The Resource Shapes and diffeomorphisms, Laurent Younes

Shapes and diffeomorphisms, Laurent Younes

Label
Shapes and diffeomorphisms
Title
Shapes and diffeomorphisms
Statement of responsibility
Laurent Younes
Creator
Subject
Language
eng
Cataloging source
StDuBDS
Dewey number
516.15
Illustrations
illustrations
Index
index present
LC call number
  • QA445
  • QA1
  • QA3
LC item number
  • .Y68 2010
  • .A647 vol. 171
  • .A6 v. 171
Literary form
non fiction
Nature of contents
bibliography
Series statement
Applied mathematical sciences,
Series volume
v. 171
Label
Shapes and diffeomorphisms, Laurent Younes
Publication
Note
"A direct application of what is presented in the book is a branch of the computerized analysis of medical images called computational anatomy"--Back cover
Bibliography note
Includes bibliographical references and index
http://library.link/vocab/branchCode
  • net
Contents
  • Contents note continued: 1.15.Invariance for Affine and Projective Transformations -- 1.15.1.Affine Group -- 1.15.2.Projective Group -- 1.15.3.Affine Curvature -- 1.15.4.Projective Curvature -- 2.Medial Axis -- 2.1.Introduction -- 2.2.Structure of the Medial Axis -- 2.3.The Skeleton of a Polygon -- 2.4.Voronoi Diagrams -- 2.4.1.Voronoi Diagrams of Line Segments -- 2.4.2.Voronoi Diagrams of the Vertices of Polygonal Curves -- 2.5.Thinning -- 2.6.Sensitivity to Noise -- 2.7.Recovering the Initial Curve -- 2.8.Generating Curves from Medial and Skeletal Structures -- 2.8.1.Skeleton with Linear Branches -- 2.8.2.Skeletal Structures -- 3.Moment-Based Representation -- 3.1.Introduction -- 3.2.Moments of Inertia and Registration -- 3.3.Algebraic Moments -- 3.4.Rotation Invariance -- 4.Local Properties of Surfaces -- 4.1.Curves in Three Dimensions -- 4.2.Regular Surfaces -- 4.2.1.Examples -- 4.2.2.Changing Coordinates -- 4.2.3.Implicit Surfaces -- 4.3.Tangent Plane and Differentials --
  • Contents note continued: 10.10.Pros and Cons of Greedy Algorithms -- 10.11.Summary of the Results of Chapter 10 -- 10.11.1.Labeled Points -- 10.11.2.Images -- 10.11.3.Measures -- 10.11.4.Plane Curves -- 10.11.5.Surfaces -- 10.11.6.Vector Fields -- 10.11.7.Frames -- 10.11.8.Tensor Matching -- 11.Diffeomorphic Matching -- 11.1.Linearized Deformations -- 11.2.The Monge-Kantorovitch Problem -- 11.3.Optimizing Over Flows -- 11.4.Euler-Lagrange Equations and Gradient -- 11.5.Conservation of Momentum -- 11.5.1.Properties of the Momentum Conservation Equation -- 11.5.2.Existence of Solutions -- 11.5.3.Time Variation of the Eulerian Momentum -- 11.5.4.Hamiltonian Form or EPDiff -- 11.5.5.Case of Measure Momenta -- 11.6.Optimization Strategies for Flow-Based Matching -- 11.6.1.Gradient Descent in X2v -- 11.6.2.Gradient in the Hamiltonian Form -- 11.6.3.Gradient in the Initial Momentum -- 11.6.4.Shooting -- 11.6.5.Gradient in the Deformable Object -- 11.6.6.Image Matching --
  • Contents note continued: 11.6.7.Pros and Cons of the Optimization Strategies -- 11.7.Numerical Aspects -- 11.7.1.Discretization -- 11.7.2.Kernel-Related Numerics -- 12.Distances and Group Actions -- 12.1.General Principles -- 12.1.1.Distance Induced by a Group Action -- 12.1.2.Distance Altered by a Group Action -- 12.1.3.Transitive Action -- 12.1.4.Infinitesimal Approach -- 12.2.Invariant Distances Between Point Sets -- 12.2.1.Introduction -- 12.2.2.Space of Planar N-Shapes -- 12.2.3.Extension to Plane Curves -- 12.3.Parametrization-Invariant Distances Between Plane Curves -- 12.4.Invariant Metrics on Diffeomorphisms -- 12.4.1.Geodesic Equation -- 12.4.2.A Simple Example -- 12.4.3.Gradient Descent -- 12.4.4.Diffeomorphic Active Contours -- 12.5.Horizontality -- 12.5.1.Riemannian Projection -- 12.5.2.The Momentum Representation -- 13.Metamorphosis -- 13.1.Definitions -- 13.2.A New Metric on M -- 13.3.Euler-Lagrange Equations -- 13.4.Applications -- 13.4.1.Labeled Point Sets --
