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Spectral Geometry Of Shapes

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Spectral Geometry of Shapes

Spectral Geometry of Shapes Book
Author : Jing Hua,Zichun Zhong
Publisher : Academic Press
Release : 2020-01-15
ISBN : 0128138424
Language : En, Es, Fr & De

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Book Description :

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource. Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc. Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practice Describes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysis Gives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

Shape Optimization and Spectral Theory

Shape Optimization and Spectral Theory Book
Author : Antoine Henrot
Publisher : De Gruyter Open
Release : 2017-05-08
ISBN : 9783110550856
Language : En, Es, Fr & De

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Book Description :

"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noel Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartlomiej A., Velichkov Bozhidar

Spectral Geometric Methods for Deformable 3D Shape Retrieval

Spectral Geometric Methods for Deformable 3D Shape Retrieval Book
Author : Chunyuan Li
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Spectral Geometric Methods for Deformable 3D Shape Retrieval book written by Chunyuan Li, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Steklov Geometry Processing

Steklov Geometry Processing Book
Author : Wang Yu (S.M.)
Publisher : Unknown
Release : 2018
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.

Old and New Aspects in Spectral Geometry

Old and New Aspects in Spectral Geometry Book
Author : M.-E. Craioveanu,Mircea Puta,Themistocles RASSIAS
Publisher : Springer Science & Business Media
Release : 2013-03-14
ISBN : 940172475X
Language : En, Es, Fr & De

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Book Description :

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.

The Geometry of Walker Manifolds

The Geometry of Walker Manifolds Book
Author : Miguel Brozos-Vázquez
Publisher : Morgan & Claypool Publishers
Release : 2009
ISBN : 1598298194
Language : En, Es, Fr & De

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Book Description :

Basic algebraic notions -- Introduction -- A historical perspective in the algebraic context -- Algebraic preliminaries -- Jordan normal form -- Indefinite geometry -- Algebraic curvature tensors -- Hermitian and para-Hermitian geometry -- The Jacobi and skew symmetric curvature operators -- Sectional, Ricci, scalar, and Weyl curvature -- Curvature decompositions -- Self-duality and anti-self-duality conditions -- Spectral geometry of the curvature operator -- Osserman and conformally Osserman models -- Osserman curvature models in signature (2, 2) -- Ivanov-Petrova curvature models -- Osserman Ivanov-Petrova curvature models -- Commuting curvature models -- Basic geometrical notions -- Introduction -- History -- Basic manifold theory -- The tangent bundle, lie bracket, and lie groups -- The cotangent bundle and symplectic geometry -- Connections, curvature, geodesics, and holonomy -- Pseudo-Riemannian geometry -- The Levi-Civita connection -- Associated natural operators -- Weyl scalar invariants -- Null distributions -- Pseudo-Riemannian holonomy -- Other geometric structures -- Pseudo-Hermitian and para-Hermitian structures -- Hyper-para-Hermitian structures -- Geometric realizations -- Homogeneous spaces, and curvature homogeneity -- Technical results in differential equations -- Walker structures -- Introduction -- Historical development -- Walker coordinates -- Examples of Walker manifolds -- Hypersurfaces with nilpotent shape operators -- Locally conformally flat metrics with nilpotent Ricci operator -- Degenerate pseudo-Riemannian homogeneous structures -- Para-Kaehler geometry -- Two-step nilpotent lie groups with degenerate center -- Conformally symmetric pseudo-Riemannian metrics -- Riemannian extensions -- The affine category -- Twisted Riemannian extensions defined by flat connections -- Modified Riemannian extensions defined by flat connections -- Nilpotent Walker manifolds -- Osserman Riemannian extensions -- Ivanov-Petrova Riemannian extensions -- Three-dimensional Lorentzian Walker manifolds -- Introduction -- History -- Three dimensional Walker geometry -- Adapted coordinates -- The Jordan normal form of the Ricci operator -- Christoffel symbols, curvature, and the Ricci tensor -- Locally symmetric Walker manifolds -- Einstein-like manifolds -- The spectral geometry of the curvature tensor -- Curvature commutativity properties -- Local geometry of Walker manifolds with -- Foliated Walker manifolds -- Contact Walker manifolds -- Strict Walker manifolds -- Three dimensional homogeneous Lorentzian manifolds -- Three dimensional lie groups and lie algebras -- Curvature homogeneous Lorentzian manifolds -- Diagonalizable Ricci operator -- Type II Ricci operator -- Four-dimensional Walker manifolds -- Introduction -- History -- Four-dimensional Walker manifolds -- Almost para-Hermitian geometry -- Isotropic almost para-Hermitian structures -- Characteristic classes -- Self-dual Walker manifolds -- The spectral geometry of the curvature tensor -- Introduction -- History -- Four-dimensional Osserman metrics -- Osserman metrics with diagonalizable Jacobi operator -- Osserman Walker type II metrics -- Osserman and Ivanov-Petrova metrics -- Riemannian extensions of affine surfaces -- Affine surfaces with skew symmetric Ricci tensor -- Affine surfaces with symmetric and degenerate Ricci tensor -- Riemannian extensions with commuting curvature operators -- Other examples with commuting curvature operators -- Hermitian geometry -- Introduction -- History -- Almost Hermitian geometry of Walker manifolds -- The proper almost Hermitian structure of a Walker manifold -- Proper almost hyper-para-Hermitian structures -- Hermitian Walker manifolds of dimension four -- Proper Hermitian Walker structures -- Locally conformally Kaehler structures -- Almost Kaehler Walker four-dimensional manifolds -- Special Walker manifolds -- Introduction -- History -- Curvature commuting conditions -- Curvature homogeneous strict Walker manifolds -- Bibliography.

