Functional and Shape Data Analysis

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.

Author: Anuj Srivastava

Publisher: Springer

ISBN: 1493940201

Category: Mathematics

Page: 447

View: 968

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.

Applied Functional Data Analysis

This book contains the ideas of functional data analysis by a number of case studies.

Author: J.O. Ramsay

Publisher: Springer

ISBN: 0387224653

Category: Mathematics

Page: 191

View: 951

This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.

S Functional Data Analysis

This book provides documentation for the S-PLUS module on functional data analysis. It will supplement our two books on this topic by Ramsay/Silverman.

Author: Douglas B. Clarkson

Publisher: Springer Science & Business Media

ISBN: 9780387249698

Category: Computers

Page: 192

View: 384

This book provides documentation for the S-PLUS module on functional data analysis. It will supplement our two books on this topic by Ramsay/Silverman.

Graphs in Biomedical Image Analysis Computational Anatomy and Imaging Genetics

Charon, N.: Analysis of geometric and functional shapes with extensions of
currents. Application to registration and atlas estimation. ... A., Klassen, E.:
Functional and Shape Data Analysis. Springer Series in Statistics. Springer, New
York ...

Author: M. Jorge Cardoso

Publisher: Springer

ISBN: 331967675X

Category: Computers

Page: 250

View: 401

This book constitutes the refereed joint proceedings of the First International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2017, the 6th International Workshop on Mathematical Foundations of Computational Anatomy, MFCA 2017, and the Third International Workshop on Imaging Genetics, MICGen 2017, held in conjunction with the 20th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2017, in Québec City, QC, Canada, in September 2017. The 7 full papers presented at GRAIL 2017, the 10 full papers presented at MFCA 2017, and the 5 full papers presented at MICGen 2017 were carefully reviewed and selected. The GRAIL papers cover a wide range of graph based medical image analysis methods and applications, including probabilistic graphical models, neuroimaging using graph representations, machine learning for diagnosis prediction, and shape modeling. The MFCA papers deal with theoretical developments in non-linear image and surface registration in the context of computational anatomy. The MICGen papers cover topics in the field of medical genetics, computational biology and medical imaging.

Shape Analysis in Medical Image Analysis

This book contains thirteen contributions from invited experts of international recognition addressing important issues in shape analysis in medical image analysis, including techniques for image segmentation, registration, modelling and ...

Author: Shuo Li

Publisher: Springer Science & Business Media

ISBN: 3319038133

Category: Technology & Engineering

Page: 442

View: 825

This book contains thirteen contributions from invited experts of international recognition addressing important issues in shape analysis in medical image analysis, including techniques for image segmentation, registration, modelling and classification and applications in biology, as well as in cardiac, brain, spine, chest, lung and clinical practice. This volume treats topics such as for example, anatomic and functional shape representation and matching; shape-based medical image segmentation; shape registration; statistical shape analysis; shape deformation; shape-based abnormity detection; shape tracking and longitudinal shape analysis; machine learning for shape modeling and analysis; shape-based computer-aided-diagnosis; shape-based medical navigation; benchmark and validation of shape representation, analysis and modeling algorithms. This work will be of interest to researchers, students and manufacturers in the fields of artificial intelligence, bioengineering, biomechanics, computational mechanics, computational vision, computer sciences, human motion, mathematics, medical imaging, medicine, pattern recognition and physics.

Shape in Medical Imaging

This method is particularly helpful in improving correspondences on objects with
complicated geometry where the standard SPHARM-PDM correspondences may
prove inadequate. 2.5 Multivariate Functional Shape Data Analysis (MFSDA) ...

Author: Martin Reuter

Publisher: Springer

ISBN: 3030047474

Category: Computers

Page: 312

View: 759

This book constitutes the proceedings of the Workshop on Shape in Medical Imaging, ShapeMI 2018, held in conjunction with the 21st International Conference on Medical Image Computing, MICCAI 2018, in Granada, Spain, in September 2018. The 26 full papers and 2 short papers presented were carefully reviewed and selected for inclusion in this volume. The papers discuss novel approaches and applications in shape and geometry processing and their use in research and clinical studies and explore novel, cutting-edge theoretical methods and their usefulness for medical applications, e.g., from the fields of geometric learning or spectral shape analysis.

Connectomics in NeuroImaging

Specifically, we use the square root velocity function (SRVF) [4,5,10] to perform
functional shape registration [11] of fMRI data. The novelty of our work includes
two aspects; a new application of the functional data analysis framework to rfMRI
 ...

Author: Guorong Wu

Publisher: Springer

ISBN: 3319671596

Category: Computers

Page: 171

View: 926

This book constitutes the refereed proceedings of the First International Workshop on Connectomics in NeuroImaging, CNI 2017, held in conjunction with MICCAI 2017 in Quebec City, Canada, in September 2017. The 19 full papers presented were carefully reviewed and selected from 26 submissions. The papers deal with new advancements in network construction, analysis, and visualization techniques in connectomics and their use in clinical diagnosis and group comparison studies as well as in various neuroimaging applications.

Elastic Shape Analysis of Three Dimensional Objects

This book develops these ideas without assuming advanced knowledge in differential geometry and statistics.

Author: Ian H. Jermyn

Publisher: Morgan & Claypool Publishers

ISBN: 1681730286

Category: Computers

Page: 185

View: 668

Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Two Topics in Functional Data Analysis

In order to study the shape of the intensity of bidding at the individual level , we
develop a novel functional method for the analysis of repeated event times ,
decomposing the local intensity function into an overall intensity factor that is a
scalar ...

Author: Shuang Wu

Publisher:

ISBN:

Category:

Page: 190

View: 133


Nonparametric Functional Data Analysis

Therefore, it becomes natural to introduce nonparametric models in order to
make as few assumptions as possible on the shape of the link. The functional
aspect of the problem is very important too, and we have to attack it in such a way
as to ...

Author: Frédéric Ferraty

Publisher: Springer Science & Business Media

ISBN: 0387366202

Category: Mathematics

Page: 260

View: 523

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Functional Data Analysis for Densities

Building on this idea , we propose a novel method for the functional data analysis
of point processes . We decompose the local intensity function into an overall
intensity factor that is a scalar random variable , and a shape function that ...

Author: Zhen Zhang

Publisher:

ISBN:

Category:

Page: 214

View: 514


Functional Data Analysis for Online Auction Data

3.2.1 Model for Functional Principal Component Analysis through Conditional
Expectation 90 3.2.2 Shape Restricted Analysis 92 3.2.3 Implementation of
Shape Restricted Analysis 94 3.3 Case Study 97 3.4 Conclusion 100 .
Bibliography 110 ...

Author: Bitao Liu

Publisher:

ISBN:

Category:

Page: 232

View: 198


Complex Data Modeling and Computationally Intensive Statistical Methods

Fast Bayesian functional data analysis of basal body temperature James M.
Ciera Abstract. ... for fast algorithms for estimating functional trajectories while
borrowing information from other patients concerning the shape and location of
features ...

Author: Pietro Mantovan

Publisher: Springer Science & Business Media

ISBN: 9788847013865

Category: Computers

Page: 164

View: 904

Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.

Astronomical Data Analysis Software and Systems

The spectrum is used to compute the object flux as a function of wavelength . The
flux is renormalized to the object magnitude over the magnitude passband . The
object shape specifies the functional form and extent of non - point source ...

Author:

Publisher:

ISBN:

Category: Astronomy

Page:

View: 176


Paleobiology

This system per termined by an eigenfunction analysis of the obmitted rapid
acquisition of high - resolution shape served shape functions . The resulting
eigenoutline data , typically consisting of about 500 shape functions are the
minimum ...

Author:

Publisher:

ISBN:

Category: Paleobiology

Page:

View: 628


Journal of the American Statistical Association

Right Censored Survival Data , Using Gibbs Sampler , ” Statistica Sinica , Our
simulation studies and data analysis show that the naïve 4 , 505 - 524 . approach
tends to alter both the functional shape of functions boch tends to alter hoth the ...

Author:

Publisher:

ISBN:

Category: Statistics

Page:

View: 493


Image Analysis

Obtaining a parameterization is closely related to denning a warp function
between the shapes under consideration. ... the reference shape Delaunay
triangulation to each of the n shapes of the data set we will obtain a one-to- one
mapping.

Author:

Publisher:

ISBN:

Category: Image processing

Page:

View: 315


Japanese Railway Engineering

Speaking of the shape data , we are of the opinion that all bodies must
essentially be defined by three - dimensional ... Formerly , the precise structural
analysis used to be made after completion of the functional design and
determination of the ...

Author:

Publisher:

ISBN:

Category: Railroad engineering

Page:

View: 903


Technometrics

Chapter Eight revisits the analysis of bone shape data discussed in Chapter Four
. The authors introduce parameterization by arc length , which is a more
meaningful way of depicting functional observations than looking at the means
alone ...

Author:

Publisher:

ISBN:

Category: Experimental design

Page:

View: 158


Medical Imaging 2006

Integrating and Classifying Parametric Features from fMRI Data for Brain
Function Characterization Yongmei Michelle ... We demonstrate that principal
component analysis (PCA) can be used for temporal shape modeling and shape
feature ...

Author:

Publisher:

ISBN:

Category: Diagnostic imaging

Page:

View: 238