Op werkdagen voor 23:00 besteld, morgen in huis Gratis verzending vanaf €20
010-4091959
Anuj Srivastava Meer over de auteurs
,

Functional and Shape Data Analysis
Specificaties
Gebonden, blz. | Engels
Springer New York | e druk, 2016
ISBN13: 9781493940189
Rubricering
Juridisch :
Springer New York e druk, 2016 9781493940189
Onderdeel van serie Springer Series in Statistics
156,99
In winkelwagen
Verwachte levertijd ongeveer 9 werkdagen
 

Samenvatting

This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges.

Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Specificaties

ISBN13:9781493940189
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer New York
Serie:Springer Series in Statistics

Inhoudsopgave

<div>Contents</div><div>1 &nbsp; &nbsp; &nbsp;Motivation for Function and Shape Analysis</div><div>1.1 &nbsp; &nbsp;Motivation</div><div>1.1.1 &nbsp; &nbsp;Need for Function and Shape Data Analysis Tools&nbsp;</div><div>1.1.2 &nbsp; &nbsp;Why Continuous Shapes? &nbsp;</div><div>1.2 &nbsp; &nbsp;Important Application Areas &nbsp;</div><div>1.3 &nbsp; &nbsp;Specific Technical Goals &nbsp;</div><div>1.4 &nbsp; &nbsp;Issues &amp; Challenges</div><div>1.5 &nbsp; &nbsp;Organization of This Textbook &nbsp;</div><div><br></div><div>2 &nbsp; &nbsp; &nbsp;Previous Techniques in Shape Analysis</div><div>2.1 &nbsp; &nbsp;Principal Component Analysis (PCA)</div><div>2.2 &nbsp; &nbsp;Point-Based Methods &nbsp;</div><div>2.2.1 &nbsp; &nbsp;ICP: Point Cloud Analysis&nbsp;</div><div>2.2.2 &nbsp; &nbsp;Active Shape Models&nbsp;</div><div>2.2.3 &nbsp; &nbsp;Kendall’s Landmark-Based Shape Analysis&nbsp;</div><div>2.2.4 &nbsp; &nbsp;Issue of Landmark Selection</div><div>2.3 &nbsp; &nbsp;Domain-Based Shape Representations</div><div>2.3.1 &nbsp; &nbsp;Level-Set Methods</div><div>2.3.2 &nbsp; &nbsp;Deformation-Based Shape Analysis</div><div>2.4 &nbsp; &nbsp;Exercises&nbsp;</div><div>2.5 &nbsp; &nbsp;Bibliographic Notes &nbsp;</div><div><br></div><div>3 &nbsp; &nbsp; &nbsp;Background: Relevant Tools from Geometry</div><div>3.1 &nbsp; &nbsp;Equivalence Relations&nbsp;</div><div>3.2 &nbsp; &nbsp;Riemannian Structure and Geodesics &nbsp;</div><div>3.3 &nbsp; &nbsp;Geodesics in Spaces of Curves on Manifolds</div><div>3.4 &nbsp; &nbsp;Parallel Transport of Vectors &nbsp;</div><div>3.5 &nbsp; &nbsp;Lie Group Actions on Manifolds</div><div>3.5.1 &nbsp; &nbsp;Actions of Single Groups&nbsp;</div><div>3.5.2 &nbsp; &nbsp;Actions of Product Groups&nbsp;</div><div>3.6 &nbsp; &nbsp;Quotient Spaces of Riemannian Manifolds&nbsp;</div><div>3.7 &nbsp; &nbsp;Quotient Spaces as Orthogonal Sections&nbsp;</div><div>3.8 &nbsp; &nbsp;General Quotient Spaces&nbsp;</div><div>3.9 &nbsp; &nbsp;Distances in Quotient Spaces: A Summary &nbsp;</div><div>3.10 &nbsp;Center of An Orbit &nbsp;</div><div>3.11 &nbsp;Exercises&nbsp;</div><div>3.11.1 &nbsp;Theoretical Exercises&nbsp;</div><div>3.11.2 &nbsp;Computational Exercises</div><div>3.12 &nbsp;Bibliographic Notes &nbsp;</div><div><br></div><div>4 &nbsp; &nbsp; &nbsp;Functional Data and