In this survey we review the image processing literature on the various approaches and models investigators have used for texture. These include statistical approaches of autocorrelation function, optical transforms, digital transforms, textural edgeness, structural element, gray tone cooccurrence, run lengths, and autoregressive models. We discuss and generalize some structural approaches to texture based on more complex primitives than gray tone. We conclude with some structural-statistical generalizations which apply the statistical techniques to the structural primitives.

Statistical and structural approaches to texture

A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >

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Watersheds in digital spaces: an efficient algorithm based on immersion simulations

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

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Computer Vision: Algorithms and Applications

1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

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Convex bodies : the Brunn-Minkowski theory

We present here a new algorithm for segmentation of intensity images which is robust, rapid, and free of tuning parameters. The method, however, requires the input of a number of seeds, either individual pixels or regions, which will control the formation of regions into which the image will be segmented. In this correspondence, we present the algorithm, discuss briefly its properties, and suggest two ways in which it can be employed, namely, by using manual seed selection or by automated procedures. >

Seeded region growing

Image Processing and Mathematical Morphology-Frank Y. Shih 2009-03-23 In the development of digital multimedia, the importance and impact of image processing and mathematical morphology are well documented in areas ranging from automated vision detection and inspection to object recognition, image analysis and pattern recognition. Those working in these ever-evolving fields require a solid grasp of basic fundamentals, theory, and related applications—and few books can provide the unique tools for learning contained in this text. Image Processing and Mathematical Morphology: Fundamentals and Applications is a comprehensive, wide-ranging overview of morphological mechanisms and techniques and their relation to image processing. More than merely a tutorial on vital technical information, the book places this knowledge into a theoretical framework. This helps readers analyze key principles and architectures and then use the author’s novel ideas on implementation of advanced algorithms to formulate a practical and detailed plan to develop and foster their own ideas. The book: Presents the history and state-of-the-art techniques related to image morphological processing, with numerous practical examples Gives readers a clear tutorial on complex technology and other tools that rely on their intuition for a clear understanding of the subject Includes an updated bibliography and useful graphs and illustrations Examines several new algorithms in great detail so that readers can adapt them to derive their own solution approaches This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.

Image Analysis and Mathematical Morphology

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described. >

/pdf/flat-zones-filtering-connected-operators-and-filters-by-2z584aji2f.pdf

Flat zones filtering, connected operators, and filters by reconstruction

Transformations morphologiques, morphologie euclidienne, erosion et notions derivees, ouvertures et fermetures, amincissements et epaississements

Introduction to mathematical morphology

Firstly, the paper proposes an axiomatic definition for the notion of "segmentation" in image processing, which is based on the idea of a maximal partition. Then a key theorem links segmentation with connection, on the one hand, and with connective criteria on the other one. A series of lattice properties are then developed. In a last part, two examples of segmentations are proposed.

http://ieeexplore.ieee.org/iel5/8824/27937/01246969.pdf

Image segmentation

This paper consists of a tutorial overview of morphological filtering, a theory introduced in 1988 in the context of mathematical morphology. Its first section is devoted to the presentation of the lattice framework. Emphasis is put on the lattices of numerical functions in digital and continuous spaces. The basic filters, namely the openings and the closings, are then described and their various versions are listed. In the third section morphological filters are defined as increasing idempotent operators, and their laws of composition are proved. The last sections are concerned with two special classes of filters and their derivations: first, the alternating sequential filters allow us to bring into play families of operators depending on a positive scale parameter. Finally, the center and the toggle mappings modify the function under study by comparing it, at each point, with a few reference transforms.

/pdf/an-overview-of-morphological-filtering-3nk8vn4e9p.pdf

Jean Serra

Papers

Image Analysis and Mathematical Morphology

Flat zones filtering, connected operators, and filters by reconstruction

Introduction to mathematical morphology

Image segmentation

An overview of morphological filtering