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Practical Handbook on IMAGE PROCESSING for SCIENTIFIC and TECHNICAL APPLICATIONS SECOND EDITION © 2004 by CRC Press LLC CRC PRESS Boca Raton London New York Washington, D.C. Practical Handbook on IMAGE PROCESSING for SCIENTIFIC and TECHNICAL APPLICATIONS Bernd Jähne University of Heidelberg SECOND EDITION © 2004 by CRC Press LLC This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microÞlming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. SpeciÞc permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identiÞcation and explanation, without intent to infringe. © 2004 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1900-5 Library of Congress Card Number 2004043570 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Library of Congress Cataloging-in-Publication Data Jèahne, Bernd, 1953- Practical handbook on image processing for scientiÞc and technical applications / Berne Jèahne.— 2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-8493-1900-5 (alk. paper) 1. Image processing—Digital techniques—Handbooks, manuals, etc. I. Title. TA1637.J347 2004 621.36¢7—dc22 2004043570 © 2004 by CRC Press LLC Visit the CRC Press Web site at www.crcpress.com Preface What This Handbook Is About Digital image processing is a fascinating subject in several aspects. Human beings perceive most of the information about their environment through their visual sense. While for a long time images could only be captured by photography, we are now at the edge of another technological revolution that allows image data to be captured, manipulated, and evaluated electronically with computers. With breathtaking pace, computers are becoming more powerful and at the same time less expensive. Thus, the hardware required for digital image processing is readily available. In this way, image processing is becoming a common tool to analyze multidi- mensional scientific data in all areas of natural science. For more and more scientists, digital image processing will be the key to studying complex scientific problems they could not have dreamed of tackling only a few years ago. A door is opening for new interdisciplinary cooperation merging computer science with corresponding research areas. Thus, there is a need for many students, engineers, and researchers in natural and technical disciplines to learn more about digital image processing. Since original image processing literature is spread over many disciplines, it is hard to gather this information. Furthermore, it is important to realize that image process- ing has matured in many areas from ad hoc, empirical approaches to a sound science based on well-established principles in mathematics and physical sciences. This handbook tries to close this gap by providing the reader with a sound basic knowledge of image processing, an up-to-date overview of advanced concepts, and a critically evaluated collection of the best algorithms, demonstrating with real-world applications. Furthermore, the handbook is augmented with usually hard-to-find prac- tical tips that will help to avoid common errors and save valuable research time. The wealth of well-organized knowledge collected in this handbook will inspire the reader to discover the power of image processing and to apply it adequately and successfully to his or her research area. However, the reader will not be overwhelmed by a mere collection of all available methods and techniques. Only a carefully and critically eval- uated selection of techniques that have been proven to solve real-world problems is presented. Many concepts and mathematical tools, which find widespread application in nat- ural sciences, are also applied to digital image processing. Such analogies are pointed out because they provide an easy access to many complex problems in digital image processing for readers with a general background in natural sciences. The author — himself educated in physics and computer science — merges basic research in digital image processing with key applications in various disciplines. This handbook covers all aspects of image processing from image formation to im- age analysis. Volumetric images and image sequences are treated as a natural extension of image processing techniques from two to higher dimensions. III © 2004 by CRC Press LLC IV Prerequisites It is assumed that the reader is familiar with elementary matrix algebra as well as the Fourier transform. Wherever possible, mathematical topics are described intuitively, making use of the fact that image processing is an ideal subject to illustrate even complex mathematical relations. transform to the extent required to understand this handbook. This appendix serves also as a convenient reference to these mathematical topics. How to Use This Handbook This handbook is organized by the tasks required to acquire images and to analyze them. Thus, the reader is guided in an intuitive way and step by step through the chain of tasks. The structure of most chapters is as follows: 1. A summary page highlighting the major topics discussed in the chapter. 2. Description of the tasks from the perspective of the application, specifying and detailing what functions the specific image processing task performs. 3. Outline of concepts and theoretical background to the extent that is required to fully understand the task. 4. Collection of carefully evaluated procedures including illustration of the theoretical performance with test images, annotated algorithms, and demonstration with real- world applications. 5. Ready-to-use reference data, practical tips, references to advanced topics, emerg- ing new developments, and additional reference material. This reference material is parted into small units, consecutively numbered within one chapter with boxed numbers, e. g., 3.1 . The reference item is referred to by this number in the follow- ing style: 3.1 and 3.3. individual chapters are written as much as possible in an internally consistent way. The glossary is unique in the sense that it covers not only image processing in a narrow sense but all important associated topics: optics, photonics, some important general terms in computer science, photogrammetry, mathematical terms of relevance, and terms from important applications of image processing. The glossary contains a brief definition of terms used in image processing with cross-references to find further infor- mation in the main text of the handbook. Thus, you can take the glossary as a starting point for a search on a specific item. All terms contained in the indices are emphasized by typesetting in italic style. Acknowledgments Many of the examples shown in this handbook are taken from my research at Scripps Institution of Oceanography (University of California, San Diego) and at the Institute for Environmental Physics and the Interdisciplinary Center for Scientific Computing (University