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LOCAL GEOMETRY OF DEFORMABLE TEMPLATES
, 2005
"... In this paper, we discuss a geometrical model of a space of deformable images or shapes, in which infinitesimal variations are combinations of elastic deformations (warping) and of photometric variations. Geodesics in this space are related to velocitybased image warping methods, which have proved ..."
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Cited by 43 (9 self)
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In this paper, we discuss a geometrical model of a space of deformable images or shapes, in which infinitesimal variations are combinations of elastic deformations (warping) and of photometric variations. Geodesics in this space are related to velocitybased image warping methods, which have proved to yield efficient and robust estimations of diffeomorphisms in the case of large deformation. Here, we provide a rigorous and general construction of this infinite dimensional “shape manifold ” on which we place a Riemannian metric. We then obtain the geodesic equations, for which we show the existence and uniqueness of solutions for all times. We finally use this to provide a geometrically founded linear approximation of the deformations of shapes in the neighborhood of a given template.
On the nonlocal geometry of turbulence
 J OF FLUID MECH
, 2008
"... A multiscale methodology for the study of the nonlocal geometry of eddy structures in turbulence is developed. Starting from a given threedimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. ..."
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Cited by 8 (3 self)
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A multiscale methodology for the study of the nonlocal geometry of eddy structures in turbulence is developed. Starting from a given threedimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages
Local geometries and stabilities of Cu
"... The local geometry, energy stabilization, and pseudolocal t 1u vibration mode of the Cu + impurity in the alkali halide crystals have been investigated with the ab initio Perturbed Ion (aiPI) clusterinthe lattice methodology. The electronic structure of different clusters, containing up to ..."
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The local geometry, energy stabilization, and pseudolocal t 1u vibration mode of the Cu + impurity in the alkali halide crystals have been investigated with the ab initio Perturbed Ion (aiPI) clusterinthe lattice methodology. The electronic structure of different clusters, containing up
Modeling and rendering of points with local geometry
 IEEE TRANS. VISUAL. COMP. GRAPH.
, 2003
"... We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry in ..."
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Cited by 23 (3 self)
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We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry
Contentbased image retrieval at the end of the early years
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2000
"... The paper presents a review of 200 references in contentbased image retrieval. The paper starts with discussing the working conditions of contentbased retrieval: patterns of use, types of pictures, the role of semantics, and the sensory gap. Subsequent sections discuss computational steps for imag ..."
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Cited by 1618 (24 self)
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for image retrieval systems. Step one of the review is image processing for retrieval sorted by color, texture, and local geometry. Features for retrieval are discussed next, sorted by: accumulative and global features, salient points, object and shape features, signs, and structural combinations thereof
Isospectral Manifolds with Different Local Geometries
, 2001
"... We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral fou ..."
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Cited by 19 (6 self)
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We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral
ON LOCAL GEOMETRY OF FINITE MULTITYPE HYPERSURFACES
"... Abstract. This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in C n+1. We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite cons ..."
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Abstract. This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in C n+1. We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite
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 513 (20 self)
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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
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
, 1983
"... For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a patternr ..."
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Cited by 2096 (5 self)
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. ” Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain “chirality ” is the torsional handedness of four consecutive Ca positions and is positive for righthanded helices and negative for ideal twisted @sheets. Curved pieces are defined as “bends
Robust wide baseline stereo from maximally stable extremal regions
 In Proc. BMVC
, 2002
"... The widebaseline stereo problem, i.e. the problem of establishing correspondences between a pair of images taken from different viewpoints is studied. A new set of image elements that are put into correspondence, the so called extremal regions, is introduced. Extremal regions possess highly desir ..."
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Cited by 1016 (35 self)
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. Significant change of scale (3.5×), illumination conditions, outofplane rotation, occlusion, locally anisotropic scale change and 3D translation of the viewpoint are all present in the test problems. Good estimates of epipolar geometry (average distance from corresponding points to the epipolar line
Results 1  10
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