Results 1  10
of
65
Robot Pose Estimation in Unknown Environments by Matching 2D Range Scans
, 1994
"... A mobile robot exploring an unknown environment has no absolute frame of reference for its position, other than features it detects through its sensors. Using distinguishable landmarks is one possible approach, but it requires solving the object recognition problem. In particular, when the robot use ..."
Abstract

Cited by 270 (9 self)
 Add to MetaCart
(Show Context)
A mobile robot exploring an unknown environment has no absolute frame of reference for its position, other than features it detects through its sensors. Using distinguishable landmarks is one possible approach, but it requires solving the object recognition problem. In particular, when the robot uses twodimensional laser range scans for localization, it is difficult to accurately detect and localize landmarks in the environment (such as corners and occlusions) from the range scans. In this paper, we develop two new iterative algorithms to register a range scan to a previous scan so as to compute relative robot positions in an unknown environment, that avoid the above problems. The first algorithm is based on matching data points with tangent directions in two scans and minimizing a distance function in order to solve the displacementbetween the scans. The second algorithm establishes correspondences between points in the two scans and then solves the pointtopoint leastsquares probl...
Krylov Projection Methods For Model Reduction
, 1997
"... This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov p ..."
Abstract

Cited by 178 (3 self)
 Add to MetaCart
(Show Context)
This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczosbased methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also developed to form a complete modelreduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multipleinput multipleoutput systems, implementing parallelism, and avoiding a need for exact factors of large matrix pencils are all examined to various degrees.
Shape Reconstruction of 3D Bilaterally Symmetric Surfaces
, 2000
"... . The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoin ..."
Abstract

Cited by 38 (1 self)
 Add to MetaCart
(Show Context)
. The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required. The basic idea is that an image taken from a general, non frontal viewpoint, under nonfrontal illuminationcan be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, oneimagevariants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence bet...
Location errors in wireless embedded sensor networks: Sources, models, and effects on applications
 ACM SIGMOBILE Mobile Computing and Communications Review
, 2002
"... Wireless sensor networks monitor the physical world by taking measurements of physical phenomena. Those measurements, and consequently the results computed from the measurements, may be significantly inaccurate. Therefore, in order to properly design and use wireless sensor networks, one must develo ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
(Show Context)
Wireless sensor networks monitor the physical world by taking measurements of physical phenomena. Those measurements, and consequently the results computed from the measurements, may be significantly inaccurate. Therefore, in order to properly design and use wireless sensor networks, one must develop methods that take error sources, error propagation through optimization software, and ultimately their impact on applications, into consideration. In this paper, we focus on location discovery induced errors. We have selected location discovery as the object of our case study since essentially all sensor network computation and communication tasks are dependent on geographical node location data. First, we model the error in input parameters of the location discovery process. Then, we study the impact of errors on three selected applications: exposure, best and worstcase coverage, and shortest path routing. Furthermore, we examine how the choice of a specific objective function optimized during the location discovery process impacts the errors in results of different applications. I.
Structured Sampling And Reconstruction Of Illumination For Image Synthesis
, 1994
"... An important goal of image synthesis is to achieve accurate, efficient and consistent sampling and reconstruction of illumination varying over surfaces in an environment. A new approach is introduced for the treatment of diffuse polyhedral environments lit by area light sources, based on the identif ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
An important goal of image synthesis is to achieve accurate, efficient and consistent sampling and reconstruction of illumination varying over surfaces in an environment. A new approach is introduced for the treatment of diffuse polyhedral environments lit by area light sources, based on the identification of important properties of illumination structure. The properties of unimodality and curvature of illumination in unoccluded environments are used to develop a high quality sampling algorithm which includes error bounds. An efficient algorithm is presented to partition the scene polygons into a mesh of cells, in which the visible part of the source has the same topology. A fast incremental algorithm is presented to calculate the backprojection, which is an abstract representation of this topology. The behaviour of illumination in the penumbral regions is carefully studied, and is shown to be monotonic and well behaved within most of the mesh cells. An algorithm to reduce the mesh siz...
A BranchandPrune Solver for Distance Constraints
 SUBMITTED TO THE IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION
"... Given some geometric elements such as points and lines in R³, subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position analysis ..."
Abstract

Cited by 14 (9 self)
 Add to MetaCart
Given some geometric elements such as points and lines in R³, subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position analysis of serial and parallel manipulators) and CAD/CAM (such as the interactive placement of objects) can be formulated in this way. The strategy herein proposed consists in looking for some of the a priori unknown distances, whose derivation permits solving the problem rather trivially. Finding these distances relies on a branchandprune technique that iteratively eliminates from the space of distances entire regions which cannot contain any solution. This elimination is accomplished by applying redundant necessary conditions derived from the theory of Distance Geometry. The experimental results qualify this approach as a promising one.
Optimal Spline Fitting to Planar Shape
, 1993
"... Parametric spline models are used extensively in representing and coding planar curves. For many applications, it is desirable to be able to derive the spline representation from a set of sample points of the planar shape. The problem we address in this paper is to find a cubic spline model to op ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
(Show Context)
Parametric spline models are used extensively in representing and coding planar curves. For many applications, it is desirable to be able to derive the spline representation from a set of sample points of the planar shape. The problem we address in this paper is to find a cubic spline model to optimally approximate a given planar shape. We solve this problem by treating the control points which define the spline as variables and apply an optimization technique to minimize an error norm so as to find the best locations of the control points. The error norm, which is defined as the total squared distance of the curve sample points from the spline model, reflects the discrepancy between the spline and the original curve. The objective function for the optimization process is the error norm plus a term which ensures convergence to the correct solution. The initial locations of the control points are selected heuristically. We also describe an extension of this method, which allow...
Evaluating the Normal Distribution
 Journal of Statistical Software
, 2004
"... This article provides a little tablefree C function that evaluates the normal distribution with absolute error less than 8 × 10−16. A small extension provides relative error near the limit available in double precision: 14 to 16 digits, the limits determined mainly by the computer’s ability to eval ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
This article provides a little tablefree C function that evaluates the normal distribution with absolute error less than 8 × 10−16. A small extension provides relative error near the limit available in double precision: 14 to 16 digits, the limits determined mainly by the computer’s ability to evaluate exp(t) for large t. Results are compared with those provided by calls to erf or erfc functions, the best of which compare favorably, others do not, and all appear to be much more complicated than need be to get either absolute accuracy less than 10−15 or relative accuracy to the exp()limited 14–16 digits. Also provided: A short history of the error function erf and its intended use, as well as, in the ‘browse files ’ attachment, various erf or erfc versions used for comparison.
Resolving the Sign Ambiguity in the Singular Value Decomposition
, 2007
"... by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any w ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy.
Optimal Sensitivity Analysis of Linear Least Squares
, 2003
"... Results from the many years of work on linear least squares problems are combined with a new approach to perturbation analysis to explain in a definitive way the sensitivity of these problems to perturbation. Simple expressions are found for the asymptotic size of optimal backward errors for least s ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
Results from the many years of work on linear least squares problems are combined with a new approach to perturbation analysis to explain in a definitive way the sensitivity of these problems to perturbation. Simple expressions are found for the asymptotic size of optimal backward errors for least squares problems. It is shown that such formulas can be used to evaluate condition numbers. For full rank problems, Frobenius norm condition numbers are determined exactly, and spectral norm condition numbers are determined within a factor of squareroottwo. As a result, the necessary and sufficient criteria for well conditioning are established. A source of ill conditioning is found that helps explain the failure of simple iterative refinement. Some textbook discussions of ill conditioning are found to be fallacious, and some error bounds in the literature are found to unnecessarily overestimate the error. Finally, several open questions are described.