Download or read book Statistical Shape Analysis of Featureless Objects written by Asger Hobolth and published by . This book was released on 2002 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Statistical Shape Analysis written by Ian L. Dryden and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Offers a detailed yet accessible treatment of statistical methods for shape analysis Includes numerous examples and applications from many disciplines Provides R code for implementing the examples Covers a wide variety of recent developments in shape analysis 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.

Download or read book Elastic Shape Analysis of Three Dimensional Objects written by Ian H. Jermyn and published by Morgan & Claypool Publishers. This book was released on 2017-09-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Object Recognition Using Statistical Shape Analysis written by Catherine Rebecca Anderson and published by . This book was released on 1996 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Innovations for Shape Analysis written by Michael Breuß and published by Springer Science & Business Media. This book was released on 2013-04-04 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe. Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithms, the book is the product of a key seminar focused on innovations in the field. It is a thorough introduction to the latest technology, especially given the tutorial style of a number of chapters. It also succeeds in identifying promising avenues for future research. The topics covered include mathematical morphology, skeletonization, statistical shape modeling, continuous-scale shape models such as partial differential equations and the theory of discrete shape descriptors. Some authors highlight new areas of enquiry such as partite skeletons, multi-component shapes, deformable shape models, and the use of distance fields. Combining the latest theoretical analysis with cutting-edge applications, this book will attract both academics and engineers.

Download or read book Statistical Shape Analysis Using Deformetrica written by Mithun Acharjee and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical shape analysis is an emerging field of research that analyzes the geometrical properties of a given set of shapes or objects using different statistical methods. Two important aspects of the shape analysis are to estimate the mean shape from a given set of shapes and to estimate a shape trajectory as close as to the observed shapes in order to determine the continuous evaluation of shapes over time. A deterministic Atlas model is used to compute the mean shape (also referred to as atlas construction) from a set of shapes which builds a generalization of a typical representation by preserving the characteristics of the original shapes. Thus mean shape is useful in forecasting trends in form or pulling out stereotypes from a set of homologous shapes. The Geodesic regression is used to estimate the continuous shape evaluation at a certain time within its intervals where the mean face obtained from the deterministic atlas model can be used as baseline shape or initial template face to initiate the program. In this thesis, we are showing the application of the deterministic atlas model and geodesic regression model using a shape analysis software called Deformetrica. We collected data from the three Dimensional Facial Norm (3DFN) database which provides craniofacial anthropometric normative data deposited in the FaceBase consortium. Our data are 3D facial mesh where each facial mesh contains a high number of landmark points. We applied the deterministic atlas model using Deformetrica accessing the GPU allocation, which helps to estimate the mean facial object. We used this mean facial object as an initial template shape on geodesic regression which provides an estimated shape trajectory of the facial objects. This geodesic shape trajectory is a geodesic flow of diffeomorphisms acting on the above baseline template shape to estimate the continuous 3D facial evaluation with age varying continuously within its range. This thesis also describes the technical details of using Deformetrica in a high-performance computing environment while dealing a 3D geometric objects with a high number of landmark points.

Download or read book Shape Analysis and Retrieval of Multimedia Objects written by Maytham H. Safar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape Analysis and Retrieval of Multimedia Objects provides a comprehensive survey of the most advanced and powerful shape retrieval techniques used in practice today. In addition, this monograph addresses key methodological issues for evaluation of the shape retrieval methods. Shape Analysis and Retrieval of Multimedia Objects is designed to meet the needs of practitioners and researchers in industry, and graduate-level students in Computer Science.

Download or read book Mathematical Methods in Computer Vision written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2003-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Comprises some of the key work presented at two IMA Wokshops on Computer Vision during fall of 2000."--Pref.

