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91
Locally weighted learning
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, ass ..."
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Cited by 594 (53 self)
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This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.
Multilevel Partition of Unity Implicits
 ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighti ..."
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Cited by 217 (8 self)
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We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape. Our approach
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 159 (7 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.
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 89 (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.
Construction of Vector Field Hierarchies
, 1999
"... We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using clustering and principal component analysis. The input to our algorithm is a discrete set of points with associated vectors. The algorithm generates a topdown segmentation o ..."
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Cited by 57 (4 self)
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We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using clustering and principal component analysis. The input to our algorithm is a discrete set of points with associated vectors. The algorithm generates a topdown segmentation of the discrete field by splitting clusters of points. We measure the error of the various approximation levels by measuring the discrepancy between streamlines generated by the original discrete field and its approximations based on much smaller discrete data sets. Our method assumes no particular structure of the field, nor does it require any topological connectivity information. It is possible to generate multiresolution representations of vector fields using this approach. Keywords: vector field visualization; Hardy's multiquadric method; binaryspace partitioning; data simplification. 1 Introduction The rapid increase in the power of computer systems coupled with the improving precis...
Spatial Free Form Deformation with Scattered Data Interpolation Methods
 GEOMETRIC MODELLING (COMPUTING SUPPL
, 1991
"... The problem of deforming a given spatial shape is treated. There are many examples of applications in visual computing: fitting surfaces to sampled data points in space, correction of distortions in tomographic imaging, modeling of free form geometric shapes, and animating metamorphoses of geometric ..."
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Cited by 42 (5 self)
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The problem of deforming a given spatial shape is treated. There are many examples of applications in visual computing: fitting surfaces to sampled data points in space, correction of distortions in tomographic imaging, modeling of free form geometric shapes, and animating metamorphoses of geometric objects. Our solution warps the space surrounding the given shape with the effect of deforming the embedded shape, too, with a function derived with scattered data interpolation methods from the displacements of a finite set of control points that can be placed arbitrarily and adaptively. We present algorithms implementing this idea on parametric surfaces and rasterized volume data.
Barycentric rational interpolation with no poles and high rates of approximation
 MATH
, 2006
"... It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that ha ..."
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Cited by 39 (7 self)
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It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no poles and arbitrarily high approximation orders, regardless of the distribution of the points. The family includes a construction of Berrut as a special case.
MemoryBased Neural Networks For Robot Learning
 Neurocomputing
, 1995
"... This paper explores a memorybased approach to robot learning, using memorybased neural networks to learn models of the task to be performed. Steinbuch and Taylor presented neural network designs to explicitly store training data and do nearest neighbor lookup in the early 1960s. In this paper their ..."
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Cited by 31 (8 self)
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This paper explores a memorybased approach to robot learning, using memorybased neural networks to learn models of the task to be performed. Steinbuch and Taylor presented neural network designs to explicitly store training data and do nearest neighbor lookup in the early 1960s. In this paper their nearest neighbor network is augmented with a local model network, which fits a local model to a set of nearest neighbors. This network design is equivalent to a statistical approach known as locally weighted regression, in which a local model is formed to answer each query, using a weighted regression in which nearby points (similar experiences) are weighted more than distant points (less relevant experiences). We illustrate this approach by describing how it has been used to enable a robot to learn a difficult juggling task. Keywords: memorybased, robot learning, locally weighted regression, nearest neighbor, local models. 1 Introduction An important problem in motor learning is approxim...
Efficient Reconstruction of Large Scattered Geometric Datasets Using the Partition of Unity and Radial Basis Functions
, 2004
"... We present a new scheme for the reconstruction of large geometric data. It is based on the wellknown radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and effi ..."
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Cited by 22 (1 self)
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We present a new scheme for the reconstruction of large geometric data. It is based on the wellknown radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and efficient solution to a great variety of 2D and 3D reconstruction problems, such as the reconstruction of implicit curves or surfaces with attributes starting from unorganized point sets, image or mesh repairing, shape morphing or shape deformation, etc. After having presented the theoretical background, the paper mainly focuses on implementation details and issues, as well as on applications and experimental results.
Surface reconstruction of noisy and defective data sets
 Proc. Visualization ’04
, 2004
"... We present a novel surface reconstruction algorithm that can recover highquality surfaces from noisy and defective data sets without any normal or orientation information. A set of new techniques are introduced to afford extra noise tolerability, robust orientation alignment, reliable outlier remov ..."
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Cited by 20 (2 self)
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We present a novel surface reconstruction algorithm that can recover highquality surfaces from noisy and defective data sets without any normal or orientation information. A set of new techniques are introduced to afford extra noise tolerability, robust orientation alignment, reliable outlier removal, and satisfactory feature recovery. In our algorithm, sample points are first organized by an octree. The points are then clustered into a set of monolithically singlyoriented groups. The inside/outside orientation of each group is determined through a robust voting algorithm. We locally fit an implicit quadric surface in each octree cell. The locally fitted implicit surfaces are then blended to produce a signed distance field using the modified Shepard’s method. We develop sophisticated iterative fitting algorithms to afford improved noise tolerance both in topology recognition and geometry accuracy. Furthermore, this iterative fitting algorithm, coupled with a local model selection scheme, provides a reliable sharp feature recovery mechanism even in the presence of bad input.