of Heidelberg). I gratefully acknowledge financial support for this research from the US National Science Foundation (OCE91-15944-02, OCE92-17002, and OCE94- 09182), the US Office of Naval Research (N00014-93-J-0093, N00014-94-1-0050), and the German Science Foundation, especially through the interdisciplinary research unit © 2004 by CRC Press LLC Exceptions from this organization are only the two introductory Chapters 1 and 2. The Another key to the usage of the handbook is the detailed indices and the glossary. Appendix B outlines linear algebra and the Fourier V FOR240 “Image Sequence Analysis to Study Dynamical Processes”. I cordially thank I would also express my sincere thanks to the staff of CRC Press for their constant interest in this handbook and their professional advice. I am most grateful for the invaluable help of my friends at AEON Verlag & Studio in proofreading, maintaining the databases, and in designing most of the drawings. I am also grateful to the many individuals, organizations, and companies that pro- vided valuable material for this handbook: • Many of my colleagues — too many to be named individually here — who worked together with me during the past seven years within the research unit “Image Se- quence Analysis to Study Dynamical Processes” at Heidelberg University • Dr. M. Bock, DKFZ Heidelberg • Dr. J. Klinke, PORD, Scripps Institution of Oceanography, University of California, San Diego • Prof. H G. Maas, Institute of Photogrammetry and Remote Sensing, University of Dresden • Prof. J. Ohser, FH Darmstadt • Dr. T. Scheuermann, Fraunhofer Institute for Chemical Technology, Pfinztal, Ger- many • Prof. Trümper, Max-Planck-Institute for Extraterrestric Physics, Munich • ELTEC Elektronik GmbH, Mainz, Germany • Dr. Klee, Hoechst AG, Frankfurt, Germany • Optische Werke G. Rodenstock, Precision Optics Division, D-80469 Munich • Prof. J. Weickert, University of Saarbrücken, Germany • Zeiss Jena GmbH, Jena, Germany • Dr. G. Zinser, Heidelberg Engineering, Heidelberg, Germany camera test program. I am grateful to the manufacturers and distributors who provided cameras at no cost: Adimec, Allied Vision, Basler Vision Technologies, IDS, PCO, Pulnix, and Stemmer Imaging (Dalsa, Jai). Most examples contained in this handbook have been processed using heurisko®, a versatile and powerful image processing package. heurisko® has been developed by AEON 1 in cooperation with the author. In a rapid progressing field such as digital image processing, a major work like this handbook is never finished or completed. Therefore, any comments on further improvements or additions to the handbook are very welcome. I am also grateful for hints on errors, omissions, or typing errors, which despite all the care taken may have slipped my attention. Heidelberg, Germany, January 2004 Bernd Jähne 1 © 2004 by CRC Press LLC my colleague F. Hamprecht. He contributed the last chapter about classification (Chap- ter 17) to this handbook. The detailed description on imaging sensors in Chapter 5 is based on an extensive AEON Verlag & Studio, Hanau, Germany, http://www.heurisko.de Contents 1 Introduction 1 1.1 Highlights 1 1.2 From Drawings to Electronic Images 2 1.3 Geometric Measurements: Gauging and Counting 3 1.3.1 Size Distribution of Pigment Particles 4 1.3.2 Gas Bubble Size Distributions 4 1.3.3 In Situ Microscopy of Cells in Bioreactors 6 1.4 Radiometric Measurements: Revealing the Invisible 8 1.4.1 Fluorescence Measurements of Concentration Fields 8 1.4.2 Thermography for Botany 11 1.4.3 Imaging of Short Ocean Wind Waves 12 1.4.4 SAR Imaging for Planetology and Earth Sciences 15 1.4.5 X-Ray Astronomy with ROSAT 19 1.4.6 Spectroscopic Imaging for Atmospheric Sciences 19 1.5 Depth Measurements: Exploring 3-D Space 21 1.5.1 Optical Surface Profiling 21 1.5.2 3-D Retina Imaging 24 1.5.3 Distribution of Chromosomes in Cell Nuclei 25 1.5.4 X-Ray and Magnetic Resonance 3-D Imaging 25 1.6 Velocity Measurements: Exploring Dynamic Processes 27 1.6.1 Particle Tracking Velocimetry 27 1.6.2 3-D Flow Tomography 28 1.6.3 Motor Proteins 30 2 Tasks and Tools 33 2.1 Highlights 33 2.2 Basic Concepts 34 2.2.1 Goals for Applications of Image Processing 34 2.2.2 Measuring versus Recognizing 36 2.2.3 Signals and Uncertainty 38 2.2.4 Representation and Algorithms 39 2.2.5 Models 41 2.2.6 Hierarchy of Image Processing Tasks 42 2.3 Tools 45 2.3.1 Overview 45 2.3.2 Camera and Frame Grabber 45 2.3.3 Computer 46 2.3.4 Software and Algorithms 50 VII © 2004 by CRC Press LLC VIII Contents I From Objects to Images 3 Quantitative Visualization 55 3.1 Highlights 55 3.2 Task 56 3.3 Concepts 58 3.3.1 Electromagnetic Waves 58 3.3.2 Particle Radiation 63 3.3.3 Acoustic Waves 64 3.3.4 Radiometric Terms 64 3.3.5 Photometric Terms 67 3.3.6 Surface-Related Interactions of Radiation with Matter 70 3.3.7 Volume-Related Interactions of Radiation with Matter 76 3.4 Procedures 82 3.4.1 Introduction 82 3.4.2 Types of Illumination 82 3.4.3 Illumination Techniques for Geometric Measurements 84 3.4.4 Illumination Techniques for Depth Measurements 86 3.4.5 Illumination Techniques for Surface Slope Measurements . . 88 3.4.6 Color and Multi-Spectral Imaging 96 3.4.7 Human Color Vision 100 3.4.8 Thermal Imaging 103 3.4.9 Imaging of Chemical Species and Material Properties 106 3.5 Advanced Reference Material 108 3.5.1 Classification of Radiation 108 3.5.2 Radiation Sources 110 3.5.3 Human Vision 113 3.5.4 Selected Optical Properties 114 3.5.5 Further References 116 4 Image Formation 119 4.1 Highlights 119 4.2 Task 120 4.3 Concepts 122 4.3.1 Coordinate Systems 122 4.3.2 Geometrical Optics 125 4.3.3 Wave Optics 137 4.3.4 Radiometry of Imaging 140 4.3.5 Linear System Theory 143 4.4 Procedures 147 4.4.1 Geometry of Imaging 147 4.4.2 Stereo Imaging 154 4.4.3 Confocal Laser Scanning Microscopy 159 4.4.4 Tomography 161 4.5 Advanced Reference Material 163 4.5.1 Data of Optical Systems for CCD Imaging 163 4.5.2 Optical Design 166 4.5.3 Further References 166 © 2004 by CRC Press LLC Contents IX 5 Imaging Sensors 169 5.1 Highlights 169 5.2 Task 169 5.3 Concepts 170 5.3.1 Overview 170 5.3.2 Detector Performance 171 5.3.3 Quantum Detectors 176 5.3.4 Thermal Detectors 176 5.3.5 Imaging Detectors 177 5.3.6 Television Video Standards 180 5.3.7 CCD Sensor Architectures 181 5.4 Procedures 185 5.4.1 Measuring Performance Parameters of Imaging Sensors 185 5.4.2 Sensor and Camera Selection 189 5.4.3 Spectral Sensitivity 191 5.4.4 Artifacts and Operation Errors 192 5.5 Advanced Reference Material 197 5.5.1 Basic Properties of Imaging Sensors 197 5.5.2 Standard Video Signals; Timing and Signal Forms 199 5.5.3 Color Video Signals 201 5.5.4 Cameras and Connectors 204 5.5.5 Further References 205 6 Digitalization and Quantization 207 6.1 Highlights 207 6.2 Task 207 6.3 Concepts 208 6.3.1 Digital Images 208 6.3.2 The Sampling Theorem 213 6.3.3 Sampling Theorem in xt Space 217 6.3.4 Reconstruction