Download or read book Statistical Shape Modeling for Custom Design and Analysis written by Xilu Wang and published by . This book was released on 2017 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this dissertation research is to use pre-existing shape data to improve efficiency and quality of custom design and analysis. The rapid advancement of sensor miniaturization and growing sensor networks and computer power has lead to wide availability of massive shape data from populations of objects. Such massive shape data range from human body shapes to longitudinal knee observations of osteoarthritis patients. Populations of shape data also include shapes of man-made objects, such as part shapes of the same model due to manufacturing process variation as well as part shapes due to shape degradation after deployment. Mining and analysis of such massive population-based shape data can result in knowledge of shape variability of the population and lead to the construction of faithful subject-specific 3D shape models from sparse measurements. It is then possible to predict shape-specific functional performance and population-wide structural performance variation. Such an ability brings about unprecedented capabilities and tantalizing opportunities for mass customization, part-specific failure prediction and just-in-time part maintenance, and patient-specific biomedical intervention and treatment. This work aims at developing efficient approaches that can: 1) construct faithful subject-specific shape models from sparse measurements; 2) predict shape-specific structural performance from a given subject-specific shape model; and 3) predict structural performance variation over a shape population. Toward this end, we present a statistical atlas based approach that incorporates statistical shape modeling in subject-specific shape reconstruction, finite element (FE) modeling and analysis. The statistical atlas contains three parts: the mean shape and the variation modes of the shape population which span a linear shape space, the FE mesh of the mean shape, and the selected feature points and sizing dimensions. The feature points and sizing dimensions are selected by maximizing the total variance they capture of the shape population. Given a subject (e.g. a person), the corresponding dimensions are measured and the subject specific shape model is synthesized. The FE mesh of the mean shape serves as the template mesh which can be morphed to the subject shape to conduct subject-specific FE analysis. The FE solution on the template mesh can also be extrapolated to the subject shape through Taylor expansion. The shape variances along the variation modes are obtained by the principal component analysis. These variances tell the amount of shape variabilities in the population and are combined with the Taylor expansion of the FE solution to obtain the structural performance variation across the population. The numerical testings with various 2D and 3D shape databases demonstrate the efficiency and effectiveness of the proposed approach for custom design and analysis. In this dissertation a statistical atlas based framework is developed for custom design and analysis. The main contributions of this work are: 1) An approach that selects feature points and sizing dimensions based on the total variance captured of the shape population. 2) Automated subject-specific FE modeling through mesh morphing based on the shape correspondence obtained by searching in the shape space. A multi-correlation based metric is developed to evaluate the quality of the obtained shape correspondences. 3) A Taylor expansion approach for predicting subject-specific structural performance and computing structural performance variation over a shape population. Multi-point Taylor expansion approach is developed for the cases that the structural performance is highly nonlinear with respect to the shape parameters.

Download or read book Elastic Statistical Shape Analysis with Landmark Constraints written by Justin Strait and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to mathematical and computational advances, the study of shape data is of great interest in numerous fields, including biology, medicine, computer vision, and biometrics. Shape can be de fined as a property of an object which remains after removing variability associated with shape-preserving transformations, including translation, scale, rotation, and, in some cases, re-parameterization. This type of data presents mathematical challenges, as objects may have identical shape despite appearing differently in Euclidean space. The complex structure of shape data requires tools from fields such as differential geometry, algebra, and functional analysis.

Download or read book Perspectives in Shape Analysis written by Michael Breuß and published by Springer. This book was released on 2016-09-30 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.​

Download or read book Shape Classification and Analysis written by Luciano da Fona Costa and published by CRC Press. This book was released on 2018-10-03 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because the properties of objects are largely determined by their geometric features, shape analysis and classification are essential to almost every applied scientific and technological area. A detailed understanding of the geometrical features of real-world entities (e.g., molecules, organs, materials and components) can provide important clues about their origin and function. When properly and carefully applied, shape analysis offers an exceedingly rich potential to yield useful applications in diverse areas ranging from material sciences to biology and neuroscience. Get Access to the Authors’ Own Cutting-Edge Open-Source Software Projects—and Then Actually Contribute to Them Yourself! The authors of Shape Analysis and Classification: Theory and Practice, Second Edition have improved the bestselling first edition by updating the tremendous progress in the field. This exceptionally accessible book presents the most advanced imaging techniques used for analyzing general biological shapes, such as those of cells, tissues, organs, and organisms. It implements numerous corrections and improvements—many of which were suggested by readers of the first edition—to optimize understanding and create what can truly be called an interactive learning experience. New Material in This Second Edition Addresses Graph and complex networks Dimensionality reduction Structural pattern recognition Shape representation using graphs Graphically reformulated, this edition updates equations, figures, and references, as well as slides that will be useful in related courses and general discussion. Like the popular first edition, this text is applicable to many fields and certain to become a favored addition to any library. Visit http://www.vision.ime.usp.br/~cesar/shape/ for Useful Software, Databases, and Videos

