Digital Image Processing

This chapter centers around the question of how to represent the infor­ mation contained in images. Together with the next two chapters it lays the mathematical foundations for low-Ievel image processing. Two key points are emphasized in this chapter. First, the information contained in images can be represented in en­ tirely different ways. The most important are the spatial representation (Section 2.2) and wave number representation (Section 2.3). These repre­ sentations just look at spatial data from different points of view. Since the various representations are complete and equivalent, they can be converted into each other. The conversion between the spatial and wave number representation is the well-known Fourier transform. This trans­ form is an example of a more general dass of operations, the unitary transforms (Section 2.4). Second, we discuss how these representations can be handled with digital computers. How are images represented by arrays of digital num­ bers in an adequate way? How are these data handled efficiently? Can fast algorithms be devised to convert one representation into another? A key example is the fast Fourier transform, discussed in Section 2.5. 2.2 Spatial Representation of Digital Images 2.2.1 Pixel and Voxel Images constitute a spatial distribution of the irradiance at a plane. This long-established and well-received monograph offers an integral view of image processing - from image acquisition to the extraction of the data of interest – written by a physical scientists for other scientists. Supplements discussion of the general concepts is supplemented with examples from applications on PC-based image processing systems and ready-to-use implementations of important algorithms. Completely revised and extended, the most notable extensions being a detailed discussion on random variables and fields, 3-D imaging techniques and a unified approach to regularized parameter estimation. Complete text of the book is now available on the accompanying CD-ROM. It is hyperlinked so that it can be used in a very flexible way. CD-ROM contains a full set of exercises to all topics covered by this book and a runtime version of the image processing software heurisko. A large collection of images, image sequences, and volumetric images is available for practice exercises This book offers an integral view of image processing from image acquisition to the extraction of the data of interest. The discussion of the general concepts is supplemented with examples from applications on PC-based image processing systems and ready-to-use implementations of important algorithms. The fifth edition has been completely revised and extended. The most notable extensions include a detailed discussion on random variables and fields, 3-D imaging techniques and a unified approach to regularized parameter estimation. The complete.text of the book is now available on the accompanying CD-ROM. It is hyperlinked so that it can be used in a very flexible way. The CD-ROM contains a full set of exercises to all topics covered by this book and a runtime version of the image processing software heurisko. A large collection of images, image sequences, and volumetric images is available for practical exercises. Front Matter....Pages I-XII Front Matter....Pages 1-1 Applications and Tools....Pages 3-27 Image Representation....Pages 29-76 Random Variables and Fields....Pages 77-97 Neighborhood Operations....Pages 99-124 Multiscale Representation....Pages 125-142 Front Matter....Pages 143-143 Quantitative Visualization....Pages 145-175 Image Formation....Pages 177-203 3-D Imaging....Pages 205-231 Digitization, Sampling, Quantization....Pages 233-244 Pixel Processing....Pages 245-280 Front Matter....Pages 281-281 Averaging....Pages 283-314 Edges....Pages 315-337 Simple Neighborhoods....Pages 339-374 Motion....Pages 375-412 Texture....Pages 413-424 Front Matter....Pages 425-425 Segmentation....Pages 427-439 Regularization and Modeling....Pages 441-480 Morphology....Pages 481-494 Shape Presentation and Analysis....Pages 495-511 Classification....Pages 513-528 Back Matter....Pages 529-585 I Foundation 1 Applications and Tools 2 Image Representation 3 Random Variables and Fields 4 Neighborhood Operations 5 Multiscale Representation II Image Formation and Preprocessing 6 Quantitative Visualization 7 Image Formation 8 3-D Imaging 9 Digitization, Sampling, Quantization 10 Pixel Processing III Feature Extraction 11 Averaging 12 Edges 13 Simple Neighborhoods 14 Motion 15 Texture IV Image Analysis 16 Segmentation 17 Regularization and Modeling 18 Morphology 19 Shape Presentation and Analysis 20 Classification V Reference Part A Reference Material B Notation.