from Sampling 218 6.3.5 Sampling and Subpixel Accurate Gauging 220 6.3.6 Quantization 221 6.4 Procedures 226 6.4.1 The Transfer Function of an Image Acquisition System 226 6.4.2 Quality Control of Quantization 228 6.5 Advanced Reference Material 230 6.5.1 Evolution of Image Acquisition Hardware 230 6.5.2 Analog Video Input 232 6.5.3 Digital Video Input 234 6.5.4 Real-Time Image Processing 236 6.5.5 Further References 238 II Handling and Enhancing Images 7 Pixels 241 7.1 Highlights 241 7.2 Task 242 7.3 Concepts 243 7.3.1 Random Variables and Probability Density Functions 243 7.3.2 Functions of Random Variables 246 7.3.3 Multiple Random Variables and Error Propagation 247 © 2004 by CRC Press LLC X Contents 7.3.4 Homogenous Point Operations 251 7.3.5 Inhomogeneous Point Operations 252 7.3.6 Point Operations with Multichannel Images 253 7.4 Procedures 255 7.4.1 Gray Value Evaluation and Interactive Manipulation 255 7.4.2 Correction of Inhomogeneous Illumination 259 7.4.3 Radiometric Calibration 262 7.4.4 Noise Variance Equalization 263 7.4.5 Histogram Equalization 264 7.4.6 Noise Reduction by Image Averaging 265 7.4.7 Windowing 266 7.5 Advanced Reference Material 267 8 Geometry 269 8.1 Highlights 269 8.2 Task 270 8.3 Concepts 271 8.3.1 Geometric Transformations 271 8.3.2 Interpolation 274 8.4 Procedures 285 8.4.1 Scaling 286 8.4.2 Translation 288 8.4.3 Rotation 288 8.4.4 Affine and Perspective Transforms 290 8.5 Advanced Reference Material 291 9 Restoration and Reconstruction 293 9.1 Highlights 293 9.2 Task 294 9.3 Concepts 294 9.3.1 Types of Image Distortions 294 9.3.2 Defocusing and Lens Aberrations 296 9.3.3 Velocity Smearing 297 9.3.4 Inverse Filtering 297 9.3.5 Model-based Restoration 299 9.3.6 Radon Transform and Fourier Slice Theorem 300 9.4 Procedures 302 9.4.1 Reconstruction of Depth Maps from Focus Series 302 9.4.2 3-D Reconstruction by Inverse Filtering 304 9.4.3 Filtered Backprojection 308 9.5 Advanced Reference Material 311 III From Images to Features 10 Neighborhoods 315 10.1 Highlights 315 10.2 Task 316 10.3 Concepts 317 10.3.1 Masks 317 10.3.2 Operators 319 10.3.3 Convolution 319 10.3.4 Point Spread Function 321 © 2004 by CRC Press LLC [...]... transmitted and received, blue component; middle: C-band, horizontally transmitted and vertically received, green component; right: L-band, horizontally transmitted and vertically received, red component A heavy rain storm with large droplets scatters the short wavelength in the X-band range and thus appears as a black cloud in the expanded image The same area shows up only faintly in the C-band image and. .. 1.4.6) Three-dimensional measurements from volumetric images (Section 1.5) • surface topography measurements of press forms and the human retina (Sections 1.5.1 and 1.5.2) • 3-D microscopy of cell nuclei (Section 1.5.3) • X-ray and magnetic resonance 3-D imaging (Section 1.5.4) Velocity measurements from image sequences (Section 1.6) • particle tracking velocimetry for 2-D flow measurements (Section 1.6.1)... Introduction 1.1 Highlights Electronic imaging and digital image processing constitute — after the invention of photography — the second revolution in the use of images in science and engineering (Section 1.2) Because of its inherently interdisciplinary nature, image processing has become a major integrating factor stimulating communication throughout engineering and natural sciences For technical and scientific... clusters and non-separable particles on size distribution 1.3.2 Gas Bubble Size Distributions Bubbles are submerged into the ocean by breaking waves and play an important role in various small-scale air-sea interaction processes They form an additional surface for the exchange of climate-relevant trace gases between the atmosphere and the ocean, are a main source for marine aerosols and acoustic noise, and. .. increasing specialization of science This section introduces typical scientific and technical applications of image processing The idea is to make the reader aware of the enormous possibilities of modern visualization techniques and digital image processing We will show how new insight is gained into scientific or technical problems by using advanced visualization techniques and digital image processing techniques... symbionts Therefore the oxygen production within the skeleton was measured in relation to various illumination intensities One result is © 2004 by CRC Press LLC 1 Introduction 10 b a c d Figure 1.10: Optical measurement of oxygen in corals: a Sample place for the coral, the lagoon of Heron Island, Capricorn Islands, Great Barrier Reef, Australia b Set-up with the coral in the glass container placed on. .. applications, images have been mostly used in science for qualitative observations and documentation of experimental results Now we are experiencing the second revolution of scientific imaging Images can be converted to electronic form, i e., digital images, that are analyzed quantitatively using computers to perform exact measurements and to visualize complex new phenomena This second revolution is more... Konrad W Röntgen, X-ray images have found widespread application in medicine, science, and technology As it is easy to have a point X-ray source, optics are not required to take an absorption image of an object from X-ray examination To take an image of an X-ray source, however, X-ray optics are required This is a very difficult task as the index of refraction for all materials is very low in the X-ray... crosswind alongwind alongwind 5 m/s b NH95-May 3, 199 5-5 .0m/s D9 1-7 7cm-100m-5.0m/s 0.002 0.002 0.001 0.0005 90 0.0002 45 0.0001 B(k) 0.0005 90 0.0002 45 1000 k [r 2000 ad/m ] θ 500 -4 5 5000 -9 0 0 200 500 k [r 1000 ad/m 2000 ] [ °] [ °] 0.0001 0 200 θ B(k) 0.001 -4 5 -9 0 Figure 1.13: a Sample images taken from the wave-riding buoy at a wind speed of about 5 m/s The left image shows the slope in horizontal... Left: X-band, Middle: C-band, Right: Lband) have been composed into a color image Pristine rain forest appears in pink colors while clear areas for agricultural usage are greenish and bluish A heavy rain storm appears in red and yellow colors since it scatters the shorter wavelength micro waves Image taken with the imaging radar-C/X-band aperture radar (SIRC/X-SAR) on April 10, 1994 on board the space . Practical Handbook on IMAGE PROCESSING for SCIENTIFIC and TECHNICAL APPLICATIONS SECOND EDITION © 2004 by CRC Press LLC CRC PRESS Boca Raton London New York Washington, D.C. Practical Handbook. Data Jèahne, Bernd, 195 3- Practical handbook on image processing for scientiÞc and technical applications / Berne Jèahne.— 2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-8 49 3-1 90 0-5 . D.C. Practical Handbook on IMAGE PROCESSING for SCIENTIFIC and TECHNICAL APPLICATIONS Bernd Jähne University of Heidelberg SECOND EDITION © 2004 by CRC Press LLC This book contains information obtained from

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  • Practical Handbook on IMAGE PROCESSING for SCIENTIFIC and TECHNICAL APPLICATIONS, SECOND EDITION

    • Preface

      • What This Handbook Is About

      • Prerequisites

      • How to Use This Handbook

      • Acknowledgments

    • Contents

    • Appendix A: Notation

    • Appendix B: Mathematical Toolbox

    • Appendix C: Glossary

    • Bibliography

    • Appendix D: Color Plates

  • Chapter 1: Introduction

    • 1.1 Highlights

    • 1.2 From Drawings to Electronic Images

    • 1.3 Geometric Measurements: Gauging and Counting

      • 1.3.1 Size Distribution of Pigment Particles

      • 1.3.2 Gas Bubble Size Distributions

      • 1.3.3 In Situ Microscopy of Cells in Bioreactors

    • 1.4 Radiometric Measurements: Revealing the Invisible

      • 1.4.1 Fluorescence Measurements of Concentration Fields

      • 1.4.2 Thermography for Botany

        • 1.4.2a Patchiness of Photosynthesis

        • 1.4.2b Uncontrolled Evaporation at Tumor Surfaces

      • 1.4.3 Imaging of Short Ocean Wind Waves

      • 1.4.4 SAR Imaging for Planetology and Earth Sciences

      • 1.4.5 X-Ray Astronomy with ROSAT

      • 1.4.6 Spectroscopic Imaging for Atmospheric Sciences

    • 1.5 Depth Measurements: Exploring 3-D Space

      • 1.5.1 Optical Surface Profiling

      • 1.5.2 3-D Retina Imaging

      • 1.5.3 Distribution of Chromosomes in Cell Nuclei

      • 1.5.4 X-Ray and Magnetic Resonance 3-D Imaging

    • 1.6 Velocity Measurements: Exploring Dynamic Processes

      • 1.6.1 Particle Tracking Velocimetry

      • 1.6.2 3-D Flow Tomography

      • 1.6.3 Motor Proteins

    • Appendix A: Notation

    • Appendix B: Mathematical Toolbox

    • Appendix C: Glossary

    • Bibliography

    • Appendix D: Color Plates

  • Chapter 2: Tasks and Tools

    • 2.1 Highlights

      • Task

      • Tools

    • 2.2 Basic Concepts

      • 2.2.1 Goals for Applications of Image Processing

      • 2.2.2 Measuring versus Recognizing

      • 2.2.3 Signals and Uncertainty

      • 2.2.4 Representation and Algorithms

      • 2.2.5 Models

      • 2.2.6 Hierarchy of Image Processing Tasks

        • 2.2.6a From Objects to Images (Part I)

        • 2.2.6b Handling and Enhancing Images (Part II)

        • 2.2.6c From Images to Features (Part III)

        • 2.2.6d From Features to Objects (Part IV)

