Skip to main content
  • Book
  • © 2005

Handbook of Geometric Computing

Applications in Pattern Recognition, Computer Vision, Neuralcomputing, and Robotics

  • Consulting textbook for graduate courses and for researchers seeking powerful geometric methods
  • Great use for specialists working in a particular field or for those who are interested in procedures for dealing with concurrent techniques of different fields like in the design of perception action systems
  • Emphasizes the modern ways and formalisms for the representation and processing of geometric entities and the numerical solutions of equations involving geometric constraints often derived from the problem context
  • The knowledge of all application domains is not required, only very basic notions on geometry
  • The mathematical background will be presented at the beginning of each chapter
  • Includes supplementary material: sn.pub/extras

Buy it now

Buying options

eBook USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (23 chapters)

  1. Front Matter

    Pages I-XV
  2. Neuroscience

    1. Symmetry, Features, and Information

      • Hamid R. Eghbalnia, Amir Assadi, Jim Townsend
      Pages 31-65
  3. Neural Networks

    1. Geometric Approach to Multilayer Perceptrons

      • Hyeyoung Park, Tomoko Ozeki, Shun-ichi Amari
      Pages 69-96
    2. A Lattice Algebraic Approach to Neural Computation

      • Gerhard X. Ritter, Laurentiu Iancu
      Pages 97-127
    3. Eigenproblems in Pattern Recognition

      • Tijl De Bie, Nello Cristianini, Roman Rosipal
      Pages 129-167
  4. Image Processing

    1. Geometric Framework for Image Processing

      • Jan J. Koenderink
      Pages 171-201
    2. Geometric Filters, Diffusion Flows, and Kernels in Image Processing

      • Alon Spira1, Nir Sochen, Ron Kimmel
      Pages 203-230
    3. Chaos-Based Image Encryption

      • Yaobin Mao, Guanrong Chen
      Pages 231-265
  5. Computer Vision

    1. One-Dimensional Retinae Vision

      • Kalle Åström
      Pages 269-304
    2. Three-Dimensional Geometric Computer Vision

      • Anders Heyden
      Pages 305-347
    3. Dynamic \(\mathcal{P}^n \) to \(\mathcal{P}^n \) Alignment

      • Amnon Shashua, Lior Wolf
      Pages 349-381
    4. Detecting Independent 3D Movement

      • Abhijit S. Ogale, Cornelia Fermüller, Yiannis Aloimonos
      Pages 383-401
  6. Perception and Action

    1. Robot Perception and Action Using Conformal Geometric Algebra

      • Eduardo Bayro-Corrochano
      Pages 405-458
  7. Uncertainty in Geometric Computations

    1. Uncertainty Modeling and Geometric Inference

      • Kenichi Kanatani
      Pages 461-491
    2. Uncertainty and Projective Geometry

      • Wolfgang Förstner
      Pages 493-534
    3. The Tensor Voting Framework

      • Gérard Medioni, Philippos Mordohai, Mircea Nicolescu
      Pages 535-568
  8. Computer Graphics and Visualization

    1. Methods for Nonrigid Image Registration

      • Lawrence H. Staib, Yongmei Michelle Wang
      Pages 571-602
  9. Geometry and Robotics

About this book

Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner.

This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.

Reviews

From the reviews:

"The Editor … has brought together some of the current up-to-date applications of geometric computing with the aim of assisting those who are constructing such systems. This includes not only researchers but also postgraduate students and assistants who are involved in developing and studying such systems. … a comprehensive list of the applications that would benefit from the contributions in this text which have been prepared by some of the leaders in fields that range from neuroscience and neural networks to medical imagery and robotics." (W. R. Howard, Kybenetes, Vol. 35 (5), 2006)

Authors and Affiliations

  • Cinvestav Unidad Guadalajara, Ciencias de la Computación, Jalisco, México

    Eduardo Bayro Corrochano

About the author

Researcher in geometric computing for cognitive systems

Full Professor at the Computer Science Department of the

Center of Research and Advanced Studies CINVESTAV, Guadalajara, Mexico

Author and editor of books on geometric computing for computer science and engineering, reviewer, chair and active organiser of workshops and conferences on geometric computing for fields related to the design and building of perception action systems. Areas of research interest: pattern recognition, computer vision, neurocomputing, robotics, multidimensional image analysis, applications of Lie algebras and Clifford geometric algebra to cognitive systems.

Bibliographic Information

Buy it now

Buying options

eBook USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access