Group Theoretical Methods In Image Processing

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Group Theoretical Methods In Image Processing

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Author : Reiner Lenz
language : en
Publisher: Springer
Release Date : 2014-03-12

Group Theoretical Methods In Image Processing written by Reiner Lenz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Computers categories.

In this volume the author gives an introduction to the theory of group representations and their applications in image science. The main feature of the presentation is a systematic treatment of the invariance principle in image processing and pattern recognition with the help of group theoretical methods. The invariance properties of a problem often largely define the solution to the problem. Invariance principles are well known in theoretical physics but their use in image processing is only a few years old. The reader will find that group theory provides a unifying framework for many problems in image science. The volume is based on graduate-level lectures given by the author, and the book is intended for students and researchers interested in theoretical aspects of computer vision.

Group Theoretical Methods In Image Understanding

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Author : Ken-ichi Kanatani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Group Theoretical Methods In Image Understanding written by Ken-ichi Kanatani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Image understanding is an attempt to extract knowledge about a 3D scene from 20 images. The recent development of computers has made it possible to automate a wide range of systems and operations, not only in the industry, military, and special environments (space, sea, atomic plants, etc.), but also in daily life. As we now try to build ever more intelligent systems, the need for "visual" control has been strongly recognized, and the interest in image under standing has grown rapidly. Already, there exists a vast body of literature-ranging from general philosophical discourses to processing techniques. Compared with other works, however, this book may be unique in that its central focus is on "mathematical" principles-Lie groups and group representation theory, in particular. In the study of the relationship between the 3D scene and the 20 image, "geometry" naturally plays a central role. Today, so many branches are inter woven in geometry that we cannot truly regard it as a single subject. Neverthe less, as Felix Klein declared in his Erlangen Program, the central principle of geometry is group theory, because geometrical concepts are abstractions of properties that are "invariant" with respect to some group of transformations. In this text, we specifically focus on two groups of transformations. One is 20 rotations of the image coordinate system around the image origin. Such coordi nate rotations are indeed irrelevant when we look for intrinsic image properties.

Group Theoretical Methods In Image Understanding

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Author : Kenichi Kanatani
language : en
Publisher: Springer
Release Date : 2011-10-05

Group Theoretical Methods In Image Understanding written by Kenichi Kanatani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Science categories.

Image understanding is an attempt to extract knowledge about a 3D scene from 20 images. The recent development of computers has made it possible to automate a wide range of systems and operations, not only in the industry, military, and special environments (space, sea, atomic plants, etc.), but also in daily life. As we now try to build ever more intelligent systems, the need for "visual" control has been strongly recognized, and the interest in image under standing has grown rapidly. Already, there exists a vast body of literature-ranging from general philosophical discourses to processing techniques. Compared with other works, however, this book may be unique in that its central focus is on "mathematical" principles-Lie groups and group representation theory, in particular. In the study of the relationship between the 3D scene and the 20 image, "geometry" naturally plays a central role. Today, so many branches are inter woven in geometry that we cannot truly regard it as a single subject. Neverthe less, as Felix Klein declared in his Erlangen Program, the central principle of geometry is group theory, because geometrical concepts are abstractions of properties that are "invariant" with respect to some group of transformations. In this text, we specifically focus on two groups of transformations. One is 20 rotations of the image coordinate system around the image origin. Such coordi nate rotations are indeed irrelevant when we look for intrinsic image properties.

Group Theoretical Methods In Image Processing

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Author : Reiner Lenz
language : en
Publisher: Lecture Notes in Computer Science
Release Date : 1990-03-07

Group Theoretical Methods In Image Processing written by Reiner Lenz and has been published by Lecture Notes in Computer Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-07 with Computers categories.

In this volume the author gives an introduction to the theory of group representations and their applications in image science. The main feature of the presentation is a systematic treatment of the invariance principle in image processing and pattern recognition with the help of group theoretical methods. The invariance properties of a problem often largely define the solution to the problem. Invariance principles are well known in theoretical physics but their use in image processing is only a few years old. The reader will find that group theory provides a unifying framework for many problems in image science. The volume is based on graduate-level lectures given by the author, and the book is intended for students and researchers interested in theoretical aspects of computer vision.

Group Theoretical Methods And Their Applications

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Author : E. Stiefel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Group Theoretical Methods And Their Applications written by E. Stiefel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

X system Ib-TEX. I wish to thank her for the beautiful work and the numerous discussions on the contents of this book. I am indebted to Peter Fassler, Neu-Technikum Buchs, Switzerland, for drafting the figures, to my students Kurt Rothermann and Stefan Strahl for computer enhancing and labeling the graphics, to Pascal Felder and Markus Wittwer for a simulation program that generated the figures in the stochastics sections. My thanks go to my new colleague at work, Daniel Neuenschwander, for the inspiring discussions related to the section in stochastics and for reading the manuscript to it. I am also grateful to Dacfey Dzung for reading the whole manuscript. Thanks go especially to Professor \Valter Gander of ETH, Zurich, who at the finishing stage and as an expert of 'JEXgenerously invested numerous hours to assist us in solving software as well as hardware problems; thanks go also to Martin Muller, Ingenieurschule Biel, who made the final layout of this book on the NeXT computer. Thanks are also due to Helmut Kopka of the Max Planck Institute, for solving software problems, and to Professor Burchard Kaup of the Uni versity of Fribourg, Switzerland for adding some useful software; also to Birkhauser Boston Inc. for the pleasant co-operation. Finally, let me be reminiscent of Professor E. Stiefel (deceased 1978) with whom I had many interesting discussions and true co-operation when writing the book in German.

Group Theoretical Methods In Image Understanding

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Author : K. Kanatani
language : it
Publisher:
Release Date :

Group Theoretical Methods In Image Understanding written by K. Kanatani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Modern Group Theoretical Methods In Physics

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Author : J. Bertrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Modern Group Theoretical Methods In Physics written by J. Bertrand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.

This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.

A Generative Theory Of Shape

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Author : Michael Leyton
language : en
Publisher: Springer
Release Date : 2003-06-30

A Generative Theory Of Shape written by Michael Leyton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Computers categories.

The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.

Groups And Computation Ii

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Author : Larry Finkelstein, William M. Kantor
language : en
Publisher: American Mathematical Soc.
Release Date :

Groups And Computation Ii written by Larry Finkelstein, William M. Kantor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Algebra categories.

The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.

Image Processing And Machine Learning

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Author : Erik Cuevas
language : en
Publisher:
Release Date : 2024

Image Processing And Machine Learning written by Erik Cuevas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Image processing categories.

"Image processing and machine learning are used in conjunction to analyze and understand images. Where image processing is used to pre-process images using techniques such as filtering, segmentation and feature extraction, machine learning learning algorithms are used to interpret the processed data through classification, clustering and object detection. This book serves as a textbook for students and instructors of image processing, covering the theoretical foundations and practical applications of some of the most prevalent image processing methods and approaches. Divided into two volumes, this first instalment explores the fundamental concepts and techniques in image processing, starting from pixel operations and their properties, exploring spatial filtering, edge detection, image segmentation, corner detection, and geometric transformations. It provides a solid foundation for readers interested in understanding the core principles and practical applications of image processing, establishing the essential groundwork necessary for further explorations covered in Volume 2. Written with instructors and students of image processing in mind, this book's intuitive organisation also contains appeal for app developers and engineers"--