Results 1  10
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216
Meshless methods: An overview and recent developments
 Computer Methods in Applied Mechanics and Engineering
, 1996
"... Meshless approximations based on moving least squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enablepadaptivity to be achieved. Methods for constructing discontinuous approx ..."
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Cited by 140 (10 self)
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Meshless approximations based on moving least squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enablepadaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least square approximations. The paper concludes with some sample calculations. 1
Is Learning The nth Thing Any Easier Than Learning The First?
 Advances in Neural Information Processing Systems
, 1996
"... This paper investigates learning in a lifelong context. Lifelong learning addresses situations in which a learner faces a whole stream of learning tasks. Such scenarios provide the opportunity to transfer knowledge across multiple learning tasks, in order to generalize more accurately from less trai ..."
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Cited by 139 (3 self)
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This paper investigates learning in a lifelong context. Lifelong learning addresses situations in which a learner faces a whole stream of learning tasks. Such scenarios provide the opportunity to transfer knowledge across multiple learning tasks, in order to generalize more accurately from less training data. In this paper, several different approaches to lifelong learning are described, and applied in an object recognition domain. It is shown that across the board, lifelong learning approaches generalize consistently more accurately from less training data, by their ability to transfer knowledge across learning tasks. 1 Introduction Supervised learning is concerned with approximating an unknown function based on examples. Virtually all current approaches to supervised learning assume that one is given a set of inputoutput examples, denoted by X , which characterize an unknown function, denoted by f . The target function f is drawn from a class of functions, F , and the learner is gi...
The approximation power of moving leastsquares
 Math. Comp
, 1998
"... Abstract. A general method for nearbest approximations to functionals on Rd, using scattereddata information is discussed. The method is actually the moving leastsquares method, presented by the BackusGilbert approach. It is shown that the method works very well for interpolation, smoothing and ..."
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Cited by 108 (6 self)
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Abstract. A general method for nearbest approximations to functionals on Rd, using scattereddata information is discussed. The method is actually the moving leastsquares method, presented by the BackusGilbert approach. It is shown that the method works very well for interpolation, smoothing and derivatives ’ approximations. For the interpolation problem this approach gives Mclain’s method. The method is nearbest in the sense that the local error is bounded in terms of the error of a local best polynomial approximation. The interpolation approximation in Rd is shown to be a C ∞ function, and an approximation order result is proven for quasiuniform sets of data points. 1.
Scattered Data Interpolation with Multilevel Splines
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1997
"... This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequen ..."
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Cited by 108 (9 self)
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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequence of bicubic Bspline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using Bspline refinement to reduce the sum of these functions into one equivalent Bspline function. Experimental results demonstrate that highfidelity reconstruction is possible from a selected set of sparse and irregular samples.
An Axiomatic Approach to Image Interpolation
, 1998
"... We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The ..."
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Cited by 85 (7 self)
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We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.
Learning Maps for Indoor Mobile Robot Navigation
 ARTIFICIAL INTELLIGENCE (ACCEPTED FOR PUBLICATION)
, 1997
"... Autonomous robots must be able to learn and maintain models of their environments. Research on mobile robot navigation has produced two major paradigms for mapping indoor environments: gridbased and topological. While gridbased methods produce accurate metric maps, their complexity often prohibits ..."
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Cited by 83 (12 self)
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Autonomous robots must be able to learn and maintain models of their environments. Research on mobile robot navigation has produced two major paradigms for mapping indoor environments: gridbased and topological. While gridbased methods produce accurate metric maps, their complexity often prohibits efficient planning and problem solving in largescale indoor environments. Topological maps, on the other hand, can be used much more efficiently, yet accurate and consistent topological maps are often difficult to learn and maintain in largescale environments, particularly if momentary sensor data is highly ambiguous. This paper describes an approach that integrates both paradigms: gridbased and topological. Gridbased maps are learned using artificial neural networks and naive Bayesian integration. Topological maps are generated on top of the gridbased maps, by partitioning the latter into coherent regions. By combining both paradigms, the approach presented here gains advantages from both worlds: accuracy/consistency and efficiency. The paper gives results for autonomous exploration, mapping and operation of a mobile robot in populated multiroom environments.
Image Warping with Scattered Data Interpolation Methods
, 1992
"... Image warping has many applications in art as well as in image processing. Usually, displacements are computed with mathematical functions or by transformations of a triangulation of control points. Here, different approaches based on scattered data interpolation methods are presented. These methods ..."
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Cited by 76 (3 self)
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Image warping has many applications in art as well as in image processing. Usually, displacements are computed with mathematical functions or by transformations of a triangulation of control points. Here, different approaches based on scattered data interpolation methods are presented. These methods provide smooth deformations with easily controllable behavior. The usefulness and performance of some selected classes of scattered data interpolation methods in this context is analyzed.
Image deformation using moving least squares
 ACM Trans. on Graph
, 2006
"... Figure 1: Deformation using Moving Least Squares. Original image with control points shown in blue (a). Moving Least Squares deformations using affine transformations (b), similarity transformations (c) and rigid transformations (d). We provide an image deformation method based on Moving Least Squar ..."
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Cited by 73 (2 self)
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Figure 1: Deformation using Moving Least Squares. Original image with control points shown in blue (a). Moving Least Squares deformations using affine transformations (b), similarity transformations (c) and rigid transformations (d). We provide an image deformation method based on Moving Least Squares using various classes of linear functions including affine, similarity and rigid transformations. These deformations are realistic and give the user the impression of manipulating realworld objects. We also allow the user to specify the deformations using either sets of points or line segments, the later useful for controlling curves and profiles present in the image. For each of these techniques, we provide simple closedform solutions that yield fast deformations, which can be performed in realtime.
Animating images with drawings
 Computer Graphics (SIGGRAPH’94
, 1994
"... The work described here extends the power of 2D animation with a form of texture mapping conveniently controlled by line drawings. By tracing points, line segments, spline curves, or filled regions on an image, the animator defines features which can be used to animate the image. Animations of the c ..."
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Cited by 70 (1 self)
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The work described here extends the power of 2D animation with a form of texture mapping conveniently controlled by line drawings. By tracing points, line segments, spline curves, or filled regions on an image, the animator defines features which can be used to animate the image. Animations of the control features deform the image smoothly. This development is in the tradition of "skeleton"based animation, and "feature"based image metamorphosis. By employing numerics developed in the computer vision community for rapid visual surface estimation, several important advantages are realized. Skeletons are generalized to include curved "bones, " the interpolating surface is better behaved, the expense of computing the animation is decoupled from the number of features in the drawing, and arbitrary holes or cuts in the interpolated surface can be accommodated. The same general scattered data interpolation technique is applied to the problem of mapping animation from one image and set of features to another, generalizing the prescriptive power of animated sequences and encouraging reuse of animated motion.
Curves and Surfaces for CAGD
, 1993
"... This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD – Computer Aided Geometric Design – until the middle 1980s. We adopt the definition that CAGD deals with the construction and representation of freeform curves, s ..."
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Cited by 52 (0 self)
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This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD – Computer Aided Geometric Design – until the middle 1980s. We adopt the definition that CAGD deals with the construction and representation of freeform curves, surfaces, or volumes. 1.