3d Shape Analysis
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3d Shape Analysis
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Author : Hamid Laga
language : en
Publisher: John Wiley & Sons
Release Date : 2019-01-07
3d Shape Analysis written by Hamid Laga and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-07 with Mathematics categories.
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.
Geometric And Topological Mesh Feature Extraction For 3d Shape Analysis
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Author : Jean-Luc Mari
language : en
Publisher: John Wiley & Sons
Release Date : 2020-01-02
Geometric And Topological Mesh Feature Extraction For 3d Shape Analysis written by Jean-Luc Mari and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Mathematics categories.
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.
3d Shape Analysis Based On Feature Curve Networks
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Author : Anne Gehre
language : en
Publisher:
Release Date : 2019*
3d Shape Analysis Based On Feature Curve Networks written by Anne Gehre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019* with categories.
Spectral Geometry Of Shapes
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Author : Jing Hua
language : en
Publisher: Academic Press
Release Date : 2020-01-15
Spectral Geometry Of Shapes written by Jing Hua and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Computers categories.
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
3d Imaging Analysis And Applications
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Author : Yonghuai Liu
language : en
Publisher: Springer Nature
Release Date : 2020-09-11
3d Imaging Analysis And Applications written by Yonghuai Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-11 with Computers categories.
This textbook is designed for postgraduate studies in the field of 3D Computer Vision. It also provides a useful reference for industrial practitioners; for example, in the areas of 3D data capture, computer-aided geometric modelling and industrial quality assurance. This second edition is a significant upgrade of existing topics with novel findings. Additionally, it has new material covering consumer-grade RGB-D cameras, 3D morphable models, deep learning on 3D datasets, as well as new applications in the 3D digitization of cultural heritage and the 3D phenotyping of crops. Overall, the book covers three main areas: ● 3D imaging, including passive 3D imaging, active triangulation 3D imaging, active time-of-flight 3D imaging, consumer RGB-D cameras, and 3D data representation and visualisation; ● 3D shape analysis, including local descriptors, registration, matching, 3D morphable models, and deep learning on 3D datasets; and ● 3D applications, including 3D face recognition, cultural heritage and 3D phenotyping of plants. 3D computer vision is a rapidly advancing area in computer science. There are many real-world applications that demand high-performance 3D imaging and analysis and, as a result, many new techniques and commercial products have been developed. However, many challenges remain on how to analyse the captured data in a way that is sufficiently fast, robust and accurate for the application. Such challenges include metrology, semantic segmentation, classification and recognition. Thus, 3D imaging, analysis and their applications remain a highly-active research field that will continue to attract intensive attention from the research community with the ultimate goal of fully automating the 3D data capture, analysis and inference pipeline.
Elastic Shape Analysis Of Three Dimensional Objects
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Author : Ian H. Jermyn
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-09-15
Elastic Shape Analysis Of Three Dimensional Objects written by Ian H. Jermyn and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with Computers categories.
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.
Mathematical Tools For Shape Analysis And Description
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Author : Silvia Biasotti
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2014-09-01
Mathematical Tools For Shape Analysis And Description written by Silvia Biasotti and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with Computers categories.
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
Optimal Designs For 3d Shape Analysis With Spherical Harmonic Descriptors
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Author : Holger Dette
language : en
Publisher:
Release Date : 2004
Optimal Designs For 3d Shape Analysis With Spherical Harmonic Descriptors written by Holger Dette and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Robust Designs For 3d Shape Analysis With Spherical Harmonic Descriptors
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Author : Holger Dette
language : en
Publisher:
Release Date : 2007
Robust Designs For 3d Shape Analysis With Spherical Harmonic Descriptors written by Holger Dette and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Diffusion Driven Wavelet Design For Shape Analysis
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Author : Tingbo Hou
language : en
Publisher: CRC Press
Release Date : 2014-10-22
Diffusion Driven Wavelet Design For Shape Analysis written by Tingbo Hou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-22 with Computers categories.
From Design Methods and Generation Schemes to State-of-the-Art Applications Wavelets are powerful tools for functional analysis and geometry processing, enabling researchers to determine the structure of data and analyze 3D shapes. Suitable for researchers in computer graphics, computer vision, visualization, medical imaging, and geometric modeling as well as graduate and senior undergraduate students in computer science, Diffusion-Driven Wavelet Design for Shape Analysis presents recent research results in wavelet designs on 3D shapes and their applications in shape analysis. It explains how to apply the design methods to various types of 3D data, such as polygonal meshes, point clouds, manifolds, and volumetric images. Extensions of Wavelet Generation on Volumetric and Manifold Data The first part of the book introduces design methods of wavelets on manifold data, incorporating interdisciplinary knowledge from differential geometry, functional analysis, Fourier transform, spectral graph theory, and stochastic processes. The authors show how wavelets are purely determined by the shape geometry and how wavelet transforms are computed as inner products of wavelet kernels and input functions. Wavelets for Solving Computer Graphics Problems The second part presents applications in shape analysis/representation. The book looks at wavelets as spectral tools for geometry processing with filters in a joint space-frequency domain and examines wavelets as detail extractors for shape feature definition and detection. Going beyond these fundamental applications, the book also covers middle- and high-level applications, including shape matching, shape registration, and shape retrieval. Easy-to-Understand Implementations and Algorithms Unlike many other wavelet books, this one does not involve complicated mathematics. Instead, the book uses simplified formulations and illustrative examples to explain deep theories. Code and other materials are available on a supplementary website.