다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

/pdf/active-contours-without-edges-2tt3qz9lq0.pdf

Active contours without edges

A novel scheme for the detection of object boundaries is presented. The technique is based on active contours deforming according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric as defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved as showed by a number of examples. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. >

/pdf/geodesic-active-contours-4wqlqxa13k.pdf

Geodesic active contours

Introduction to support vector learning roadmap. Part 1 Theory: three remarks on the support vector method of function estimation, Vladimir Vapnik generalization performance of support vector machines and other pattern classifiers, Peter Bartlett and John Shawe-Taylor Bayesian voting schemes and large margin classifiers, Nello Cristianini and John Shawe-Taylor support vector machines, reproducing kernel Hilbert spaces, and randomized GACV, Grace Wahba geometry and invariance in kernel based methods, Christopher J.C. Burges on the annealed VC entropy for margin classifiers - a statistical mechanics study, Manfred Opper entropy numbers, operators and support vector kernels, Robert C. Williamson et al. Part 2 Implementations: solving the quadratic programming problem arising in support vector classification, Linda Kaufman making large-scale support vector machine learning practical, Thorsten Joachims fast training of support vector machines using sequential minimal optimization, John C. Platt. Part 3 Applications: support vector machines for dynamic reconstruction of a chaotic system, Davide Mattera and Simon Haykin using support vector machines for time series prediction, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel. Part 4 Extensions of the algorithm: reducing the run-time complexity in support vector machines, Edgar E. Osuna and Federico Girosi support vector regression with ANOVA decomposition kernels, Mark O. Stitson et al support vector density estimation, Jason Weston et al combining support vector and mathematical programming methods for classification, Bernhard Scholkopf et al.

Advances in kernel methods: support vector learning

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 interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical “snakes” based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.

Geodesic Active Contours

1 Introduction to Lie Groups- 11 Manifolds- Change of Coordinates- Maps Between Manifolds- The Maximal Rank Condition- Submanifolds- Regular Submanifolds- Implicit Submanifolds- Curves and Connectedness- 12 Lie Groups- Lie Subgroups- Local Lie Groups- Local Transformation Groups- Orbits- 13 Vector Fields- Flows- Action on Functions- Differentials- Lie Brackets- Tangent Spaces and Vectors Fields on Submanifolds- Frobenius' Theorem- 14 Lie Algebras- One-Parameter Subgroups- Subalgebras- The Exponential Map- Lie Algebras of Local Lie Groups- Structure Constants- Commutator Tables- Infinitesimal Group Actions- 15 Differential Forms- Pull-Back and Change of Coordinates- Interior Products- The Differential- The de Rham Complex- Lie Derivatives- Homotopy Operators- Integration and Stokes' Theorem- Notes- Exercises- 2 Symmetry Groups of Differential Equations- 21 Symmetries of Algebraic Equations- Invariant Subsets- Invariant Functions- Infinitesimal Invariance- Local Invariance- Invariants and Functional Dependence- Methods for Constructing Invariants- 22 Groups and Differential Equations- 23 Prolongation- Systems of Differential Equations- Prolongation of Group Actions- Invariance of Differential Equations- Prolongation of Vector Fields- Infinitesimal Invariance- The Prolongation Formula- Total Derivatives- The General Prolongation Formula- Properties of Prolonged Vector Fields- Characteristics of Symmetries- 24 Calculation of Symmetry Groups- 25 Integration of Ordinary Differential Equations- First Order Equations- Higher Order Equations- Differential Invariants- Multi-parameter Symmetry Groups- Solvable Groups- Systems of Ordinary Differential Equations- 26 Nondegeneracy Conditions for Differential Equations- Local Solvability- In variance Criteria- The Cauchy-Kovalevskaya Theorem- Characteristics- Normal Systems- Prolongation of Differential Equations- Notes- Exercises- 3 Group-Invariant Solutions- 31 Construction of Group-Invariant Solutions- 32 Examples of Group-Invariant Solutions- 33 Classification of Group-Invariant Solutions- The Adjoint Representation- Classification of Subgroups and Subalgebras- Classification of Group-Invariant Solutions- 34 Quotient Manifolds- Dimensional Analysis- 35 Group-Invariant Prolongations and Reduction- Extended Jet Bundles- Differential Equations- Group Actions- The Invariant Jet Space- Connection with the Quotient Manifold- The Reduced Equation- Local Coordinates- Notes- Exercises- 4 Symmetry Groups and Conservation Laws- 41 The Calculus of Variations- The Variational Derivative- Null Lagrangians and Divergences- Invariance of the Euler Operator- 42 Variational Symmetries- Infinitesimal Criterion of Invariance- Symmetries of the Euler-Lagrange Equations- Reduction of Order- 43 Conservation Laws- Trivial Conservation Laws- Characteristics of Conservation Laws- 44 Noether's Theorem- Divergence Symmetries- Notes- Exercises- 5 Generalized Symmetries- 51 Generalized Symmetries of Differential Equations- Differential Functions- Generalized Vector Fields- Evolutionary Vector Fields- Equivalence and Trivial Symmetries- Computation of Generalized Symmetries- Group Transformations- Symmetries and Prolongations- The Lie Bracket- Evolution Equations- 52 Recursion Operators, Master Symmetries and Formal Symmetries- Frechet Derivatives- Lie Derivatives of Differential Operators- Criteria for Recursion Operators- The Korteweg-de Vries Equation- Master Symmetries- Pseudo-differential Operators- Formal Symmetries- 53 Generalized Symmetries and Conservation Laws- Adjoints of Differential Operators- Characteristics of Conservation Laws- Variational Symmetries- Group Transformations- Noether's Theorem- Self-adjoint Linear Systems- Action of Symmetries on Conservation Laws- Abnormal Systems and Noether's Second Theorem- Formal Symmetries and Conservation Laws- 54 The Variational Complex- The D-Complex- Vertical Forms- Total Derivatives of Vertical Forms- Functionals and Functional Forms- The Variational Differential- Higher Euler Operators- The Total Homotopy Operator- Notes- Exercises- 6 Finite-Dimensional Hamiltonian Systems- 61 Poisson Brackets- Hamiltonian Vector Fields- The Structure Functions- The Lie-Poisson Structure- 62 Symplectic Structures and Foliations- The Correspondence Between One-Forms and Vector Fields- Rank of a Poisson Structure- Symplectic Manifolds- Maps Between Poisson Manifolds- Poisson Submanifolds- Darboux' Theorem- The Co-adjoint Representation- 63 Symmetries, First Integrals and Reduction of Order- First Integrals- Hamiltonian Symmetry Groups- Reduction of Order in Hamiltonian Systems- Reduction Using Multi-parameter Groups- Hamiltonian Transformation Groups- The Momentum Map- Notes- Exercises- 7 Hamiltonian Methods for Evolution Equations- 71 Poisson Brackets- The Jacobi Identity- Functional Multi-vectors- 72 Symmetries and Conservation Laws- Distinguished Functionals- Lie Brackets- Conservation Laws- 73 Bi-Hamiltonian Systems- Recursion Operators- Notes- Exercises- References- Symbol Index- Author Index

Applications of Lie Groups to Differential Equations

1 Geometric foundations 2 Lie groups 3 Representation theory 4 Jets and contact transformations 5 Differential invariants 6 Symmetries of differential equations 7 Symmetries of variational problems 8 Equivalence of coframes 9 Formulation of equivalence problems 10 Cartan's equivalence method 11 Involution 12 Prolongation of equivalence problems 13 Differential systems 14 Frobenius' theorem 15 The Cartan-Kahler existence theorem

/pdf/equivalence-invariants-and-symmetry-4i1xou04no.pdf

Equivalence, invariants, and symmetry

In this paper, we analyze the geometric active contour models discussed previously from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and efficiently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. >

/pdf/gradient-flows-and-geometric-active-contour-models-1hm3ut8mob.pdf

Gradient flows and geometric active contour models

A simple scaling argument shows that most integrable evolutionary systems, which are known to admit a bi-Hamiltonian structure, are, in fact, governed by a compatible trio of Hamiltonian structures. We demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons (solitary-wave solutions having compact support), or cusped and/or peaked solitons. A general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified Korteweg--de Vries equation, the nonlinear Schr\"odinger equation, the integrable Boussinesq system used to model the two-way propagation of shallow water waves, and the Ito system of coupled nonlinear wave equations. These hierarchies include a remarkable variety of interesting integrable nonlinear differential equations. \textcopyright{} 1996 The American Physical Society.

Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support.

We employ the new geometric active contour models, previously formulated, for edge detection and segmentation of magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound medical imagery. Our method is based on defining feature-based metrics on a given image which in turn leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus, the snake is attracted very quickly and efficiently to the desired feature.

/pdf/a-geometric-snake-model-for-segmentation-of-medical-imagery-3xjtyfbtt2.pdf

Peter J. Olver

Papers

Applications of Lie Groups to Differential Equations

Equivalence, invariants, and symmetry

Gradient flows and geometric active contour models

Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support.

A geometric snake model for segmentation of medical imagery