Distributed and Collaborative Synthetic Environments

Fast graphics workstations and increased computing power, together with improved interface technologies, have created new and diverse possibilities for developing and interacting with synthetic environments. A synthetic environment system is generally characterized by input/output devices that constitute the interface between the human senses and the synthetic environment generated by the computer; and a computation system running a real-time simulation of the environment. A basic need of a synthetic environment system is that of giving the user a plausible reproduction of the visual aspect of the objects with which he is interacting. The goal of our Shastra research project is to provide a substrate of geometric data structures and algorithms which allow the distributed construction and modification of the environment, efficient querying of objects attributes, collaborative interaction with the environment, fast computation of collision detection and visibility information for efficient dynamic simulation and real-time scene display. In particular, we address the following issues: (1) A geometric framework for modeling and visualizing synthetic environments and interacting with them. We highlight the functions required for the geometric engine of a synthetic environment system. (2) A distribution and collaboration substrate that supports construction, modification, and interaction with synthetic environments on networked desktop machines

Theory and Practice of I/O efficient Algorithms for Multidimensional Batched Searching Problems

Extended AbstractWe describe a powerful framework for designing efficient batch algorithms for certain large-scale dynamic problems that must be solved using external memory. The class of problems we consider, which we call colorable external decomposable problems, include rectangle intersection, orthogonal line segment intersection, range searching, and point location. We are particularly interested in these problems in two and higher dimensions. They have numerous applications in geographic information systems (GIS), spatial databases, and VLSI and CAD design. We present simplified algorithms for problems previously solved by more complicated approaches (such as rectangle intersection), and we present efficient algorithms for problems not previously solved in an efficient way (such as point location and higher dimensional versions of range searching and rectangle intersection). We give experimental results concerning the running time for our approach applied to the red-blue rectangle intersection problem, which is a key component of the extremely important database operation spatial join. Our algorithm scales well with the problem size, and for large problems sizes it greatly outperforms the well-known sweepline approach

Multibody Multipole Methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: 1) a deterministic series expansion-based method; 2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic

Similarity K-d tree method for sparse point pattern matching with underlying non-rigidity

We propose a method for matching non-affinely related sparse model and data point-sets of identical cardinality, similar spatial distribution and orientation. To establish a one-to-one match, we introduce a new similarity K-dimensional tree. We construct the tree for the model set using spatial sparsity priority order. A corresponding tree for the data set is then constructed, following the sparsity information embedded in the model tree. A matching sequence between the two point sets is generated by traversing the identically structured trees. Experiments on synthetic and real data confirm that this method is applicable to robust spatial matching of sparse point-sets under moderate non-rigid distortion and arbitrary scaling, thus contributing to non-rigid point-pattern matching. © 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved

Automatic Merging of Lidar Point-Clouds Using Data from Low-Cost GPS/IMU Systems

Stationary lidar (Light Detection and Ranging) systems are often used to collect 3-D data (point clouds) that can be used for terrain modelling. The lidar gathers scans which are then merged together to map a terrain. Typically this is done using a variant of the well-known Iterated Closest Point (ICP) algorithm when position and pose of the lidar scanner is not accurately known. One difficulty with the ICP algorithms is that they can give poor results when points that are not common to both scans (outliers) are matched together. With the advent of MEMS (microelectromechanical systems)-based GPS/IMU systems, it is possible to gather coarse position and pose information at a low cost. This information is not accurate enough to merge point clouds directly, but can be used to assist the ICP algorithm during the merging process. This paper presents a method called Sphere Outlier Removal (SOR), which accurately identifies outliers and inliers, a necessary prerequisite to using the ICP algorithm. SOR incorporates the information from a low cost GPS/IMU to perform this identification. Examples are presented which illustrate the improvement in the accuracy of merged point clouds when the SOR algorithm is used

LAZY SHORTEST PATH COMPUTATION IN DYNAMIC GRAPHS

We address the problem of single-source shortest path computation in digraphs with non-negative edge weights subjected to frequent edge weight decreases such that only some shortest paths are requested in-between updates. We optimise a recent semidynamic algorithm for weight decreases previously reported to be the fastest one in various conditions, resulting in important time savings that we demonstrate for the problem of incremental path map construction in usersteered image segmentation. Moreover, we extend the idea of lazy shortest path computation to digraphs subjected to both edge weight increases and decreases, comparing favourably to the fastest recent state-of-the-art algorithm