    • 2.3 Tools

      • 2.3.1 Overview

      • 2.3.2 Camera and Frame Grabber

      • 2.3.3 Computer

        • 2.3.3a Image Display

        • 2.3.3b Memory

        • 2.3.3c Data Transfer Bandwidth

        • 2.3.3d Computing Power

      • 2.3.4 Software and Algorithms

    • Appendix A: Notation

    • Appendix B: Mathematical Toolbox

    • Appendix C: Glossary

    • Bibliography

    • Appendix D: Color Plates

  • Part I: From Objects to Images

    • Chapter 3: Quantitative Visualization

      • 3.1 Highlights

      • 3.2 Task

      • 3.3 Concepts

        • 3.3.1 Electromagnetic Waves

          • 3.3.1a Dispersion

          • 3.3.1b Superposition Principle; Nonlinear Effects

          • 3.3.1c Polarization

          • 3.3.1d Coherence

          • 3.3.1e Energy Flux Density

          • 3.3.1f Particulate Nature of Electromagnetic Waves: Photons

        • 3.3.2 Particle Radiation

        • 3.3.3 Acoustic Waves

        • 3.3.4 Radiometric Terms

          • 3.3.4a Radiant Energy and Radiant Flux

          • 3.3.4b Areal Densities of Radiant Quantities

          • 3.3.4c Intensities and Solid Angle

          • 3.3.4d Radiance

          • 3.3.4e Spectroradiometry

        • 3.3.5 Photometric Terms

          • 3.3.5a Spectral Response of the Human Eye

          • 3.3.5b Photometric Quantities

          • 3.3.5c Radiation Luminous Efficacy

          • 3.3.5d Lighting System Luminous Efficacy

        • 3.3.6 Surface-Related Interactions of Radiation with Matter

          • 3.3.6a Thermal Emission

          • 3.3.6b Refraction

          • 3.3.6c Reflection and Transmission at Specular Surfaces

          • 3.3.6d Reflection at Rough Surfaces

        • 3.3.7 Volume-Related Interactions of Radiation with Matter

          • 3.3.7a Absorptance and Transmittance

          • 3.3.7b Scattering

          • 3.3.7c Optical Activity

          • 3.3.7d Luminescence

          • 3.3.7e Doppler Effect

      • 3.4 Procedures

        • 3.4.1 Introduction

        • 3.4.2 Types of Illumination

        • 3.4.3 Illumination Techniques for Geometric Measurements

          • 3.4.3a Specular Illumination

          • 3.4.3b Diffuse Illumination

          • 3.4.3c Rear Illumination

        • 3.4.4 Illumination Techniques for Depth Measurements

          • 3.4.4a Structured Light

          • 3.4.4b Pulsed Illumination

          • 3.4.4c Modulated Illumination

        • 3.4.5 Illumination Techniques for Surface Slope Measurements

          • 3.4.5a Telecentric Illumination System

          • 3.4.5b Shape From Shading for Lambertian Surfaces

          • 3.4.5c Shape From Shading for Specular Surfaces: Stilwell Photography

          • 3.4.5d Shape From Refraction for Specular Surfaces

          • 3.4.5e Ratio Imaging for Shape from Shading Techniques

        • 3.4.6 Color and Multi-Spectral Imaging

          • 3.4.6a Line sampling

          • 3.4.6b Band sampling

          • 3.4.6c Model-Guided Spectral Sampling

          • 3.4.6d Measurement of Chemical Species by Imaging Spectroscopy

        • 3.4.7 Human Color Vision

          • 3.4.7a 3-D Color Space

          • 3.4.7b Primary Colors

          • 3.4.7c Chromaticity

          • 3.4.7d Hue and Saturation

          • 3.4.7e IHS Color Coordinate System

        • 3.4.8 Thermal Imaging

        • 3.4.9 Imaging of Chemical Species and Material Properties

          • 3.4.9a Measurement of the Concentration of Dissolved Oxygen

          • 3.4.9b Measurement of the pH Value

      • 3.5 Advanced Reference Material

        • 3.5.1 Classification of Radiation

          • Subpartitioning of the ultraviolet part of the electromagnetic spectrum

          • Wavelength ranges for colors; some important emission lines of elements in the gaseous state are also included

          • Subpartitioning of the infrared part of the electromagnetic spectrum

          • Radar frequency bands

        • 3.5.2 Radiation Sources

          • Lighting system luminous efficiency, Ks, for some common light sources

          • Typical energy conversion in different light sources 3.8

        • 3.5.3 Human Vision

          • Relative efficacy V(lamda) for photopic human vision (Fig. 3.6)

          • Relative efficacy V´(lamda) for scotopic human vision (Fig. 3.6) 3.12

        • 3.5.4 Selected Optical Properties

          • Transmissivity of water from the ultraviolet to infrared range of the electromagnetic spectrum