Download or read book Shape Curve Analysis Using Curvature written by James Miller and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical shape analysis is a field for which there is growing demand. One of the major drivers for this growth is the number of practical applications which can use statistical shape analysis to provide useful insight. An example of one of these practical applications is investigating and comparing facial shapes. An ever improving suite of digital imaging technology can capture data on the three-dimensional shape of facial features from standard images. A field for which this offers a large amount of potential analytical benefit is the reconstruction of the facial surface of children born with a cleft lip or a cleft lip and palate. This thesis will present two potential methods for analysing data on the facial shape of children who were born with a cleft lip and/or palate using data from two separate studies. One form of analysis will compare the facial shape of one year old children born with a cleft lip and/or palate with the facial shape of control children. The second form of analysis will look for relationships between facial shape and psychological score for ten year old children born with a cleft lip and/or palate. While many of the techniques in this thesis could be extended to different applications much of the work is carried out with the express intention of producing meaningful analysis of the cleft children studies. Shape data can be defined as the information remaining to describe the shape of an object after removing the effects of location, rotation and scale. There are numerous techniques in the literature to remove the effects of location, rotation and scale and thereby define and compare the shapes of objects. A method which does not require the removal of the effects of location and rotation is to define the shape according to the bending of important shape curves. This method can naturally provide a technique for investigating facial shape. When considering a child s face there are a number of curves which outline the important features of the face. Describing these feature curves gives a large amount of information on the shape of the face. This thesis looks to define the shape of children s faces using functions of bending, called curvature functions, of important feature curves. These curvature functions are not only of use to define an object, they are apt for use in the comparison of two or more objects. Methods to produce curvature functions which provide an accurate description of the bending of face curves will be introduced in this thesis. Furthermore, methods to compare the facial shape of groups of children will be discussed. These methods will be used to compare the facial shape of children with a cleft lip and/or palate with control children. There is much recent literature in the area of functional regression where a scalar response can be related to a functional predictor. A novel approach for relating shape to a scalar response using functional regression, with curvature functions as predictors, is discussed and illustrated by a study into the psychological state of ten year old children who were born with a cleft lip or a cleft lip and palate. The aim of this example is to investigate whether any relationship exists between the bending of facial features and the psychological score of the children, and where relationships exist to describe their nature. The thesis consists of four parts. Chapters 1 and 2 introduce the data and give some background to the statistical techniques. Specifically, Chapter 1 briefly introduces the idea of shape and how the shape of objects can be defined using curvature. Furthermore, the two studies into facial shape are introduced which form the basis of the work in this thesis. Chapter 2 gives a broad overview of some standard shape analysis techniques, including Procrustes methods for alignment of objects, and gives further details of methods based on curvature. Functional data analysis techniques which are of use throughout the thesis are also discussed. Part 2 consists of Chapters 3 to 5 which describe methods to find curvature functions that define the shape of important curves on the face and compare these functions to investigate differences between control children and children born with a cleft lip and/or palate. Chapter 3 considers the issues with finding and further analysing the curvature functions of a plane curve whilst Chapter 4 extends the methods to space curves. A method which projects a space curve onto two perpendicular planes and then uses the techniques of Chapter 3 to calculate curvature is introduced to facilitate anatomical interpretation. Whilst the midline profile of a control child is used to illustrate the methods in Chapters 3 and 4, Chapter 5 uses curvature functions to investigate differences between control children and children born with a cleft lip and/or palate in terms of the bending of their upper lips. Part 3 consists of Chapters 6 and 7 which introduce functional regression techniques and use these to investigate potential relationships between the psychological score and facial shape, defined by curvature functions, of cleft children. Methods to both display graphically and formally analyse the regression procedure are discussed in Chapter 6 whilst Chapter 7 uses these methods to provide a systematic analysis of any relationship between psychological score and facial shape. The final part of the thesis presents conclusions discussing both the effectiveness of the methods and some brief anatomical/psychological findings. There are also suggestions of potential future work in the area.

Download or read book Statistical Models of Shape written by Rhodri Davies and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of image interpretation is to convert raw image data into me- ingful information. Images are often interpreted manually. In medicine, for example, a radiologist looks at a medical image, interprets it, and tra- lates the data into a clinically useful form. Manual image interpretation is, however, a time-consuming, error-prone, and subjective process that often requires specialist knowledge. Automated methods that promise fast and - jective image interpretation have therefore stirred up much interest and have become a signi?cant area of research activity. Early work on automated interpretation used low-level operations such as edge detection and region growing to label objects in images. These can p- ducereasonableresultsonsimpleimages,butthepresenceofnoise,occlusion, andstructuralcomplexity oftenleadstoerroneouslabelling. Furthermore,- belling an object is often only the ?rst step of the interpretation process. In order to perform higher-level analysis, a priori information must be incor- rated into the interpretation process. A convenient way of achieving this is to use a ?exible model to encode information such as the expected size, shape, appearance, and position of objects in an image. The use of ?exible models was popularized by the active contour model, or ‘snake’ [98]. A snake deforms so as to match image evidence (e.g., edges) whilst ensuring that it satis?es structural constraints. However, a snake lacks speci?city as it has little knowledge of the domain, limiting its value in image interpretation.

Download or read book Statistical Shape Analysis for Image Segmentation and Physical Model based Non rigid Registration written by Yongmei Wang and published by . This book was released on 1999 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Shape Analysis and Classification written by Luciano da Fontoura Costa and published by CRC Press. This book was released on 2010-12-12 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, traditio

Download or read book Nonrigid Shape Correspondence for Statistical Shape Analysis written by Theodor Dan Richardson and published by . This book was released on 2006 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: