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2008 | Book

Shape Analysis and Structuring

Editors: Leila De Floriani, Michela Spagnuolo

Publisher: Springer Berlin Heidelberg

Book Series : Mathematics and Visualization

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About this book

Several techniques have been developed in the literature for processing different aspects of the geometry of shapes, for representing and manipulating a shape at different levels of detail, and for describing a shape at a structural level as a concise, part-based, or iconic model. Such techniques are used in many different contexts, such as industrial design, biomedical applications, entertainment, environmental monitoring, or cultural heritage. This book covers a variety of topics related to preserving and enhancing shape information at a geometric level, and to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.

Table of Contents

Frontmatter
1. Shape Interrogation
Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where “class A” surfaces are required and no surface imperfections are allowed, shape interrogation has become recently an important tool for various other types of surface representations such as triangulated or polygonal surfaces, subdivision surface, and algebraic surfaces. In this paper we present the state-of-the-art of shape interrogation methods including methods for detecting surface imperfections, surface analysis tools and methods for visualizing intrinsic surface properties. Furthermore we focus on stable numerical and symbolic solving of algebraic systems of equations, a problem that arises in most shape interrogation methods.
Stefanie Hahmann, Alexander Belyaev, Laurent Busé, Gershon Elber, Bernard Mourrain, Christian Rössl
2. Recent Advances in Remeshing of Surfaces
Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and error-driven remeshing.We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research.
Pierre Alliez, Giuliana Ucelli, Craig Gotsman, Marco Attene
3. Multiresolution Analysis
Multiresolution analysis has received considerable attention in recent years by researchers in the fields of computer graphics, geometric modeling and visualization. They are now considered a powerful tool for efficiently representing functions at multiple levels-ofdetail with many inherent advantages, including compression, Level-Of-Details (LOD) display, progressive transmission and LOD editing.
This survey chapter attempts to provide an overview of the recent results on the topic of multiresolution, with special focus on the work of researchers who are participating in the AIM@SHAPE European Networks of Excellence.
Georges-Pierre Bonneau, Gershon Elber, Stefanie Hahmann, Basile Sauvage
4. Subdivision Surfaces and Applications
After a short introduction on the fundamentals of subdivision surfaces, the more advanced material of this chapter focuses on two main aspects. First, shape interrogation issues are discussed; in particular, artifacts, typical of subdivision surfaces, are analysed. The second aspect is related to how structuring the geometric information: a multi-resolution approach is a natural choice for this geometric representation, and it can be seen as a possible way to structure geometry. Moreover, a first semantic structure can be given by a set of meaningful geometric constraints that the shape has to preserve, often due to the specific application context. How subdivision surfaces can cope with constraint-based modelling is treated in the chapter with a special attention to applications.
Chiara Eva Catalano, Ioannis Ivrissimtzis, Ahmad Nasri
5. Skeletal Structures
Shape Descriptors are compact and expressive representations of objects suitable for solving problems like recognition, classification, or retrieval of shapes, tasks that are computationally expensive if performed on huge data sets. Skeletal structures are a particular class of shape descriptors, which attempt to quantify shapes in ways that agree with human intuition. In fact, they represent the essential structure of objects and the way basic components connect to form a whole.
In the large amount of literature devoted to a wide variety of skeletal structures, this Chapter provides a concise and non-exhaustive introduction to the subject: indeed the first structural descriptor, the medial axis, dates back to 1967, which means forty years of literature on the topic.
Silvia Biasotti, Dominique Attali, Jean-Daniel Boissonnat, Herbert Edelsbrunner, Gershon Elber, Michela Mortara, Gabriella Sanniti di Baja, Michela Spagnuolo, Mirela Tanase, Remco Veltkamp
6. Morphological Representations of Scalar Fields
We consider the problem of representing and extracting morphological information from scalar fields. We focus on the analysis and comparison of algorithms for morphological representation of both 2D and 3D scalar fields. We review algorithms which compute a decomposition of the domain of a scalar field into a Morse and Morse-Smale complex and algorithms which compute a topological representation of the level sets of a scalar field, called a contour tree. Extensions of the morphological representations discussed in the chapter are briefly discussed.
Silvia Biasotti, Leila De Floriani, Bianca Falcidieno, Laura Papaleo
7. Topological Representations of Vector Fields
This chapter gives an overview on topological methods for vector field processing. After introducing topological features for 2D and 3D vector fields, we discuss how to extract and use them as visualization tools for complex flow phenomena. We do so both for static and dynamic fields. Finally, we introduce further applications of topological methods for compressing, simplifying, comparing, and constructing vector fields.
Holger Theisel, Christian Rössl, Tino Weinkauf
8. Control Structure and Multi-Resolution Techniques for Virtual Human Representation
A virtual human is a typical instance of articulated physical objects: it does not have only one shape but many, corresponding to all the possible postures that the underlying articulated skeleton can reach. For realistic rendering results, a high-quality texture is usually associated to the shape and skeleton structure. Controlling and animating a virtual human model requires simultaneously many graphics and computational resources.
The first part of this chapter discusses the control articulated skeleton structure and different approaches to build skeletons [10] and bind it to the geometry. The second part addresses the production of LoDs for virtual humans, both for the 3D shape (geometry) and the articulated skeleton (motion and animation).
Thomas di Giacomo, HyungSeok Kim, Laurent Moccozet, Nadia Magnenat-Thalmann
Backmatter
Metadata
Title
Shape Analysis and Structuring
Editors
Leila De Floriani
Michela Spagnuolo
Copyright Year
2008
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-33265-7
Print ISBN
978-3-540-33264-0
DOI
https://doi.org/10.1007/978-3-540-33265-7

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