Elastic Registration</div><div>4.1 &nbsp; &nbsp;Goals and Challenges&nbsp;</div><div>4.2 &nbsp; &nbsp;Estimating Function Variables from Discrete Data&nbsp;</div><div>4.3 &nbsp; &nbsp;Geometries of Some Function Spaces</div><div>4.3.1 &nbsp; &nbsp;Geometry of Hilbert Spaces &nbsp;</div><div>4.3.2 &nbsp; &nbsp;Unit Hilbert Sphere &nbsp;</div><div>4.3.3 &nbsp; &nbsp;Group of Warping Functions&nbsp;</div><div>4.4 &nbsp; &nbsp;Function Registration Problem&nbsp;</div><div>4.5 &nbsp; &nbsp;Use of L2-Norm And Its Limitations&nbsp;</div><div>4.6 &nbsp; &nbsp;Square-Root Slope Function (SRSF) Representation &nbsp;</div><div>4.7 &nbsp; &nbsp;Definition of Phase &amp; Amplitude Components</div><div>4.7.1 &nbsp; &nbsp;Amplitude of a Function&nbsp;</div><div>4.7.2 &nbsp; &nbsp;Relative Phase Between Functions&nbsp;</div><div>4.7.3 &nbsp; &nbsp;A Convenient Approximation</div><div>4.8 &nbsp; &nbsp;SRSF-Based Registration&nbsp;</div><div>4.8.1 &nbsp; &nbsp;Registration Problem</div><div>4.8.2 &nbsp; &nbsp;SRSF Alignment Using Dynamic Programming &nbsp;</div><div>4.8.3 &nbsp; &nbsp;Examples of Functional Alignments&nbsp;</div><div>4.9 &nbsp; &nbsp;Connection to the Fisher-Rao Metric&nbsp;</div><div>4.10 &nbsp;Phase and Amplitude Distances</div><div>4.10.1 &nbsp;Amplitude Space and A Metric Structure&nbsp;</div><div>4.10.2 &nbsp;Phase Space and A Metric Structure&nbsp;</div><div>4.11 &nbsp;Different Warping Actions and PDFs</div><div>4.11.1 &nbsp;Listing of Different Actions &nbsp;</div><div>4.11.2 &nbsp;Probability Density Functions&nbsp;</div><div>4.12 &nbsp;Exercises &nbsp;</div><div>4.12.1 &nbsp;Theoretical Exercises&nbsp;</div><div>4.12.2 &nbsp;Computational Exercises</div><div>4.13 &nbsp;Bibliographic Notes&nbsp;</div><div><br></div><div>5 &nbsp; &nbsp; &nbsp;Shapes of Planar Curves</div><div>5.1 &nbsp; &nbsp;Goals &amp; Challenges&nbsp;</div><div>5.2 &nbsp; &nbsp;Parametric Representations of Curves&nbsp;</div><div>5.3 &nbsp; &nbsp;General Framework</div><div>5.3.1 &nbsp; &nbsp;Mathematical Representations of Curves&nbsp;</div><div>5.3.2 &nbsp; &nbsp;Shape-Preserving Transformations</div><div>5.4 &nbsp; &nbsp;Pre-Shape Spaces&nbsp;</div><div>5.4.1 &nbsp; &nbsp;Riemannian Structure&nbsp;</div><div>5.4.2 &nbsp; &nbsp;Geodesics in Pre-Shape Spaces</div><div>5.5 &nbsp; &nbsp;Shape Spaces</div><div>5.5.1 &nbsp; &nbsp;Removing Parameterization &nbsp;</div><div>5.6 &nbsp; &nbsp;Motivation for SRVF Representation &nbsp;</div><div>5.6.1 &nbsp; &nbsp;What is an Elastic Metric?</div><div>5.6.2 &nbsp; &nbsp;Significance of the Square-Root Representation&nbsp;</div><div>5.7 &nbsp; &nbsp;Geodesic Paths in Shape Spaces &nbsp;</div><div>5.7.1 &nbsp; &nbsp;Optimal Re-Parameterization for Curve Matching</div><div>5.7.2 &nbsp; &nbsp;Geodesic Illustrations</div><div>5.8 &nbsp; &nbsp;Gradient-Based Optimization Over Re-Parameterization Group</div><div>5.9 &nbsp; &nbsp;Summary&nbsp;</div><div>5.10 &nbsp;Exercises &nbsp;</div><div>5.10.1 &nbsp;Theoretical Exercises</div><div>5.10.2 &nbsp;Computational Exercises</div><div>5.11 &nbsp;Bibliographic Notes</div><div><br></div><div>6 &nbsp; &nbsp; &nbsp;Shapes of Planar Closed Curves</div><div>6.1 &nbsp; &nbsp;Goals and Challenges</div><div>6.2 &nbsp; &nbsp;Representations of Closed Curves</div><div>6.2.1 &nbsp; &nbsp;Pre-Shape Spaces</div><div>6.2.2 &nbsp; &nbsp;Riemannian Structures&nbsp;</div><div>6.2.3 &nbsp; &nbsp;Removing Parameterization &nbsp;</div><div>6.3 &nbsp; &nbsp;Projection on a Manifold&nbsp;</div><div>6.4 &nbsp; &nbsp;Geodesic Computation</div><div>6.5 &nbsp; &nbsp;Geodesic Computation: Shooting Method&nbsp;</div><div>6.5.1 &nbsp; &nbsp;Example 1: Geodesics on S2</div><div>6.5.2 &nbsp; &nbsp;Example 2: Geodesics in Non-Elastic Pre-Shape Space&nbsp;</div><div>6.6 &nbsp; &nbsp;Geodesic Computation: Path Straightening Method &nbsp;</div><div>6.6.1 &nbsp; &nbsp;Theoretical Background&nbsp;</div><div>6.6.2 &nbsp; &nbsp;Numerical Implementation&nbsp;</div><div>6.6.3 &nbsp; &nbsp;Example 1: Geodesics on S2</div><div>6.6.4 &nbsp; &nbsp;Example 2: Geodesics in Elastic Pre-Shape Space&nbsp;</div><div>6.7 &nbsp; &nbsp;Geodesics in Shape Spaces</div><div>6.7.1 &nbsp; &nbsp;Geodesics in Non-Elastic Shape Space &nbsp;</div><div>6.7.2 &nbsp; &nbsp;Geodesics in Elastic Shape Space</div><div>6.8 &nbsp; &nbsp;Examples of Elastic Geodesics&nbsp;</div><div>6.8.1 &nbsp; &nbsp;Elastic Matching: Gradient Versus Dynamic Programming Algorithm</div><div>6.8.2 &nbsp; &nbsp;Fast Approximate Elastic Matching of Closed Curves</div><div>6.9 &nbsp; &nbsp;Elastic versus Non-Elastic Deformations&nbsp;</div><div>6.10 &nbsp;Parallel Transport of Shape Deformations&nbsp;</div><div>6.10.1 &nbsp;Prediction of Silhouettes from Novel Views&nbsp;</div><div>6.10.2 &nbsp;Classification of 3D Objects Using Predicted Silhouettes</div><div>6.11 &nbsp;Symmetry Analysis of Planar Shapes</div><div>6.12 &nbsp;Exercises &nbsp;</div><div>6.12.1 &nbsp;Theoretical Exercises</div><div>6.12.2 &nbsp;Computational Exercises</div><div>6.13 &nbsp;Bibliographic Notes&nbsp;</div><div><br></div><div>7 &nbsp; &nbsp; &nbsp;Statistical Modeling on Nonlinear Manifolds</div><div>7.1 &nbsp; &nbsp;Goals &amp; Challenges &nbsp;</div><div>7.2 &nbsp; &nbsp;Basic Setup &nbsp;</div><div>7.3 &nbsp; &nbsp;Probability Densities on Manifolds</div><div>7.4 &nbsp; &nbsp;Summary Statistics on Manifolds &nbsp;</div><div>7.4.1 &nbsp; &nbsp;Intrinsic Statistics</div><div>7.4.2 &nbsp; &nbsp;Extrinsic Statistics &nbsp;</div><div>7.5 &nbsp; &nbsp;Examples on Some Useful Manifolds</div><div>7.5.1 &nbsp; &nbsp;Statistical Analysis on S1</div><div>7.5.2 &nbsp; &nbsp;Statistical Analysis on S2</div><div>7.5.3 &nbsp; &nbsp;Space of Probability Density Functions</div><div>7.5.4 &nbsp; &nbsp;Space of Warping Functions</div><div>7.6 &nbsp; &nbsp;Statistical Analysis on a Quotient Space M=G</div><div>7.6.1 &nbsp; &nbsp;Quotient Space as Orthogonal Section</div><div>7.6.2 &nbsp; &nbsp;General Case: Without Using Sections&nbsp;</div><div>7.7 &nbsp; &nbsp;Exercises</div><div>7.7.1 &nbsp; &nbsp;Theoretical Exercises</div><div>7.7.2 &nbsp; &nbsp;Computational Exercises&nbsp;</div><div>7.8 &nbsp; &nbsp;Bibliographic Notes&nbsp;</div><div><br></div><div>8 &nbsp; &nbsp; &nbsp;Statistical Modeling of Functional Data</div><div>8.1 &nbsp; &nbsp;Goals and Challenges&nbsp;</div><div>8.2 &nbsp; &nbsp;Template-Based Alignment &amp; L2 Metric&nbsp;</div><div>8.3 &nbsp; &nbsp;Elastic Phase-Amplitude Separation</div><div>8.3.1 &nbsp; &nbsp;Karcher Mean of Amplitudes&nbsp;</div><div>8.3.2 &nbsp; &nbsp;Template: Center of the Mean Orbit</div><div>8.3.3 &nbsp; &nbsp;Phase-Amplitude Separation Algorithm &nbsp;</div><div>8.4 &nbsp; &nbsp;Alternate Interpretation as Estimation of Model Parameters&nbsp;</div><div>8.5 &nbsp; &nbsp;Phase-Amplitude Separation After Transformation</div><div>8.6 &nbsp; &nbsp;Penalized Function Alignment</div><div>8.7 &nbsp; &nbsp;Function Components, Alignment and Modeling&nbsp;</div><div>8.8 &nbsp; &nbsp;Sequential Approach&nbsp;</div><div>8.8.1 &nbsp; &nbsp;FPCA of Amplitude Functions: A-FPCA &nbsp;</div><div>8.8.2 &nbsp; &nbsp;FPCA of Phase Functions: P-FPCA</div><div>8.8.3 &nbsp; &nbsp;Joint Modeling of Principle Coefficients&nbsp;</div><div>8.9 &nbsp; &nbsp;Joint Approach: Elastic FPCA</div><div>8.9.1 &nbsp; &nbsp;Model-Based Elastic FPCA in Function Space F</div><div>8.9.2 &nbsp; &nbsp;Elastic FPCA Using SRSF Representation &nbsp;</div><div>8.10 &nbsp;Exercises &nbsp;</div><div>8.10.1 &nbsp;Theoretical Exercises</div><div>8.10.2 &nbsp;Computational Exercises&nbsp;</div><div>8.11 &nbsp;Bibliographic Notes&nbsp;</div><div><br></div><div>9 &nbsp; &nbsp; &nbsp;Statistical Modeling of Planar Shapes</div><div>9.1 &nbsp; &nbsp;Goals &amp; Challenges &nbsp;</div><div>9.2 &nbsp; &nbsp;Clustering in Shape Spaces</div><div>9.2.1 &nbsp; &nbsp;Hierarchical Clustering &nbsp;</div><div>9.2.2 &nbsp; &nbsp;A Minimum-Dispersion Clustering&nbsp;</div><div>9.3 &nbsp; &nbsp;A Finite Representation of Planar Shapes&nbsp;</div><div>9.3.1 &nbsp; &nbsp;Shape Representation: A Brief Review&nbsp;</div><div>9.3.2 &nbsp; &nbsp;Finite Shape Representation: Planar Curves &nbsp;</div><div>9.3.3 &nbsp; &nbsp;Finite Representation: Planar Closed Curves &nbsp;</div><div>9.4 &nbsp; &nbsp;Models for Planar Curves as Elements of S2</div><div>9.4.1 &nbsp; &nbsp;Truncated Wrapped-Normal (TWN) Model &nbsp;</div><div>9.4.2 &nbsp; &nbsp;Learning TWN Model from Training Shapes in S2</div><div>9.5 &nbsp; &nbsp;Models for Planar Closed Curves&nbsp;</div><div>9.6 &nbsp; &nbsp;Beyond TWN Shape Models</div><div>9.7 &nbsp; &nbsp;Modeling Nuisance Variables&nbsp;</div><div>9.7.1 &nbsp; &nbsp;Modeling Re-Parameterization Function</div><div>9.7.2 &nbsp; &nbsp;Modeling Shape Orientations&nbsp;</div><div>9.8 &nbsp; &nbsp;Classification of Shapes With Contour Data &nbsp;</div><div>9.8.1 &nbsp; &nbsp;Nearest-Neighbor Classification&nbsp;</div><div>9.8.2 &nbsp; &nbsp;Probabilistic Classification&nbsp;</div><div>9.9 &nbsp; &nbsp;Detection/Classification of Shapes in Cluttered Point Clouds &nbsp;</div><div>9.9.1 &nbsp; &nbsp;Point Process Models for Cluttered