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QuasiInterpolation for Surface Reconstruction from Scattered Data with Radial Basis Function
"... Radial Basis Function (RBF) has been used in surface reconstruction methods to interpolate or approximate scattered data points, which involves solving a large linear system. The linear systems for determining coefficients of RBF may be illconditioned when processing a large point set, which lead ..."
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Radial Basis Function (RBF) has been used in surface reconstruction methods to interpolate or approximate scattered data points, which involves solving a large linear system. The linear systems for determining coefficients of RBF may be illconditioned when processing a large point set, which
QUADRATUREFREE QUASIINTERPOLATION ON THE SPHERE
"... Abstract. We construct certain quasiinterpolatory operators for approximation of functions on the sphere, using tensor product scattered data satisfying certain symmetry conditions. Our operators are constructed without using any quadrature formulas. We use instead a special class of orthonormal bi ..."
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Cited by 1 (1 self)
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Abstract. We construct certain quasiinterpolatory operators for approximation of functions on the sphere, using tensor product scattered data satisfying certain symmetry conditions. Our operators are constructed without using any quadrature formulas. We use instead a special class of orthonormal
Quasiinterpolants and Quasiinterpolation: Important Properties and Propositions of Terminology
, 1994
"... This paper is a reflexion on the main properties we demand to a quasiinterpolant. We give and compare the interest of the most used criteria, and explain the importance of the transfer function and of the "interpolating power of φ" to evaluate how far from the data (a, y_a)a&i ..."
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This paper is a reflexion on the main properties we demand to a quasiinterpolant. We give and compare the interest of the most used criteria, and explain the importance of the transfer function and of the "interpolating power of φ" to evaluate how far from the data (a, y
QuasiInterpolation in Shift Invariant Spaces
, 2000
"... Let s # 1 be an integer, # : R s # R be a compactly supported function, and S(#) denote the linear span of {#(  k) : k # Z s }. We consider the problem of approximating a continuous function f : R s # R on compact subsets of R s from the classes S(#(h)), h > 0, based on samples ..."
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Cited by 4 (2 self)
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on samples of the function at scattered sites in R s . We demonstrate how classical polynomial inequalities lead to the construction of local, quasiinterpolatory operators for this purpose. 1 Introduction An important subject in approximation theory is the study of shiftinvariant spaces generated by a
Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition
, 1998
"... Abstract. This paper is a survey of the inverse scattering problem for timeharmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newtontype methods for solving the inverse scattering problem for acoustic waves, including a brief discussi ..."
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Cited by 1072 (45 self)
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discussion of Tikhonov’s method for the numerical solution of illposed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 500 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs
Scatter/Gather: A Clusterbased Approach to Browsing Large Document Collections
, 1992
"... Document clustering has not been well received as an information retrieval tool. Objections to its use fall into two main categories: first, that clustering is too slow for large corpora (with running time often quadratic in the number of documents); and second, that clustering does not appreciably ..."
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Cited by 772 (12 self)
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Document clustering has not been well received as an information retrieval tool. Objections to its use fall into two main categories: first, that clustering is too slow for large corpora (with running time often quadratic in the number of documents); and second, that clustering does not appreciably improve retrieval. We argue that these problems arise only when clustering is used in an attempt to improve conventional search techniques. However, looking at clustering as an information access tool in its own right obviates these objections, and provides a powerful new access paradigm. We present a document browsing technique that employs document clustering as its primary operation. We also present fast (linear time) clustering algorithms which support this interactive browsing paradigm. 1 Introduction Document clustering has been extensively investigated as a methodology for improving document search and retrieval (see [15] for an excellent review). The general assumption is that mutua...
A formal basis for architectural connection
 ACM TRANSACTIONS ON SOJIWARE ENGINEERING AND METHODOLOGY
, 1997
"... ..."
Bsplines and quasiinterpolants
, 2012
"... We present the construction of a multivariate normalized Bspline basis for the quadratic C 1continuous spline space defined over a triangulation in R s (s ≥ 1) with a generalized PowellSabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of u ..."
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of local function values. The multivariate quasiinterpolants reproduce quadratic polynomials and have an optimal approximation order.
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