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139,351
Arrangements of Planar Curves
"... Abstract: Computing arrangements of curves is a fundamental and challenging problem in computational geometry as leading to many practical applications in a wide range of fields, especially in robot motion planning and computer vision. In this survey paper we present the state of the art for computi ..."
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for computing the arrangement of planar curves, considering various classes of curves, from lines to arbitrary curves. 1
Measuring Linearity of Planar Curves
"... Abstract In this paper we define a new linearity measure which can be applied to open planar curve segments. We have considered the sum of the distances between the curve end points and the curve centroid. We have shown that this sum is bounded from above by the length of the curve segment considere ..."
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Abstract In this paper we define a new linearity measure which can be applied to open planar curve segments. We have considered the sum of the distances between the curve end points and the curve centroid. We have shown that this sum is bounded from above by the length of the curve segment
Intrinsic stabilizers of planar curves
 IN THIRD EUROPEAN CONFERENCE ON COMPUTER VISION (ECCV'94
, 1994
"... Regularization offers a powerful framework for signal reconstruction by enforcing weak constraints through the use of stabilizers. Stabilizers are functionals measuring the degree of smoothness of a surface. The nature of those functionals constrains the properties of the reconstructed signal. In th ..."
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Cited by 7 (5 self)
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shape distortion. We first introduce an extension of Tikhonov stabilizers that offers natural scale control of regularity. We then introduce the intrinsic stabilizers for planar curves that apply smoothness constraints on the curvature pro le instead of the parameter space.
Planar Curve Representation and Matching
 In British Machine Vision Conference
, 1998
"... In this paper, we discuss a method for representing and matching planar curves. The technique is based on using calculations from concentric circles to represent each curve by two sets of angles. The angles are defined by vectors constructed from the center point of the circles and the points on ..."
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Cited by 1 (0 self)
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In this paper, we discuss a method for representing and matching planar curves. The technique is based on using calculations from concentric circles to represent each curve by two sets of angles. The angles are defined by vectors constructed from the center point of the circles and the points
The KhintchineGroshev theorem for planar curves
, 1999
"... The analogue of the classical Khintchine{Groshev theorem, a fundamental result in metric Diophantine approximation, is established for smooth planar curves with nonvanishing curvature almost everywhere. ..."
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Cited by 3 (2 self)
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The analogue of the classical Khintchine{Groshev theorem, a fundamental result in metric Diophantine approximation, is established for smooth planar curves with nonvanishing curvature almost everywhere.
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
, 1991
"... This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set o ..."
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Cited by 307 (2 self)
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This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set
INHOMOGENEOUS DIOPHANTINE APPROXIMATION ON PLANAR CURVES
, 903
"... Abstract. The inhomogeneous metric theory for the set of simultaneously ψapproximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous KhintchineJarník type theorems recently established in [3] and [10]. The key lies in obtaining essentially the best p ..."
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Cited by 8 (2 self)
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Abstract. The inhomogeneous metric theory for the set of simultaneously ψapproximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous KhintchineJarník type theorems recently established in [3] and [10]. The key lies in obtaining essentially the best
Homotopic Morphing of Planar Curves
"... This paper presents an algorithm for morphing between closed, planar piecewiseC1 curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed curve ..."
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This paper presents an algorithm for morphing between closed, planar piecewiseC1 curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed
Scalebased description and recognition of planar curves and twodimensional shapes
, 1986
"... The problem of finding a description, at varying levels of detail, for planar curves and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Pathbased Gaussian smoothing techniques are applied to the curve to ..."
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Cited by 213 (3 self)
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The problem of finding a description, at varying levels of detail, for planar curves and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Pathbased Gaussian smoothing techniques are applied to the curve
Multiresolution morphing of planar curves
 Computing
, 2007
"... We present a multiresolution morphing algorithm using “asrigidaspossible ” shape interpolation combined with an anglelength based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details ..."
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Cited by 2 (1 self)
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We present a multiresolution morphing algorithm using “asrigidaspossible ” shape interpolation combined with an anglelength based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage
Results 1  10
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