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The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
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 505 (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
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 660 (8 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately
A comparison and evaluation of multiview stereo reconstruction algorithms.
 In Proc. Computer Vision and Pattern Recognition ’06,
, 2006
"... Abstract This paper presents a quantitative comparison of several multiview stereo reconstruction algorithms. Until now, the lack of suitable calibrated multiview image datasets with known ground truth (3D shape models) has prevented such direct comparisons. In this paper, we first survey multiv ..."
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Cited by 530 (14 self)
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Abstract This paper presents a quantitative comparison of several multiview stereo reconstruction algorithms. Until now, the lack of suitable calibrated multiview image datasets with known ground truth (3D shape models) has prevented such direct comparisons. In this paper, we first survey multi
On active contour models and balloons
 CVGIP: Image
"... The use.of energyminimizing curves, known as “snakes, ” to extract features of interest in images has been introduced by Kass, Witkhr & Terzopoulos (Znt. J. Comput. Vision 1, 1987,321331). We present a model of deformation which solves some of the problems encountered with the original method. ..."
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Cited by 588 (43 self)
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curve need no longer be close to the solution to converge. The curve passes over weak edges and is stopped only if the edge is strong. We give examples of extracting a ventricle in medical images. We have also made a first step toward 3D object reconstruction, by tracking the extracted contour on a
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 540 (59 self)
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’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2
Geodesic Active Contours
, 1997
"... A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both in ..."
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Cited by 1425 (47 self)
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demonstrate its power. The results may be extended to 3D object segmentation as well.
Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging
 MAGNETIC RESONANCE IN MEDICINE 58:1182–1195
, 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample kspace. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
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Cited by 538 (11 self)
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demonstrate improved spatial resolution and accelerated acquisition for multislice fast spinecho brain imaging and 3D contrast enhanced angiography.
3D Curves Reconstruction from Multiple Images
"... Abstract—In this paper, we propose a new approach for reconstructing 3D curves from a sequence of 2D images taken by uncalibrated cameras. A curve in 3D space is represented by a sequence of 3D points sampled along the curve, and the 3D points are reconstructed by minimizing the distances from their ..."
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method can reconstruct multiple 3D curves simultaneously from multiple images and it readily handles images with missing and/or partially occluded curves. Keywords3D curve reconstruction; partial occlusion; uncalibrated cameras I.
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 428 (21 self)
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the wavelet decomposition of the object. For instance, the nterm partial reconstruction f C n obtained by selecting the n largest terms in the curvelet series obeys ‖f − f C n ‖ 2 L2 ≤ C · n−2 · (log n) 3, n → ∞. This rate of convergence holds uniformly over a class of functions which are C 2 except
Results 1  10
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18,973