Mathematical Tools For Shape Analysis And Description

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Mathematical Tools for Shape Analysis and Description

Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo
Mathematical Tools for Shape Analysis and Description Book PDF

Author : Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo
Publisher : Springer Nature
Page : 124 pages
File Size : 44,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031795589

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Mathematical Tools for Shape Analysis and Description by Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo Pdf

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

3D Shape Analysis

Hamid Laga,Yulan Guo,Hedi Tabia,Robert B. Fisher,Mohammed Bennamoun
3D Shape Analysis Book PDF

Author : Hamid Laga,Yulan Guo,Hedi Tabia,Robert B. Fisher,Mohammed Bennamoun
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 44,7 Mb
Release : 2019-01-07
Category : Mathematics
ISBN : 9781119405108

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3D Shape Analysis by Hamid Laga,Yulan Guo,Hedi Tabia,Robert B. Fisher,Mohammed Bennamoun Pdf

An in-depth description of the state-of-the-art of 3D shape analysis techniques and their applications This book discusses the different topics that come under the title of "3D shape analysis". It covers the theoretical foundations and the major solutions that have been presented in the literature. It also establishes links between solutions proposed by different communities that studied 3D shape, such as mathematics and statistics, medical imaging, computer vision, and computer graphics. The first part of 3D Shape Analysis: Fundamentals, Theory, and Applications provides a review of the background concepts such as methods for the acquisition and representation of 3D geometries, and the fundamentals of geometry and topology. It specifically covers stereo matching, structured light, and intrinsic vs. extrinsic properties of shape. Parts 2 and 3 present a range of mathematical and algorithmic tools (which are used for e.g., global descriptors, keypoint detectors, local feature descriptors, and algorithms) that are commonly used for the detection, registration, recognition, classification, and retrieval of 3D objects. Both also place strong emphasis on recent techniques motivated by the spread of commodity devices for 3D acquisition. Part 4 demonstrates the use of these techniques in a selection of 3D shape analysis applications. It covers 3D face recognition, object recognition in 3D scenes, and 3D shape retrieval. It also discusses examples of semantic applications and cross domain 3D retrieval, i.e. how to retrieve 3D models using various types of modalities, e.g. sketches and/or images. The book concludes with a summary of the main ideas and discussions of the future trends. 3D Shape Analysis: Fundamentals, Theory, and Applications is an excellent reference for graduate students, researchers, and professionals in different fields of mathematics, computer science, and engineering. It is also ideal for courses in computer vision and computer graphics, as well as for those seeking 3D industrial/commercial solutions.

Perspectives in Shape Analysis

Michael Breuß,Alfred Bruckstein,Petros Maragos,Stefanie Wuhrer
Perspectives in Shape Analysis Book PDF

Author : Michael Breuß,Alfred Bruckstein,Petros Maragos,Stefanie Wuhrer
Publisher : Springer
Page : 370 pages
File Size : 43,7 Mb
Release : 2016-09-30
Category : Mathematics
ISBN : 9783319247267

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Perspectives in Shape Analysis by Michael Breuß,Alfred Bruckstein,Petros Maragos,Stefanie Wuhrer Pdf

This book presents recent advances in the field of shape analysis. Written by experts in the fields of continuous-scale shape analysis, discrete shape analysis and sparsity, and numerical computing who hail from different communities, it provides a unique view of the topic from a broad range of perspectives. Over the last decade, it has become increasingly affordable to digitize shape information at high resolution. Yet analyzing and processing this data remains challenging because of the large amount of data involved, and because modern applications such as human-computer interaction require real-time processing. Meeting these challenges requires interdisciplinary approaches that combine concepts from a variety of research areas, including numerical computing, differential geometry, deformable shape modeling, sparse data representation, and machine learning. On the algorithmic side, many shape analysis tasks are modeled using partial differential equations, which can be solved using tools from the field of numerical computing. The fields of differential geometry and deformable shape modeling have recently begun to influence shape analysis methods. Furthermore, tools from the field of sparse representations, which aim to describe input data using a compressible representation with respect to a set of carefully selected basic elements, have the potential to significantly reduce the amount of data that needs to be processed in shape analysis tasks. The related field of machine learning offers similar potential. The goal of the Dagstuhl Seminar on New Perspectives in Shape Analysis held in February 2014 was to address these challenges with the help of the latest tools related to geometric, algorithmic and numerical concepts and to bring together researchers at the forefront of shape analysis who can work together to identify open problems and novel solutions. The book resulting from this seminar will appeal to researchers in the field of shape analysis, image and vision, from those who want to become more familiar with the field, to experts interested in learning about the latest advances.​

Mathematics Of Shapes And Applications

Sergey Kushnarev,Anqi Qiu,Laurent Younes
Mathematics Of Shapes And Applications Book PDF

Author : Sergey Kushnarev,Anqi Qiu,Laurent Younes
Publisher : World Scientific
Page : 220 pages
File Size : 49,9 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9789811200144

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Mathematics Of Shapes And Applications by Sergey Kushnarev,Anqi Qiu,Laurent Younes Pdf

Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.

Elastic Shape Analysis of Three-Dimensional Objects

Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava
Elastic Shape Analysis of Three Dimensional Objects Book PDF

Author : Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava
Publisher : Morgan & Claypool Publishers
Page : 187 pages
File Size : 55,8 Mb
Release : 2017-09-15
Category : Computers
ISBN : 9781681730288

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Elastic Shape Analysis of Three-Dimensional Objects by Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava Pdf

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.

