from an experiment, our approach is more precise than the antenna system. Approximately 10 to 20 lines