  • Contents note continued: 13.4.2.Deformable Images -- 13.4.3.Discretization of Image Metamorphosis -- 13.4.4.Application: Comparison of Plane Curves -- A.Elements from Hilbert Space Theory -- A.1.Definition and Notation -- A.2.Examples -- A.2.1.Finite-Dimensional Euclidean spaces -- A.2.2.l2 Space of Real Sequences -- A.2.3.L2 Space of Functions -- A.3.Orthogonal Spaces and Projection -- A.4.Orthonorma] Sequences -- A.5.The Riesz Representation Theorem -- A.6.Embeddings and the Duality Paradox -- A.6.1.Definition -- A.6.2.Examples -- A.6.3.The Duality Paradox -- A.7.Weak Convergence in a Hilbert Space -- A.8.The Fourier Transform -- B.Elements from Differential Geometry -- B.1.Introduction -- B.2.Differential Manifolds -- B.2.1.Definition -- B.2.2.Vector Fields, Tangent Spaces -- B.2.3.Maps Between Two Manifolds -- B.3.Submanifolds -- B.4.Lie Groups -- B.4.1.Definitions -- B.4.2.Lie Algebra of a Lie Group -- B.4.3.Finite-Dimensional Transformation Groups -- B.5.Group Action --
  • Contents note continued: 4.3.1.Tangent Plane -- 4.3.2.Differentials -- 4.4.Orientation and Normals -- 4.5.Integration on an Orientable Surface -- 4.6.The First Fundamental Form -- 4.6.1.Definition and Properties -- 4.6.2.The Divergence Theorem on Surfaces -- 4.7.Curvature and Second Fundamental Form -- 4.8.Curvature in Local Coordinates -- 4.9.Implicit Surfaces -- 4.9.1.The Delta-Function Trick -- 4.10.Gauss-Bonnet Theorem -- 4.11.Triangulated Surfaces -- 4.11.1.Definition and Notation -- 4.11.2.Estimating the Curvatures -- 5.Isocontours and Isosurfaces -- 5.1.Computing Isocontours -- 5.2.Computing Isosurfaces -- 6.Evolving Curves and Surfaces -- 6.1.Curve Evolution -- 6.1.1.Grassfires -- 6.1.2.Curvature Motion -- 6.1.3.Implicit Representation of the Curvature Motion -- 6.1.4.More on the Implementation -- 6.2.Surface Evolution -- 6.2.1.Mean Curvature Surface Flow -- 6.3.Gradient Flows -- 6.4.Active Contours -- 6.4.1.Introduction -- 6.4.2.First Variation and Gradient Descent --
  • Contents note continued: 6.4.3.Numerical Implementation -- 6.4.4.Initialization and Other Driving Techniques -- 6.4.5.Evolution of the Parametrization -- 6.4.6.Geometric Methods -- 6.4.7.Controlled Curve Evolution -- 6.4.8.Geometric Active Surfaces -- 6.4.9.Designing the V Function -- 6.4.10.Inside/Outside Optimization -- 6.4.11.Sobolev Active Contours -- 7.Deformable templates -- 7.1.Linear Representations -- 7.1.1.Energetic Representation -- 7.2.Probabilistic Decompositions -- 7.2.1.Deformation Axes -- 7.3.Stochastic Deformations Models -- 7.3.1.Generalities -- 7.3.2.Representation and Deformations of Planar Polygonal Shapes -- 7.4.Segmentation with Deformable Templates -- 8.Ordinary Differential Equations and Groups of Diffeomorphisms -- 8.1.Introduction -- 8.2.Flows and Groups of Diffeomorphisms -- 8.2.1.Definitions -- 8.2.2.Admissible Banach Spaces -- 8.2.3.Induced Group of Diffeomorphisms -- 8.2.4.A Distance on Gv -- 8.2.5.Properties of the Distance --
