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This book constitutes the refereed proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery, DGCI '97, held in Montpellier, France, in December 1997. The volume presents 17 revised full papers together with three invited full papers. The contributions are organized in sections on 2D recognition, discrete shapes and planes, surfaces, topology, features, and from principles to applications. ... Read more

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Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing.
This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification. ... Read more

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This seminal book is a primer on geometry-driven, nonlineardiffusion as a promising new paradigm for vision, with an emphasis onthe tutorial. It gives a thorough overview of current linear andnonlinear scale-space theory, presenting many viewpoints such asthe variational approach, curve evolution and nonlinear diffusionequations.
The book is meant for computer vision scientists and students, with acomputer science, mathematics or physics background. Appendicesexplain the terminology. Many illustrated applications are given, e.g.in medical imaging, vector valued (or coupled) diffusion, generalimage enhancement (e.g. edge preserving noise suppression) andmodeling of the human front-end visual system. Some examples are givento implement the methods in modern computer-algebra systems.

From the Preface by Jan J. Koenderink:
` I have read through the manuscript of this book infascination. Most of the approaches that have been explored to tweakscale-space into practical tools are represented here. It is easy toappreciate how both the purist and the engineer find problems of greatinterest in this area. The book is certainly unique in its scope andhas appeared at a time where this field is booming and newcomers canstill potentially leave their imprint on the core corpus of scalerelated methods that still slowly emerge. As such the book is a verytimely one. It is quite evident that it would be out of the questionto compile anything like a textbook at this stage: this book is asnapshot of the field that manages to capture its current state verywell and in a most lively fashion. I can heartily recommend itsreading to anyone interested in the issues of image structure, scaleand resolution. ' ... Read more

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Proceedings of the 9th International Conference: DGCI 2000, held in Uppsala, Sweden, December 13-15, 2000. Topics covered include topology, discrete images, surfaces and volumes, shape representation, and shape understanding. Softcover. ... Read more

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This book constitutes the refereed proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery, DGCI'96, held in Lyon, France, in November 1996. Computer imaging essentially depends on discrete models for coding, processing, recognition, representation, etc. The volume presents 24 revised full papers selected from 41 submissions together with 3 invited contributions and a tutorial paper, which bridges the gap between theory and practice. The issues addressed are topology, geometry, shape representation, 3D surfaces and volumes, models for discrete space, image transformation and generation. ... Read more

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This book constitutes the strictly refereed post-workshop proceedings of the Second International Workshop on Automated Deduction in Geometry, ADG'98, held in Beijing, China in August 1998. The 14 revised papers presented were selected from the papers accepted for the workshop after careful reviewing. The papers address all current issues in the area, in particular automated geometry theorem proving, automated geometry problem solving, plane Euclidean reasoning, Clifford algebraic methods for geometric reasoning, decomposing algebraic varieties, applciations in computer vision, mechanical CAGD, etc. ... Read more

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Computational geometry concerns itself with designing andanalyzing algorithms for solving geometric problems. Thefield has reached a high level of sophistication, and verycomplicated algorithms have been designed.However, it isalso useful to develop more practical algorithms, so longasthey are based on rigorous methods. One such method is theuse ofrandomized algorithms. These algorithms have becomemore and more popular,turning into one of the hottest areasof recent years. Dynamic algorithms are particularlyinteresting because in practice the data of a problemareoften acquired progressively. In this monograph the authorstudiesthe theoretical complexity and practical efficiencyof randomized dynamic algorithms. ... Read more

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Computer vision is one of the most active fields of research in computer science. The articles in this work explore the connection between theories of learning and the studies of geometric shapes to influence pattern recognition, and examine applications to problems associated with computer vision. ... Read more

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The ultimate goal of all 3D graphics systems is to render 3Dobjects on a two-dimensional surface such as plotter outputor a workstation screen. The approach adopted by mostgraphics systems is to perform a central orparallelprojection of the objects onto the view surface. Thesesystems have to make use of the mathematical results ofprojectivegeometry.This monograph has as its aim the derivation of a frameworkfor analyzing the behavior of projective transformationsingraphics systems. It is shown that a mathematicallyprecisedescription of the projective geometrical nature of agraphicssystem leads not only to a deeper understanding ofthe system but also to new approaches which result in fasteror more precise algorithms.A further aim of the book is to show the importance ofadvanced mathematics for computer science. Many problemsbecome easier to describe or to solve when the appropriatemathematical tools are used. The author demonstrates thatprojective geometry has a major role to play in computergraphics. ... Read more

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This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009.