Moving Shape Analysis and Control

Marwan Moubachir,Jean-Paul Zolesio
Moving Shape Analysis and Control Book PDF

Author : Marwan Moubachir,Jean-Paul Zolesio
Publisher : CRC Press
Page : 312 pages
File Size : 47,7 Mb
Release : 2006-01-13
Category : Mathematics
ISBN : 9781420003246

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Moving Shape Analysis and Control by Marwan Moubachir,Jean-Paul Zolesio Pdf

Problems involving the evolution of two- and three-dimensional domains arise in many areas of science and engineering. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains. The book illustrates the efficie

Shape Analysis and Structuring

Leila de Floriani,Michela Spagnuolo
Shape Analysis and Structuring Book PDF

Author : Leila de Floriani,Michela Spagnuolo
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 52,6 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783540332657

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Shape Analysis and Structuring by Leila de Floriani,Michela Spagnuolo Pdf

With a lot of recent developments in the field, this much-needed book has come at just the right time. It covers a variety of topics related to preserving and enhancing shape information at a geometric level. The contributors also cover subjects that are relevant to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.

Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis

Jean-Luc Mari,Franck Hétroy-Wheeler,Gérard Subsol
Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis Book PDF

Author : Jean-Luc Mari,Franck Hétroy-Wheeler,Gérard Subsol
Publisher : John Wiley & Sons
Page : 194 pages
File Size : 43,5 Mb
Release : 2020-01-02
Category : Mathematics
ISBN : 9781786300416

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Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis by Jean-Luc Mari,Franck Hétroy-Wheeler,Gérard Subsol Pdf

Three-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.

Shapes and Geometries

Michel C. Delfour,J. P. Zolesio
Shapes and Geometries Book PDF

Author : Michel C. Delfour,J. P. Zolesio
Publisher : SIAM
Page : 512 pages
File Size : 46,8 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0898714893

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Shapes and Geometries by Michel C. Delfour,J. P. Zolesio Pdf

The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.

Functional and Shape Data Analysis

Anuj Srivastava,Eric P. Klassen
Functional and Shape Data Analysis Book PDF

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 40,7 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

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.

Shapes and Geometries

M. C. Delfour,J.-P. Zolesio
Shapes and Geometries Book PDF

Author : M. C. Delfour,J.-P. Zolesio
Publisher : SIAM
Page : 638 pages
File Size : 52,5 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719826

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Shapes and Geometries by M. C. Delfour,J.-P. Zolesio Pdf

This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.

Shape Analysis and Classification

Luciano da Fontoura Costa,Roberto Marcond Cesar, Jr.
Shape Analysis and Classification Book PDF

Author : Luciano da Fontoura Costa,Roberto Marcond Cesar, Jr.
Publisher : CRC Press
Page : 680 pages
File Size : 50,7 Mb
Release : 2000-12-20
Category : Technology & Engineering
ISBN : 0849334934

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Shape Analysis and Classification by Luciano da Fontoura Costa,Roberto Marcond Cesar, Jr. Pdf

Advances in shape analysis impact a wide range of disciplines, from mathematics and engineering to medicine, archeology, and art. Anyone just entering the field, however, may find the few existing books on shape analysis too specific or advanced, and for students interested in the specific problem of shape recognition and characterization, traditional books on computer vision are too general. Shape Analysis and Classification: Theory and Practice offers an integrated and conceptual introduction to this dynamic field and its myriad applications. Beginning with the basic mathematical concepts, it deals with shape analysis, from image capture to pattern classification, and presents many of the most advanced and powerful techniques used in practice. The authors explore the relevant aspects of both shape characterization and recognition, and give special attention to practical issues, such as guidelines for implementation, validation, and assessment. Shape Analysis and Classification provides a rich resource for the computational characterization and classification of general shapes, from characters to biological entities. Both students and researchers can directly use its state-of-the-art concepts and techniques to solve their own problems involving the characterization and classification of visual shapes.

Statistical Shape Analysis

Ian L. Dryden,Kanti V. Mardia
Statistical Shape Analysis Book PDF

Author : Ian L. Dryden,Kanti V. Mardia
Publisher : John Wiley & Sons
Page : 496 pages
File Size : 48,8 Mb
Release : 2016-06-28
Category : Mathematics
ISBN : 9781119072508

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Statistical Shape Analysis by Ian L. Dryden,Kanti V. Mardia Pdf

A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded `Statistical Shape Analysis’ by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis .

Mathematical Basics of Motion and Deformation in Computer Graphics

Ken Anjyo,Hiroyuki Ochiai
Mathematical Basics of Motion and Deformation in Computer Graphics Book PDF

Author : Ken Anjyo,Hiroyuki Ochiai
Publisher : Morgan & Claypool Publishers
Page : 97 pages
File Size : 46,9 Mb
Release : 2017-04-13
Category : Computers
ISBN : 9781627059848

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Mathematical Basics of Motion and Deformation in Computer Graphics by Ken Anjyo,Hiroyuki Ochiai Pdf

This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation.

Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition

Ken Anjyo,Hiroyuki Ochiai
Mathematical Basics of Motion and Deformation in Computer Graphics Second Edition Book PDF

Author : Ken Anjyo,Hiroyuki Ochiai
Publisher : Springer Nature
Page : 79 pages
File Size : 49,8 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025921

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Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition by Ken Anjyo,Hiroyuki Ochiai Pdf

This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation.