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The integrable dynamics of discrete and continuous curves ∗
, 1994
"... We show that the following geometric properties of the motion of discrete and continuous curves select integrable dynamics: i) the motion of the curve takes place in the N dimensional sphere of radius R, ii) the curve does not stretch during the motion, iii) the equations of the dynamics do not depe ..."
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We show that the following geometric properties of the motion of discrete and continuous curves select integrable dynamics: i) the motion of the curve takes place in the N dimensional sphere of radius R, ii) the curve does not stretch during the motion, iii) the equations of the dynamics do
Pal’s problem for continuous curves
"... In 1940 J.F. Pal posed the following problem [2]: Let (X, ρ) be a metric space and let c: [0, 1] → X be a continuous curve and n a positive integer. Is there a partition 0 < s1 < s2 < · · · sn < 1 such that ρ(c(si−1), c(si)) = ρ(c(si), c(si+1)), for i = 1, 2,..., n, where s0 = 0 and ..."
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In 1940 J.F. Pal posed the following problem [2]: Let (X, ρ) be a metric space and let c: [0, 1] → X be a continuous curve and n a positive integer. Is there a partition 0 < s1 < s2 < · · · sn < 1 such that ρ(c(si−1), c(si)) = ρ(c(si), c(si+1)), for i = 1, 2,..., n, where s0 = 0
Contour Tracking By Stochastic Propagation of Conditional Density
, 1996
"... . In Proc. European Conf. Computer Vision, 1996, pp. 343356, Cambridge, UK The problem of tracking curves in dense visual clutter is a challenging one. Trackers based on Kalman filters are of limited use; because they are based on Gaussian densities which are unimodal, they cannot represent s ..."
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Cited by 655 (23 self)
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simultaneous alternative hypotheses. Extensions to the Kalman filter to handle multiple data associations work satisfactorily in the simple case of point targets, but do not extend naturally to continuous curves. A new, stochastic algorithm is proposed here, the Condensation algorithm  Conditional
Characterization of absolutely continuous curves in wasserstein spaces
 Calc. Var. Partial Differential Equations
, 1997
"... Abstract. Let X be a separable, complete metric space and Pp(X) be the space of Borel probability measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this paper we prove that every absolutely continuous curve with finite penergy in the space Pp(X) can be represent ..."
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Cited by 30 (3 self)
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Abstract. Let X be a separable, complete metric space and Pp(X) be the space of Borel probability measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this paper we prove that every absolutely continuous curve with finite penergy in the space Pp(X) can
Continuous curves from infinite Kempe linkages
, 2009
"... In 1876 Kempe showed that any algebraic curve in the plane may be realised as the locus of one of the joints of a finite barjoint linkage. An often cited illustration of this is that there is a linkage that can write a person’s signature to any particular accuracy. An infinite analogue is establis ..."
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Cited by 6 (4 self)
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is established showing that any continuous curve in the plane is the curve of motion of a joint of an infinite barjoint linkage. This is curious, as continuous curves can be space filling. Moreover, there is a single infinite linkage that simultaneously traces everybody’s signature with no error whatsoever.
High Quality Rendering of TwoDimensional Continuous Curves
"... Abstract. This paper presents a new prefiltering technique for antialiasing twodimensional continuous curves which enables the correct handling of the geometry (self intersections, small loops, cusps, curves with high and small radius of curvature, etc.) using a generic class of filters. Moreover, ..."
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Abstract. This paper presents a new prefiltering technique for antialiasing twodimensional continuous curves which enables the correct handling of the geometry (self intersections, small loops, cusps, curves with high and small radius of curvature, etc.) using a generic class of filters. Moreover
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 510 (20 self)
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functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.
Seismic Response Analysis of Railway Continuous Curved Rigid
"... Abstract. To study the effects of seismic wave’s directions on bridges, the time history analytic method was used. Two bridge types, the railway continuous curved rigid frame bridge and the railway continuous straight rigid frame bridge, have been taken into account. Both the two same span bridges w ..."
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Abstract. To study the effects of seismic wave’s directions on bridges, the time history analytic method was used. Two bridge types, the railway continuous curved rigid frame bridge and the railway continuous straight rigid frame bridge, have been taken into account. Both the two same span bridges
TwoDimensional Visibility Charts for Continuous Curves
 PROC. OF ACM SYMPOSIUM ON SOLID MODELING AND APPLICATIONS, ANN ARBOR
"... This paper considers computation of visibility for twodimensional shapes whose boundaries are C continuous curves. We assume we are given a oneparameter family of candidate viewpoints, which may be interior or exterior to the object, and at finite or infinite locations. We consider how to comput ..."
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Cited by 2 (1 self)
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This paper considers computation of visibility for twodimensional shapes whose boundaries are C continuous curves. We assume we are given a oneparameter family of candidate viewpoints, which may be interior or exterior to the object, and at finite or infinite locations. We consider how
Dimension (in)equalities and Hölder continuous curves in fractal percolation
, 2010
"... We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the “dust”). In two dimensions, we also show that the set consisting of connected components lar ..."
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larger than one point is a.s. the union of nontrivial Hölder continuous curves, all with the same exponent. Finally, we give a short proof of the fact that in two dimensions, any curve in the limiting set must have Hausdorff dimension strictly larger than 1.
Results 1  10
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1,126,150