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67,171
Point Set Surfaces
, 2001
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
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Cited by 299 (41 self)
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We
Defining PointSet Surfaces
, 2005
"... The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. ..."
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Cited by 180 (2 self)
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The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field
Algebraic point set surfaces
 IN PROCEEDINGS SIGGRAPH ’07
, 2007
"... In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar M ..."
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Cited by 80 (8 self)
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In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar
Registration of Multiple Point Sets
 Proc. 13 th Int. Conf. on Pattern Recognition
, 1996
"... Registering 3D point sets subject to rigid body motion is a common problem in computer vision. The optimal transformation is usually specified to be the minimum of a weighted least squares cost. The case of 2 point sets has been solved by several authors using analytic methods such as SVD. In this p ..."
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Cited by 67 (1 self)
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Registering 3D point sets subject to rigid body motion is a common problem in computer vision. The optimal transformation is usually specified to be the minimum of a weighted least squares cost. The case of 2 point sets has been solved by several authors using analytic methods such as SVD
Wavelets on Irregular Point Sets
 Phil. Trans. R. Soc. Lond. A
, 1999
"... this article we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In particular we focus on subdivision schemes and commutation rules. Several examples are included. ..."
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Cited by 49 (0 self)
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this article we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In particular we focus on subdivision schemes and commutation rules. Several examples are included.
FixedPoint Sets of Autohomeomorphisms . . .
 PROC. OF THE AMERICAN MATHEMATICAL SOCIETY
, 1995
"... We investigate fixedpoint sets of autohomeomorphisms of compact Fspaces. If the space in question is finite dimensional (in the sense of covering dimension), then the fixedpoint set is a Pset; on the other hand there is an infinitedimensional compact Fspace with an involution whose fixedpo ..."
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We investigate fixedpoint sets of autohomeomorphisms of compact Fspaces. If the space in question is finite dimensional (in the sense of covering dimension), then the fixedpoint set is a Pset; on the other hand there is an infinitedimensional compact Fspace with an involution whose fixedpoint
Anisotropic smoothing of point sets
 COMPUTER AIDED GEOMETRIC DESIGN
, 2005
"... The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set ..."
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Cited by 20 (0 self)
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The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set
HOMEOMORPHISMS OF TWOPOINT SETS
"... Abstract. Given a cardinal κ ≤ c, a subset of the plane is said to be a κpoint set if and only it it meets every line in precisely κ many points. In response to a question of Cobb, we show that for all 2 ≤ κ, λ < c there exists a κpoint set which is homeomorphic to a λpoint set, and further, w ..."
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Abstract. Given a cardinal κ ≤ c, a subset of the plane is said to be a κpoint set if and only it it meets every line in precisely κ many points. In response to a question of Cobb, we show that for all 2 ≤ κ, λ < c there exists a κpoint set which is homeomorphic to a λpoint set, and further
Halving Point Sets
, 1998
"... Given n points in R d , a hyperplane is called halving if it has at most bn=2c points on either side. How many partitions of a point set (into the points on one side, on the hyperplane, and on the other side) by halving hyperplanes can be realized by an npoint set in R d? ..."
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Cited by 5 (0 self)
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Given n points in R d , a hyperplane is called halving if it has at most bn=2c points on either side. How many partitions of a point set (into the points on one side, on the hyperplane, and on the other side) by halving hyperplanes can be realized by an npoint set in R d?
Symmetries of twopoint sets
, 2008
"... A twopoint set is a subset of the plane which meets every planar line in exactly twopoints. We discuss the problem “What are the topological symmetries of a twopoint set?”. Our main results assert the existence of twopoint sets which are rigid and the existence of twopoint sets which are invari ..."
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Cited by 2 (2 self)
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A twopoint set is a subset of the plane which meets every planar line in exactly twopoints. We discuss the problem “What are the topological symmetries of a twopoint set?”. Our main results assert the existence of twopoint sets which are rigid and the existence of twopoint sets which
Results 1  10
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67,171