Data</div><div>9.9.2 &nbsp; &nbsp;Maximum Likelihood Estimation of Model Parameters &nbsp;</div><div>9.10 &nbsp;Problems</div><div>9.10.1 &nbsp;Theoretical Problems&nbsp;</div><div>9.10.2 &nbsp;Computational Problems&nbsp;</div><div>9.11 &nbsp;Bibliographic Notes&nbsp;</div><div>&nbsp;</div><div>10 &nbsp; &nbsp;Shapes of Curves in Higher Dimensions</div><div>10.1 &nbsp;Goals &amp; Challenges &nbsp;</div><div>10.2 &nbsp;Mathematical Representations of Curves&nbsp;</div><div>10.3 &nbsp;Elastic and Non-Elastic Metrics</div><div>10.4 &nbsp;Shapes Spaces of Curves in Rn</div><div>10.4.1 &nbsp;Under Direction Function Representation&nbsp;</div><div>10.4.2 &nbsp;Under SRVF Representation</div><div>10.4.3 &nbsp;Hierarchical Clustering of Elastic Curves &nbsp;</div><div>10.4.4 &nbsp;Sample Statistics and Modeling of Elastic Curves in Rn</div><div>10.5 &nbsp;Registration of Curves&nbsp;</div><div>10.5.1 &nbsp;Pairwise Registration of Curves in Rn</div><div>10.5.2 &nbsp;Registration of Multiple Curves&nbsp;</div><div>10.6 &nbsp;Shapes of Closed Curves in Rn</div><div>10.6.1 &nbsp;Non-Elastic Closed Curves&nbsp;</div><div>10.6.2 &nbsp;Elastic Closed Curves &nbsp;</div><div>10.7 &nbsp;Shape Analysis of Augmented Curves</div><div>10.7.1 &nbsp;Joint Representation of Augmented Curves&nbsp;</div><div>10.7.2 &nbsp;Invariances and Equivalence Classes</div><div>10.8 &nbsp;Problems</div><div>10.8.1 &nbsp;Theoretical Problems&nbsp;</div><div>10.8.2 &nbsp;Computational Problems&nbsp;</div><div>10.9 &nbsp;Bibliographic Notes&nbsp;</div><div><br></div><div>11 &nbsp; &nbsp;Related Topics in Shape Analysis of Curves</div><div>11.1 &nbsp;Goals and Challenges&nbsp;</div><div>11.2 &nbsp;Joint Analysis of Shape and Other Features&nbsp;</div><div>11.2.1 &nbsp;Geodesics and Geodesic Distances on Feature Spaces</div><div>11.2.2 &nbsp;Feature-Based Clustering</div><div>11.3 &nbsp;Affine-Invariant Shape Analysis of Planar Curves&nbsp;</div><div>11.3.1 &nbsp;Global Section Under the Affine Action &nbsp;</div><div>11.3.2 &nbsp;Geodesics Using Path-Straightening Algorithm</div><div>11.4 &nbsp;Registration of Trajectories on Nonlinear Manifolds</div><div>11.4.1 &nbsp;Transported SRVF for Trajectories</div><div>11.4.2 &nbsp;Analysis of Trajectories on S2</div><div>11.5 &nbsp;Problems&nbsp;</div><div>11.5.1 &nbsp;Theoretical Problems</div><div>11.5.2 &nbsp;Computational Problems</div><div>11.6 &nbsp;Bibliographic Notes &nbsp;</div><div><br></div><div>A &nbsp; &nbsp; Background Material</div><div>A.1 &nbsp; Basic Differential Geometry</div><div>A.1.1 &nbsp; Tangent spaces on a manifold</div><div>A.1.2 &nbsp; Submanifolds&nbsp;</div><div>A.2 &nbsp; Basic Algebra&nbsp;</div><div>A.3 &nbsp; Basic Geometry of Function Spaces</div><div>A.3.1 &nbsp; Hilbert Manifolds &amp; Submanifolds&nbsp;</div><div><br></div><div>B &nbsp; &nbsp; The Dynamic Programming Algorithm</div><div>B.1 &nbsp; Theoretical Setup</div><div>B.2 &nbsp; Computer Implementation &nbsp;</div><div><br></div><div>References</div><div><br></div><div>Index</div><div><br></div>