The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.

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This book constitutes the thoroughly refereed post-proceedings of the 5th International Workshop on Automated Deduction in Geometry, ADG 2004, held at Gainesville, FL, USA in September 2004.

The 12 revised full papers presented were carefully selected from the papers accepted for the workshop after careful reviewing. All current issues in the area are addressed - theoretical and methodological topics as well as applications thereof - in particular automated geometry theorem proving, automated geometry problem solving, problems of dynamic geometry, and an object-oriented language for geometric objects.

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This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow.

The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it.

Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem. ... Read more

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Contemporary Interdisciplinary Practice in Architecture
'Game Set and Match II' is a 600-page collective volume, which consists of more than 70 papers on contemporary interdisciplinary architectural practice written by well-known architects, designers, engineers, computer scientists and human scientists (including Kas Oosterhuis, Robert Aish, Ole Bouman, Bernard Cache, Georg Flachbart, John Frazer, Marcos Novak, Tom Verebes, Peter Weibel et al.). The book is divided in three parts: Game (Play: Architecture and Gaming), Set (Geometry: Architecture and Advanced Geometries) and Match (Open Source: Architecture and Digital Technologies). It is a great source for anyone interested in the transformation taking place within the architectural profession and the new ideas concerning the conception and design of space. Some of the topics covered in 'Game Set and Match II' are: swarm architecture, parametric design, virtual environments, interactive architecture, kinetic structures, smart materials, collective intelligence, open source, and more. ... Read more

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In this monograph the author presents a thorough computational geometry approach to handling theoretical and practical problems arising from numerically controlled pocket machining. The approach unifies two scientific disciplines: computational geometry and mechanical engineering. Topics of practical importance that are dealt with include the selection of tool sizes, the determination of tool paths, and the optimization of tool paths. Full details of the algorithms are given from a practical point of view, including information on implementation issues. This practice-minded approach is embedded in a rigorous theoretical framework enabling concise statement of definitions and proof of the correctness and efficiency of the algorithms. In particular, the construction of Voronoi diagrams and their use for offset calculations are investigated in great detail. Based on Voronoi diagrams, a graph-like structure is introduced that serves as a high-level abstraction of the pocket geometry and provides the basis for algorithmically performing shape interrogation and path planning tasks. Finally, the efficiency and robustness of the approach is illustrated with figures showing pocketing examples that have been processed by the author's own implementation. ... Read more

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This anthology is based on the First ACM Workshop on Applied Computational Geometry, WACG '96, held in Philadelphia, PA, USA, in May 1996, as part of the FCRC Conference. Today, CG is in transition and applied computational geometry has established itself as a fertile meeting ground for theorists from core computational geometry and practitioners from the potential application areas to exchange their ideas and identify issues of common interest. The book presents 11 invited contributions and state-of-the-art reports by leading experts together with 12 refereed full papers selected from 32 submissions. It points the way towards geometrical engineering and addresses researchers and professionals sharing an interest in geometric algorithms and techniques and their use in computational sciences and engineering. ... Read more

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This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects which cannot be easily done with a ruler and compass.

Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically without using computer where possible so that readers can compare the strengths and weaknesses of both approaches.

Contents: Automatic Theorem Proving; Generalization of the Formula of Heron; Simson Wallace Theorem; Transversals in a Polygon; Petr Douglas Neumann's Theorem; Geometric Inequalities; Regular Polygons. ... Read more

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This volume constitutes the proceedings of the DIMACS International Workshop on Graph Drawing, GD '94, held in Princeton, New Jersey in October 1994. The 50 papers and system descriptions presented address the problem of constructing geometric representations of abstract graphs, networks and hypergraphs, with applications to key technologies such as software engineering, databases, visual interfaces, and circuit layout; they are organized in sections on three-dimensional drawings, orthogonal drawings, planar drawings, crossings, applications and systems, geometry, system demonstrations, upward drawings, proximity drawings, declarative and other approaches; in addition reports on a graph drawing contest and a poster gallery are included. ... Read more

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This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometrical images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry.

Well-illustrated with more than 350 figures--reproduceable using the Maple programs in the book--the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, many of the programs can be downloaded from the author's website.

Aimed at a broad audience of students, instructors of mathematics, computer scientists and engineers who have a knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, "Geometry of Curves and Surfaces with Maple" will integrate traditional differential and non-Euclidean geometries with more current computer algebra systems in a practical and user-friendly format. ... Read more