Quantum Gravity and Spectral Geometry

Quantum Gravity and Spectral Geometry Book
Author : Giampiero Esposito,Gennaro Miele,Bruno Preziosi
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Quantum Gravity and Spectral Geometry book written by Giampiero Esposito,Gennaro Miele,Bruno Preziosi, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

3d Surface Registration Using Geometric Spectrum of Shapes

3d Surface Registration Using Geometric Spectrum of Shapes Book
Author : Hajar Hamidian
Publisher : Unknown
Release : 2019
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The function is deƠ̐1ned by the integration of a smooth term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efƠ̐1ciency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. The variation of the shape is expressed using a scale function deƠ̐1ned at each vertex. Consequently, the total energy function to align the two given surfaces can be deƠ̐1ned using the linear interpolation of the scale function derivatives. Through the optimization the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point to point correspondence of the surfaces. Therefore, the proposed method can accurately deƠ̐1ne the displacement of the vertices. For both methods, we evaluate them by conducting some experiments on synthetic and real data using hippocampus and heart data. These experiments demonstrate the advantages and accuracy of our methods. We then integrate our methods to a workƠ̐2ow system named DataView. Using this workƠ̐2ow system, users can design, save, run, and share their workƠ̐2ow using their web-browsers without the need of installing any software and regardless of the power of their computers. We have also integrated Grid to this system therefore the same task can be executed on up to 64 different cases which will increase the performance of the system enormously.

Applications of Representation Theory to Dynamics and Spectral Geometry

Applications of Representation Theory to Dynamics and Spectral Geometry Book
Author : Craig J. Sutton
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Applications of Representation Theory to Dynamics and Spectral Geometry book written by Craig J. Sutton, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Sound Synthesis from Shape changing Geometric Models

Sound Synthesis from Shape changing Geometric Models Book
Author : Cynthia Maxwell
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Sound Synthesis from Shape changing Geometric Models book written by Cynthia Maxwell, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematical Tools for Shape Analysis and Description

Mathematical Tools for Shape Analysis and Description Book
Author : Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo
Publisher : Morgan & Claypool Publishers
Release : 2014-09-01
ISBN : 1627053646
Language : En, Es, Fr & De

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Book Description :

This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice. Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies

Science

Science Book
Author : Anonim
Publisher : Unknown
Release : 1969
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Science Spectrum

Science Spectrum Book
Author : Holt Rinehart & Winston,Holt, Rinehart and Winston Staff
Publisher : Unknown
Release : 2003-03
ISBN : 9780030690785
Language : En, Es, Fr & De

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Book Description :

Download Science Spectrum book written by Holt Rinehart & Winston,Holt, Rinehart and Winston Staff, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Revista

Revista Book
Author : Unión matemática argentina, Buenos Aires
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Revista book written by Unión matemática argentina, Buenos Aires, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Visual Communications and Image Processing 92

Visual Communications and Image Processing  92 Book
Author : Anonim
Publisher : Unknown
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Visual Communications and Image Processing 92 book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Nuclear Science and Engineering

Nuclear Science and Engineering Book
Author : Anonim
Publisher : Unknown
Release : 1986
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Download Nuclear Science and Engineering book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Differential Geometry and Its Applications

Differential Geometry and Its Applications Book
Author : János Szenthe,L. Tamássy
Publisher : North Holland
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Differential Geometry and Its Applications book written by János Szenthe,L. Tamássy, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.