        • 3.5.5 Further References

          • Basics and general references

          • Special topics

          • Applications

          • Lamps and light sources

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 4: Image Formation

      • 4.1 Highlights

      • 4.2 Task

      • 4.3 Concepts

        • 4.3.1 Coordinate Systems

          • 4.3.1a World and Camera Coordinates

          • 4.3.1b Image Coordinates and Principal Point

          • 4.3.1c Homogeneous Coordinates

        • 4.3.2 Geometrical Optics

          • 4.3.2a Pinhole Camera Model: Perspective Projection

          • 4.3.2b Pixel Coordinates and Intrinsic Camera Parameters

          • 4.3.2c Perfect Optical Systems

          • 4.3.2d Depth of Focus and Depth of Field

          • 4.3.2e Telecentric and Hypercentric Imaging

          • 4.3.2f Lens Aberrations

          • 4.3.2g Geometric Distortions

        • 4.3.3 Wave Optics

          • 4.3.3a Diffraction-limited Optics

          • 4.3.3b Gaussian Beams

        • 4.3.4 Radiometry of Imaging

          • 4.3.4a Radiance Invariance

          • 4.3.4b Irradiance on the Image Plane

        • 4.3.5 Linear System Theory

          • 4.3.5a Point Spread Function

          • 4.3.5b Optical Transfer Function

          • 4.3.5c Interpretation of the 3-D OTF

          • 4.3.5d 2-D OTF of a Diffraction-Limited Optical System

          • 4.3.5e Modulation Transfer Function

          • 4.3.5f Coherent Versus Incoherent Imaging

      • 4.4 Procedures

        • 4.4.1 Geometry of Imaging

          • 4.4.1a Depth of Field

          • 4.4.1b Radiometry and Photometry of Imaging

          • 4.4.1c Telecentric Imaging for Optical Gauging

        • 4.4.2 Stereo Imaging

          • 4.4.2a Stereo Setup with Parallel Camera Axes

          • 4.4.2b Stereo Setup with Verging Camera Axes

          • 4.4.2c Case Study Stereo Imaging of Ocean Surface Waves

        • 4.4.3 Confocal Laser Scanning Microscopy

        • 4.4.4 Tomography

          • 4.4.4a Principle

          • 4.4.4b Homogeneity of Tomographic Projection

      • 4.5 Advanced Reference Material

        • 4.5.1 Data of Optical Systems for CCD Imaging

          • Standard focal lengths for CCD lenses

          • Miniature CCD lenses

          • Achromats as CCD lenses

          • Macro lenses

        • 4.5.2 Optical Design

        • 4.5.3 Further References

          • General references

          • Optical engineering

          • Special image formation techniques and applications

          • Organizations and technical societies

          • Magazines covering optics and photonics

          • Manufacturers and distributors of optical components

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 5: Imaging Sensors

      • 5.1 Highlights

      • 5.2 Task

      • 5.3 Concepts

        • 5.3.1 Overview

        • 5.3.2 Detector Performance

          • 5.3.2a Responsivity

          • 5.3.2b Quantum Efficiency

          • 5.3.2c Signal Irradiance Relation

          • 5.3.2d Dark Current

          • 5.3.2e Noise Equivalent Exposure

          • 5.3.2f Saturation Equivalent Exposure

          • 5.3.2g Photon Noise Limited Performance

          • 5.3.2h Noise Model for Image Sensors

          • 5.3.2i Dynamic Range

          • 5.3.2j Signal-to-Noise Ratio

          • 5.3.2k Nonuniform Responsivity

        • 5.3.3 Quantum Detectors

          • 5.3.3a Photoemissive Detectors

          • 5.3.3b Photovoltaic and Photoconductive Detectors

        • 5.3.4 Thermal Detectors

        • 5.3.5 Imaging Detectors

          • 5.3.5a The Charge Coupled Device

          • 5.3.5b CMOS Imaging Sensors

          • 5.3.5c Detectable Wavelength Range

          • 5.3.5d Quantum Efficiency

          • 5.3.5e Dark Current

          • 5.3.5f Full-Well Capacity and Saturation Exposure

        • 5.3.6 Television Video Standards

        • 5.3.7 CCD Sensor Architectures

          • 5.3.7a Frame Transfer

          • 5.3.7b Interline Transfer

          • 5.3.7c Electronic Shutter

          • 5.3.7d Micro Lens Arrays

          • 5.3.7e Progressive Scanning

      • 5.4 Procedures

        • 5.4.1 Measuring Performance Parameters of Imaging Sensors

          • 5.4.1a Responsivity and Linearity

          • 5.4.1b Noise and Signal-to-Noise Relation

          • 5.4.1c Spatial Inhomogeneities

        • 5.4.2 Sensor and Camera Selection

          • 5.4.2a Demands from Applications

          • 5.4.2b Sensitivity versus Quality

        • 5.4.3 Spectral Sensitivity

        • 5.4.4 Artifacts and Operation Errors

          • 5.4.4a Offsets and Nonlinearities by Misadjustments

          • 5.4.4b Blooming and Smear

          • 5.4.4c Dirt on the CCD Cover Glass

          • 5.4.4d Motion Artifacts by Interlaced Exposure

          • 5.4.4e Electronic Interferences

          • 5.4.4f Color Carrier Signal in Gray Scale Images

      • 5.5 Advanced Reference Material

        • 5.5.1 Basic Properties of Imaging Sensors

          • Nominal sizes of imaging sensors

          • Basic data of some Kodak interline CCD imaging sensors

        • 5.5.2 Standard Video Signals; Timing and Signal Forms

          • Timing of analog video signals

          • Video timing diagram for the RS170 norm

          • Video timing diagram for the CCIR norm

        • 5.5.3 Color Video Signals

          • Color bar

        • 5.5.4 Cameras and Connectors

          • Firewire (IEEE1394)

          • Camera link cameras

        • 5.5.5 Further References

          • General References

          • Manufacturers of imaging sensors and cameras

          • References to solid-state imaging

          • References to special topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 6: Digitalization and Quantization

      • 6.1 Highlights

      • 6.2 Task

      • 6.3 Concepts

        • 6.3.1 Digital Images

          • 6.3.1a Pixel or Pel

          • 6.3.1b Neighborhood Relations

          • 6.3.1c Discrete Geometry

          • 6.3.1d Moiré-Effect and Aliasing

        • 6.3.2 The Sampling Theorem

          • 6.3.2a Image Formation

          • 6.3.2b Spatial and Temporal Integration by Sensor Element

          • 6.3.2c Sampling

          • 6.3.2d Limitation to a Finite Window

        • 6.3.3 Sampling Theorem in xt Space

        • 6.3.4 Reconstruction from Sampling

        • 6.3.5 Sampling and Subpixel Accurate Gauging

        • 6.3.6 Quantization

          • 6.3.6a Uniform Quantization

          • 6.3.6b Quantization Error

          • 6.3.6c Accuracy and Precision of Gray Value Measurements

          • 6.3.6d Unsigned and Signed Representation

          • 6.3.6e Human Perception of Luminance Levels

      • 6.4 Procedures

        • 6.4.1 The Transfer Function of an Image Acquisition System

          • 6.4.1a Test Pattern for OTF Measurements

          • 6.4.1b Moiré Pattern

          • 6.4.1c Modulation Transfer Function and Depth of Field

        • 6.4.2 Quality Control of Quantization

      • 6.5 Advanced Reference Material

        • 6.5.1 Evolution of Image Acquisition Hardware

          • 6.5.1a Hardwired Frame Grabbers

          • 6.5.1b Modular Image Processing Systems with a Pipelined Video Bus

          • 6.5.1c Frame Grabber with Programmable Processor

          • 6.5.1d Frame Grabbers with Direct Image Transfer to PC RAM

        • 6.5.2 Analog Video Input

          • 6.5.2a Analog Video Signal Processing

          • 6.5.2b Synchronization

          • 6.5.2c Digitization

          • 6.5.2d Pros and Cons of Analog Video Input

        • 6.5.3 Digital Video Input

          • 6.5.3a Pros and Cons of Digital Video Input

          • 6.5.3b Standards for Digital Video Input

        • 6.5.4 Real-Time Image Processing

        • 6.5.5 Further References

          • Graphics file formats

          • List of some manufacturers of image acquisition hardware

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

  • Part II: Handling and Enhancing Images

    • Chapter 7: Pixels

      • 7.1 Highlights

      • 7.2 Task

      • 7.3 Concepts

        • 7.3.1 Random Variables and Probability Density Functions

          • 7.3.1a Continuous and Discrete Random Variables

          • 7.3.1b Mean, Variance, and Moments

          • 7.3.1c Normal Distribution

          • 7.3.1d Binomial Distribution

          • 7.3.1e Poisson Distribution

          • 7.3.1f Histograms

        • 7.3.2 Functions of Random Variables

        • 7.3.3 Multiple Random Variables and Error Propagation

          • 7.3.3a Joint Probability Density Functions

          • 7.3.3b Covariance and Correlation

          • 7.3.3c Functions of Multiple Random Variables

        • 7.3.4 Homogenous Point Operations

          • 7.3.4a Look-Up Tables

        • 7.3.5 Inhomogeneous Point Operations

        • 7.3.6 Point Operations with Multichannel Images

          • 7.3.6a Linear Multicomponent Point Operations

          • 7.3.6b Nonlinear Multicomponent Point Operations

          • 7.3.6c Dyadic Point Operations

      • 7.4 Procedures

        • 7.4.1 Gray Value Evaluation and Interactive Manipulation

          • 7.4.1a Evaluation of Homogeneous Illuminance

          • 7.4.1b Detection of Underflow and Overflow

          • 7.4.1c Interactive Gray Scale Manipulation

        • 7.4.2 Correction of Inhomogeneous Illumination

        • 7.4.3 Radiometric Calibration

        • 7.4.4 Noise Variance Equalization

        • 7.4.5 Histogram Equalization

        • 7.4.6 Noise Reduction by Image Averaging

        • 7.4.7 Windowing

      • 7.5 Advanced Reference Material

        • Statistics and random processes

        • Radiometric calibration of sensors and cameras

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 8: Geometry

      • 8.1 Highlights

      • 8.2 Task

      • 8.3 Concepts

        • 8.3.1 Geometric Transformations

          • 8.3.1a Forward and Inverse Mapping

          • 8.3.1b Affine Transform

          • 8.3.1c Perspective Transform

        • 8.3.2 Interpolation

          • 8.3.2a Interpolation in Fourier space

          • 8.3.2b Polynomial Interpolation

          • 8.3.2c Spline-Based Interpolation

          • 8.3.2d Least Squares Optimal Interpolation

      • 8.4 Procedures

        • 8.4.1 Scaling

        • 8.4.2 Translation

        • 8.4.3 Rotation

        • 8.4.4 Affine and Perspective Transforms

      • 8.5 Advanced Reference Material

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 9: Restoration and Reconstruction