Net verschenen

Rubrieken

Uw cookie-instellingen
Deze website maakt gebruik van verschillende soorten cookies. Sommige cookies worden geplaatst door diensten van derden die op onze pagina's worden weergegeven. Om deze externe content te kunnen tonen is nodig dat u toestemming geeft voor het zetten van persoonlijke en marketingcookies. U kunt uw toestemming op elk moment wijzigen of intrekken. In onze cookieverklaring vindt u meer informatie.

    Personen

      Trefwoorden

        Functional and Shape Data Analysis

        Recensiebeleid
        Noordhoff terugkoopgarantie

        Noordhoff koopt jouw boek terug, zonder zorgen!

        Heb je jouw boeken niet meer nodig?

        Als je jouw studieboeken gekocht hebt bij hanzestudybook.nl, kun je geselecteerde titels moeiteloos terugverkopen aan Noordhoff. Geen vragen, geen gedoe en lekker duurzaam.

        Volledige informatie op Noordhoff.nl

        AI-book

        Wat is een AI-book?

        Een AI-book is niet een boek dat geschreven is door AI maar een boek dat verrijkt is met AI. Het maakt de inhoud van een boek interactief via WhatsApp, zodat je ermee kunt chatten. Zie het als een razend slimme assistent die het boek perfect begrijpt en er alles uit onthouden heeft. Jij kunt deze assistent alles vragen. Vraag bijvoorbeeld hoe je iets kunt toepassen op jouw persoonlijke situatie, om een korte samenvatting, of wat de belangrijkste inzichten zijn. AI-books zijn alleen te gebruiken via WhatsApp, je hoeft er geen aparte app voor te installeren.
        Meer informatie over AI-books

        ?

        Geef uw beoordeling

        Functional and Shape Data Analysis

        Verwijder uw beoordeling