  • Contents note continued: 9.Building Admissible Spaces -- 9.1.Reproducing Kernel Hilbert Spaces -- 9.1.1.The Scalar Case -- 9.1.2.The Vector Case -- 9.2.Building V from Operators -- 9.3.Invariance of the Inner Product -- 9.3.1.Invariance: the Operator Side -- 9.3.2.Invariance: the Kernel Side -- 9.3.3.Examples of Radial Kernels -- 9.4.Mercer's Theorem -- 9.5.Thin-Plate Interpolation -- 9.6.Asymptotically Affine Kernels -- 10.Deformable Objects and Matching Functionals -- 10.1.General Principles -- 10.2.Variation with Respect to Diffeomorphisms -- 10.3.Labeled Point Matching -- 10.4.Image Matching -- 10.5.Measure Matching -- 10.5.1.Matching Densities -- 10.5.2.Dual RKHS Norms on Measures -- 10.6.Matching Curves and Surfaces -- 10.6.1.Curve Matching with Measures -- 10.6.2.Curve Matching with Vector Measures -- 10.6.3.Surface Matching -- 10.6.4.Induced Actions and Currents -- 10.7.Matching Vector Fields -- 10.8.Matching Fields of Frames -- 10.9.Tensor Matching --
  • Contents note continued: B.5.1.Definitions -- B.5.2.Homogeneous Spaces -- B.5.3.Infinitesimal Action -- B.6.Riemannian Manifolds -- B.6.1.Introduction -- B.6.2.Geodesic Distance -- B.6.3.Lie Groups with a Right-Invariant Metric -- B.6.4.Covariant Derivatives -- B.6.5.Parallel Transport -- B.6.6.A Hamiltonian Formulation -- C.Ordinary Differential Equations -- C.1.Differentials in Banach Space -- C.2.A Class of Ordinary Differential Equations -- C.2.1.Existence and Uniqueness -- C.2.2.Flow Associated to an ODE -- C.3.Numerical Integration of ODEs -- D.Optimization Algorithms -- D.1.Directions of Descent and Line Search -- D.2.Gradient Descent -- D.3.Newton and Quasi-Newton Directions -- D.4.Conjugate Gradient -- D.4.1.Linear Conjugate Gradient -- D.4.2.Nonlinear Conjugate Gradient -- E.Principal Component Analysis -- E.1.General Setting -- E.2.Computation of the Principal Components -- E.2.1.Small Dimension -- E.2.2.Large Dimension --
  • Contents note continued: E.3.Statistical Interpretation and Probabilistic PCA -- F.Dynamic Programming -- F.1.Minimization of a Function on a Tree -- F.2.Shortest Path on a Graph: a First Solution -- F.3.Dijkstra Algorithm -- F.4.Shortest Path in Continuous Space
  • Machine generated contents note: 1.Parametrized Plane Curves -- 1.1.Definitions -- 1.2.Geometric Equivalence -- 1.2.1.Open Curves -- 1.2.2.Closed Curves -- 1.3.Unit Tangent and Normal -- 1.4.Arc Length and Curvature -- 1.5.Expression in Coordinates -- 1.5.1.Cartesian Coordinates -- 1.5.2.Polar Coordinates -- 1.6.Euclidean Invariance -- 1.7.Enclosed Area and Green (Stokes) Formula -- 1.8.Rotation Index and Winding Number -- 1.9.More on Curvature -- 1.10.Discrete Curves and Curvature -- 1.10.1.Least-Squares Approximation -- 1.10.2.Curvature and Distance Maps -- 1.11.Invariance -- 1.11.1.Euclidean Invariance -- 1.11.2.Scale Invariance -- 1.11.3.Special Affine Transformations -- 1.11.4.Generalized Curvature -- 1.12.Characterization of a Bounded Convex Set -- 1.13.Non-Local Representations -- 1.13.1.Semi-Local Invariants -- 1.13.2.The Shape Context -- 1.13.3.Conformal Welding -- 1.14.Implicit Representation -- 1.14.1.Introduction -- 1.14.2.Implicit Polynomials --
Control code
000046520445
Dimensions
25 cm
Extent
xvii, 434 p.
Isbn
9783642120541
Lccn
2010926972
Other physical details
ill.
http://library.link/vocab/recordID
.b27160257
System control number
  • (OCoLC)632088149
  • springer3642120547

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
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