By Laurent Najman, Hugues Talbot (eds.)
Mathematical Morphology enables the research and processing of geometrical buildings utilizing innovations in response to the fields of set concept, lattice idea, topology, and random services. it's the foundation of morphological photograph processing, and unearths purposes in fields together with electronic picture processing (DSP), in addition to parts for graphs, floor meshes, solids, and different spatial constructions. This ebook offers an updated therapy of mathematical morphology, in line with the 3 pillars that made it a tremendous box of theoretical paintings and useful program: an exceptional theoretical starting place, a wide physique of functions and a good implementation.
The publication is split into 5 elements and contains 20 chapters. The 5 elements are dependent as follows:
- Part I units out the basic features of the self-discipline, beginning with a normal creation, by means of extra theory-focused chapters, one addressing its mathematical constitution and together with an up to date formalism, that's the results of numerous a long time of work.
- Part II extends this formalism to a couple non-deterministic points of the speculation, specifically detailing hyperlinks with different disciplines corresponding to stereology, geostatistics and fuzzy logic.
- Part III addresses the speculation of morphological filtering and segmentation, that includes glossy attached techniques, from either theoretical and sensible aspects.
- Part IV positive factors useful elements of mathematical morphology, specifically the best way to take care of colour and multivariate information, hyperlinks to discrete geometry and topology, and a few algorithmic features; with no which functions will be impossible.
- Part V showcases the entire formerly famous fields of labor via a pattern of fascinating, consultant and sundry applications.
Content:
Chapter 1 advent to Mathematical Morphology (pages 1–33): Laurent Najman and Hugues Talbot
Chapter 2 Algebraic Foundations of Morphology (pages 35–80): Christian Ronse and Jean Serra
Chapter three Watersheds in Discrete areas (pages 81–107): Gilles Bertrand, Michel Couprie, Jean Cousty and Laurent Najman
Chapter four An creation to size idea for photo research (pages 109–131): Hugues Talbot, Jean Serra and Laurent Najman
Chapter five Stochastic tools (pages 133–153): Christian Lantuejoul
Chapter 6 Fuzzy units and Mathematical Morphology (pages 155–176): Isabelle Bloch
Chapter 7 attached Operators in accordance with Tree Pruning suggestions (pages 177–198): Philippe Salembier
Chapter eight Levelings (pages 199–228): Jean Serra, Corinne Vachier and Fernand Meyer
Chapter nine Segmentation, minimal Spanning Tree and Hierarchies (pages 229–261): Fernand Meyer and Laurent Najman
Chapter 10 Distance, Granulometry and Skeleton (pages 263–289): Michel Couprie and Hugues Talbot
Chapter eleven colour and Multivariate photos (pages 291–321): Jesus Angulo and Jocelyn Chanussot
Chapter 12 Algorithms for Mathematical Morphology (pages 323–353): Thierry Geraud, Hugues Talbot and Marc Van Droogenbroeck
Chapter thirteen Diatom id with Mathematical Morphology (pages 355–365): Michael Wilkinson, Erik Urbach, Andre Jalba and Jos Roerdink
Chapter 14 Spatio?Temporal Cardiac Segmentation (pages 367–373): Jean Cousty, Laurent Najman and Michel Couprie
Chapter 15 3D Angiographic photo Segmentation (pages 375–383): Benoit Naegel, Nicolas Passat and Christian Ronse
Chapter sixteen Compression (pages 385–391): Beatriz Marcotegui and Philippe Salembier
Chapter 17 satellite tv for pc Imagery and electronic Elevation versions (pages 393–405): Pierre Soille
Chapter 18 rfile photograph purposes (pages 407–420): Dan Bloomberg and Luc Vincent
Chapter 19 research and Modeling of 3D Microstructures (pages 421–444): Dominique Jeulin
Chapter 20 Random Spreads and wooded area Fires (pages 445–455): Jean Serra
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4); – the functions with bounded variation, where ω(d) tends towards an horizontal asymptote for large values of d, such as ω(d) = C(1 − e−θd). The Fω have three basic properties. For every module ω: 1) the constant functions belong to Fω ; 2) a ∈ R and F ∈ Fω imply that a + F ∈ Fω ; 3) F ∈ Fω implies that −F ∈ Fω . E Conversely [MAT 96], every complete sublattice L of R satisfying these three properties and supF ∈L |F (y) − F (x)| < +∞ for all x, y ∈ E must be of type Fω for some metric on E. When we state the incredible series of properties that the Fω do satisfy, it is a wonder that they fit the morphological requirements so well [MAT 96, SER 92a, SER 02]: 1) If function F ∈ Fω is finite at one point x ∈ E, then it is finite everywhere.
1), that x ≤ y and y ≤ x. Here x = y so that α is a bijection. Anamorphoses can be equivalently described in terms of supremum and infimum, as follows. – Given a map α : L → M, the following three statements are equivalent: 1) α is an anamorphosis; 2) α is a bijection that preserves the non-empty infimum: for every non-empty family {xi | i ∈ I} in L we have: α xi = α(xi ); i∈I i∈I 3) α is a bijection that preserves the non-empty supremum: for every non-empty family {xi | i ∈ I} in L we have: xi = α i∈I α(xi ).
2. – Any complete lattice which is totally ordered is referred to as a complete chain, for example: the completed Euclidean line R = R ∪ {−∞, +∞} or its discrete version Z = Z ∪ {−∞, +∞}. The sets R+ and Z+ , restrictions of the previous sets to numbers ≥ 0, are also complete chains. Clearly, the three chains R, R+ and [0, 1] are isomorphic, but Z and Z+ are not. In R, the ordering topology leads to the same results as the sequential monotone continuity, namely that the two operations of numerical supremum and infimum are continuous.