      • 9.1 Highlights

      • 9.2 Task

      • 9.3 Concepts

        • 9.3.1 Types of Image Distortions

        • 9.3.2 Defocusing and Lens Aberrations

        • 9.3.3 Velocity Smearing

        • 9.3.4 Inverse Filtering

        • 9.3.5 Model-based Restoration

        • 9.3.6 Radon Transform and Fourier Slice Theorem

      • 9.4 Procedures

        • 9.4.1 Reconstruction of Depth Maps from Focus Series

        • 9.4.2 3-D Reconstruction by Inverse Filtering

        • 9.4.3 Filtered Backprojection

          • 9.4.3a Principle

          • 9.4.3b Continuous Case

          • 9.4.3c Discrete Case

      • 9.5 Advanced Reference Material

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

  • Part III: From Images to Features

    • Chapter 10: Neighborhoods

      • 10.1 Highlights

      • 10.2 Task

      • 10.3 Concepts

        • 10.3.1 Masks

        • 10.3.2 Operators

        • 10.3.3 Convolution

        • 10.3.4 Point Spread Function

        • 10.3.5 Transfer Function

        • 10.3.6 General Properties of Convolution Operators

          • 10.3.6a Linearity

          • 10.3.6b Shift Invariance

          • 10.3.6c Commutativity

          • 10.3.6d Associativity

          • 10.3.6e Separability

          • 10.3.6f Distributivity over Addition

          • 10.3.6g Eigenfunctions

          • 10.3.6h Inverse Operators

        • 10.3.7 Error Propagation with Filtering

        • 10.3.8 Recursive Convolution

          • 10.3.8a Definition

          • 10.3.8b Recursive Filters and Linear Systems

          • 10.3.8c Resistor-Capacitor Circuit; Relaxation Process

          • 10.3.8d Second-Order Recursive Filter; Damped Harmonic Oscillator

          • 10.3.8e Linear System Theory and Modeling

        • 10.3.9 Rank-Value Filters

        • 10.3.10 Strategies for Adaptive Filtering

          • 10.3.10a Limitations of Linear Filters

          • 10.3.10b Problem-Specific Nonlinear Filters

          • 10.3.10c Pixels With Certainty Measures

          • 10.3.10d Adaptive Filtering

          • 10.3.10e Nonlinear Filters by Combining Point Operations and Linear Filter Operations

      • 10.4 Procedures

        • 10.4.1 Filter Design Criteria

          • 10.4.1a Classical Criteria for Filter Design

          • 10.4.1b Filter Design Criteria for Image Processing

        • 10.4.2 Filter Design by Windowing

        • 10.4.3 Recursive Filters for Image Processing

        • 10.4.4 Design by Filter Cascading

        • 10.4.5 Efficient Computation of Neighborhood Operations

          • 10.4.5a In Place Nonrecursive Neighborhood Operations with 2-D masks

          • 10.4.5b Separable Neighborhood Operations

        • 10.4.6 Filtering at Image Borders

        • 10.4.7 Test Patterns

          • 10.4.7a Concentric Ring Test Pattern

          • 10.4.7b Test Image for Edge and Line Detection

      • 10.5 Advanced Reference Material

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 11: Regions

      • 11.1 Highlights

      • 11.2 Task

      • 11.3 Concepts

        • 11.3.1 General Properties of Averaging Filters

          • 11.3.1a Preservation of Object Position

          • 11.3.1b Preservation of Mean Value

          • 11.3.1c Nonselective Smoothing

          • 11.3.1d Isotropy

          • 11.3.1e Symmetric Masks

          • 11.3.1f Separable Masks

          • 11.3.1g Standard Deviation

          • 11.3.1h Noise Suppression

        • 11.3.2 Weighted Averaging

        • 11.3.3 Controlled Averaging

          • 11.3.3a Averaging as Diffusion

          • 11.3.3b Inhomogeneous Diffusion

          • 11.3.3c Anisotropic Diffusion

        • 11.3.4 Steerable Averaging

        • 11.3.5 Averaging in Multichannel Images

      • 11.4 Procedures

        • 11.4.1 Box Filters

          • 11.4.1a Summary of Properties

          • 11.4.1b 1-D Box Filters RB

          • 11.4.1c 2-D Box Filters RRyRRx

          • 11.4.1d 3-D Box Filters RRzRRyRRx

          • 11.4.1e Cascaded Box Filters

        • 11.4.2 Binomial Filters

          • 11.4.2a Summary of Properties

          • 11.4.2b 1-D Binomial Filters BR

          • 11.4.2c 2-D Binomial Filters BRBRX

          • 11.4.2d 3-D Binomial Filters BRzBRyBRx

        • 11.4.3 Cascaded Multistep Filters

          • 11.4.3a Principle

          • 11.4.3b Efficient Implementation

        • 11.4.4 Cascaded Multigrid Filters

        • 11.4.5 Recursive Smoothing

        • 11.4.6 Inhomogeneous and Anisotropic Diffusion

        • 11.4.7 Steerable Directional Smoothing

      • 11.5 Advanced Reference Material

        • Equations for symmetric masks with odd-numbered size in 2-D and 3-D

        • Equations for symmetric masks with even-numbered size in 2-D and 3-D

        • Transfer functions for symmetric 2-D masks with even and odd number of coefficients

        • Transfer functions for symmetric 3-D masks with even and odd number of coefficients

        • Reference to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 12: Edges and Lines

      • 12.1 Highlights

      • 12.2 Task

      • 12.3 Concepts

        • 12.3.1 Edge Models

        • 12.3.2 Principal Methods for Edge Detection

          • 12.3.2a The Gradient Vector

          • 12.3.2b The Laplacian Operator

          • 12.3.2c Edge Coefficient

        • 12.3.3 General Properties

          • 12.3.3a Preservation of Object Position

          • 12.3.3b No Response to Mean Value

          • 12.3.3c Nonselective Derivation

          • 12.3.3d Noise sensitivity

          • 12.3.3e Symmetrical Masks

        • 12.3.4 Edges in Multichannel Images

        • 12.3.5 Regularized Edge Detection

      • 12.4 Procedures

        • 12.4.1 First-Order Derivation

          • 12.4.1a First-Order Discrete Differences

          • 12.4.1b Higher-order approximations by Taylor expansion

          • 12.4.1c Differentiation of a Spline Representation

          • 12.4.1d Least-Squares First-Order Derivation

        • 12.4.2 Second-Order Derivation

          • 12.4.2a Least-Squares Second-Order Derivation

        • 12.4.3 Regularized Edge Detectors

          • 12.4.3a Classical Edge Detectors

          • 12.4.3b Derivatives of Gaussian

        • 12.4.4 LoG and DoG Filter

        • 12.4.5 Optimized Regularized Edge Detectors

      • 12.5 Advanced Reference Material

        • Reference to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 13: Orientation and Velocity

      • 13.1 Highlights

      • 13.2 Task

      • 13.3 Concepts

        • 13.3.1 Simple Neighborhoods

          • 13.3.1a Definition

          • 13.3.1b Representation in Fourier Space

          • 13.3.1c Orientation versus Direction

          • 13.3.1d Vector Representation of Local Orientation

        • 13.3.2 Classification of Local Structures

          • 13.3.2a Simple Objects

          • 13.3.2b Texture

          • 13.3.2c Image Sequence

        • 13.3.3 First-Order Tensor Representation

          • 13.3.3a Two-Dimensional Eigenvalue Analysis

          • 13.3.3b Three-Dimensional Eigenvalue Analysis

      • 13.4 Procedures

        • 13.4.1 Set of Directional Quadrature Filters

          • 13.4.1a Introductionary Remarks

          • 13.4.1b Polar Separable Quadrature Filters

          • 13.4.1c Computation of Orientation Vector

          • 13.4.1d Evaluation

        • 13.4.2 2-D Tensor Method

          • 13.4.2a Computation of the Tensor Components

          • 13.4.2b Computation of the Orientation Vector

          • 13.4.2c Orientation Coherency

          • 13.4.2d Color Coding of the Structure Tensor

          • 13.4.2e Theoretical Performance and Systematic Errors

          • 13.4.2f Accurate Implementation

          • 13.4.2g Fast Implementation

          • 13.4.2h Statistical Errors

        • 13.4.3 Motion Analysis in Space-Time Images

      • 13.5 Advanced Reference Material

        • References for orientation and motion analysis

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 14: Scale and Texture

      • 14.1 Highlights

      • 14.2 Task

      • 14.3 Concepts

        • 14.3.1 What Is Texture?

        • 14.3.2 The Wave Number Domain

        • 14.3.3 Hierarchy of Scales

        • 14.3.4 Gaussian Pyramid

          • 14.3.4a Principle

          • 14.3.4b Fast and Accurate Filters

        • 14.3.5 Laplacian Pyramid

        • 14.3.6 Directio-Pyramidal Decomposition

        • 14.3.7 Phase and Local Wave Number

          • 14.3.7a Local Wave Number

          • 14.3.7b Hilbert Transform and Analytic Signal

          • 14.3.7c Riesz Transform and Monogenic Signal

      • 14.4 Procedures

        • 14.4.1 Texture Energy

        • 14.4.2 Phase Determination

          • 14.4.2a Quadrature Pair Filters

          • 14.4.2b Hilbert Filters

        • 14.4.3 Local Wave Number

          • 14.4.3a Principle

          • 14.4.3b Phase Gradient

      • 14.5 Advanced Reference Material

        • References to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

  • Part IV: From Features to Objects

    • Chapter 15: Segmentation

      • 15.1 Highlights

      • 15.2 Task

      • 15.3 Concepts

        • 15.3.1 Pixel-Based Segmentation

        • 15.3.2 Region-Based Segmentation

        • 15.3.3 Edge-Based Segmentation

        • 15.3.4 Model-Based Segmentation

          • 15.3.4a Introduction

          • 15.3.4b Model Spaces

      • 15.4 Procedures

        • 15.4.1 Global Thresholding

        • 15.4.2 Pyramid Linking

        • 15.4.3 Orientation-Based Fast Hough Transformation

      • 15.5 Advanced Reference Material

        • References to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 16: Size and Shape

      • 16.1 Highlights

      • 16.2 Task

      • 16.3 Concepts

        • 16.3.1 Morphological Operators

          • 16.3.1a Neighborhood Operations on Binary Images

          • 16.3.1b General Properties of Morphological Operations

          • 16.3.1c Hit-Miss Operator

        • 16.3.2 Run-Length Code

        • 16.3.3 Chain Code

        • 16.3.4 Fourier Descriptors

        • 16.3.5 Moments

          • 16.3.5a Definitions

          • 16.3.5b Normalized Moments

          • 16.3.5c Second-Order Moments; the Inertia Tensor

      • 16.4 Procedures

        • 16.4.1 Object Shape Manipulation

          • 16.4.1a Removal of Small Objects

          • 16.4.1b Filling Holes and Cracks

          • 16.4.1c Shape Detection and Selection

        • 16.4.2 Extraction of Object Boundaries

        • 16.4.3 Basic Shape Parameters

          • 16.4.3a Area

          • 16.4.3b Perimeter

          • 16.4.3c Form Parameters

          • 16.4.3d Object Orientation

        • 16.4.4 Scale and Rotation Invariant Shape Parameters

      • 16.5 Advanced Reference Material

        • References to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Chapter 17: Classification

      • 17.1 Highlights

      • 17.2 Task

      • 17.3 Concepts

        • 17.3.1 Statistical Decision Theory

        • 17.3.2 Model Optimization and Validation

      • 17.4 Procedures

        • 17.4.1 Linear Discriminant Analysis (LDA)

        • 17.4.2 Quadratic Discriminant Analysis (QDA)

        • 17.4.3 k-Nearest Neighbors (k-NN)

        • 17.4.4 Cross-Validation

      • 17.5 Advanced Reference Material

        • References to advanced topics

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

  • Part V: Appendices

    • Appendix A: Notation

      • A.1 General

      • A.2 Image Operators

      • A.3 Alphabetical List of Symbols and Constants

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Appendix B: Mathematical Toolbox

      • B.1 Matrix Algebra

        • B.1.1 Vectors and Matrices

        • B.1.2 Operations with Vectors and Matrices

        • B.1.3 Types of Matrices

      • B.2 Least-Squares Solution of Linear Equation Systems

      • B.3 Fourier Transform

        • B.3.1 Definition

        • B.3.2 Properties of the Fourier Transform

        • B.3.3 Important Fourier Transform Pairs

      • B.4 Discrete Fourier Transform (DFT)

        • B.4.1 Definition

        • B.4.2 Important Properties

        • B.4.3 Important Transform Pairs

      • B.5 Suggested Further Readings

      • Appendix A: Notation

      • Appendix C: Glossary

      • Bibliography

      • Appendix D: Color Plates

    • Appendix C: Glossary

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Bibliography

      • Appendix D: Color Plates

    • Bibliography

      • Appendix A: Notation

      • Appendix B: Mathematical Toolbox

      • Appendix C: Glossary

      • Appendix D: Color Plates

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