دانلود کتاب Image Analysis and Mathematical Morphology, Volume 1

From the Preface------------------Mathematical morphology was born in 1964 when G. Matheron was asked to investigate the relationships between the geometry of porous media and their permeabilities, and when at the same time, I was asked to quantify the petrography of iron ores, in order to predict their milling properties. This initial period (1964-1968) has resulted in a first body of theoretical notions (Hit or Miss transformations, openings and closings, Boolean models), and also in the first prototype of the texture analyser. It was also the time of the creation of the Centre de Morphologie Mathematique on the campus of the Paris School of Mines at Fontainebleau (France). Above all, the new group had found its own style, made of a symbiosis between theoretical research, applications and design of devices. These have the following idea in common: the notion of a geometrical structure, or texture, is not purely objective. It does not exist in the phenomenon itself, nor in the observer, but somewhere in between the two. Mathematical morphology quantifies this intuition by introducing the concept of structuring elements. Chosen by the morphologist, they interact with the object under study, modifying its shape and· reducing it to a sort of caricature which is more expressive than the actual initial phenomenon. The power of the approach, but also its difficulty, lies in this structural sorting. Indeed, the need for a general theory for the rules of deformations appeared soon. The method progressed as a result of an interchange between intellectual intuitions and practical demands coming from the applications. This finally lead to the content of this book. On the way, several researchers joined the initial team and constituted what is now called the "Fontainebleau School". Among them, we can quote J. C. Klein, P. Delfiner, H. Digabel, M. Gauthier, D. Jeulin, E. Kolomenski, Y. Sylvestre, Ch. Lantuejoul, F. Meyer and S. Beucher.A new theory never appears by spontaneous generation. It starts from some initial knowledge and grows in a certain context. The family tree of mathematical morphology essentially comprises the two branches of integral geometry and geometrical probabilities, plus a few collateral ancestors (harmonic analysis, stochastic processes, algebraic topology). Apart from mathematical morphology, three other parallel branches may be considered as current descendants of the same tree. They are stereology, point processes and stochastic geometry as developed by D. G. Kendall's School at Cambridge. Stereology, unlike the other two, is oriented towards applications. The stereologists have succeeded in putting the major theorems of integral geometry into practice. Indeed their society regroups biologists and specialists of the material sciences whose mutual interest lies in the quantitative description of structures, principally at the microscopic scale.The other and more recent branch of "picture processing" appeared in the United States at the beginning of the 1960s as a consequence of the N.A.S.A. activities. Today, its scope has extended to domains other than satellite imagery, its audience has become more international and is now represented by scientific societies such as that of pattern recognition. These scientists are regrouped more by a common class of problems (enhancement and segmentation of pictures, feature extraction, remote sensing) than by a specific methodology. Here, the theoretical tools often belong to the convolution and filtering methods (Fourier, Karhuhen-Loeve etc.); they also use some algorithms of mathematical morphology without connecting them with the general underlying notions. Finally, to a lesser extent, they borrow their techniques from syntactic and relaxation methods.The last tree to which mathematical morphology belongs is that of image analysers. It began in 1951, when J. Von Neumann proposed an automatic process which compared each pixel with its immediate neighbours. Over the past twenty years, about thirty prototypes of devices have been built for digital image analysis. Among the few of them which were commercialized, we can quote the quantimets, based on classical stereology, and the Leitz texture analyser, which was the best-selling image analyser at the end of the 1970s.The necessity to construct a device which could easily perform morphological operations on actual specimens appeared very early in my work. I wanted to design an equivalent of the computer for geometry, where the Hit or Miss transformation and its derivatives would replace the basic algebraic operations cabled in the usual computers. I called this invention the texture analyser, and with an increasing participation of J. C. Klein, I built four prototypes between 1965 and 1975. The Wild-Leitz Company bought the licence in 1970 and currently produces this instrument, after having remodelled it for commercial promotion. Although the quasi-totality of the examples and of the photographs of this book come from texture analysers, I have systematically avoided describing technology and hardware. Anyway, this particular system, like all computer components, will soon become obsolete. The technologies will change, certain specific routines will be pre-programmed by microprocessors, the internal structure will be made more parallel, or more pipelined, but the concept of the texture analyser will remain the same. This is because, via the basic morphological operations, it links the actual experiments to very fundamental prerequisites of the experimentation of geometrical structures.Schematically, 40% of the material of this book has not been published before, another 40% comes from works of the Fontainebleau school but is not always well known, and the rest comes from other sources. I have set the level of the book at the interface of applications and theory, and have emphasized the links between modes of operation and general underlying concepts. A comprehensive set of pure mathematical results can be found in G. Matheron (I 975). I quote, without proofs, his most important theorems.This book is directed to the triple audience of the users of the method (biologists, metallographers, geologists, geographers of aerial imagery ... ), the specialists of picture processing and the theoreticians (probabilists, statisticians). These different categories of readers are not used to the same formalism, neither do they formulate their thoughts in a common language. Therefore, I had to find a common ground for the three, which is not an easy task. I hope the reader will excuse me if I have not completely succeeded. For example, I have avoided using programming languages and even flow charts, preferring to present the morphological notions within the more general framework of set geometry. Strange terms such as "idempotence" or "antiextensivity" are likely to shock many naturalists; I know this, but their geometrical interpretations are so intuitive that every experimenter will soon grasp their meaning.Apart from the language of mathematical morphology, its methodological deductions may bewilder the reader used to another conceptual background. Perhaps this difficulty will be lessened if I make a few comments on the subject.Mathematical morphology deals with sets in Euclidean or digital spaces, and considers the functions defined in an n-dimensional space as particular sets of dimension n + l (classically, in picture processing, the function is the primary notion and the set is a particular case). To invert the priority between sets and functions leads us to emphasize the non-linear operations of sup and inf to the detriment of addition and subtraction.Basically, the objects under study are considered as being embedded in the usual Euclidean space; afterwards they are digitalized (in contrast to this, picture processing is essentially digital). Suitable topologies then allow the robustness of the morphological operations to be studied. This would be impossible in a pure digital framework, where the reference of the Euclidean space is missing. I know that general topology is not familiar to the majority of the readers, but it is the price we have to pay for analysing the stability, the quality, i.e. finally the meaning of all the practical algorithms.As we have seen, the main objective of morphology is to reveal the structure of the objects by transforming the sets which model them (such a purpose generalizes that of integral geometry and of stereology, which consists of transforming bounded sets into significant numbers). However, all set transformations are not at the same level. Algorithms are governed by more general criteria, which in tum satisfy a few universal constraints. Anyone wishing to master mathematical morphology must assimilate this vertical hierarchy (picture processing is incomparably more "horizontal"). As a consequence, we did not design the book according to various problems such as image enhancement, filtering, or segmentation, but on a classification based on criteria and related questions. Every morphological criterion may help to segment an image, depending upon the type of image and the initial knowledge of it that we possess. It is precisely this information which orients us towards one or another type of criteria.A strong counterpoint interlaces criteria to models. It generally brings set models into play, but the introduction of probabilistic notions opens the door to the more specific class of random set models. This gives rise to the four main parts of the book: theoretical tools, partial knowledge, criteria, random models.This book can be read in several different ways, depending upon the field of interest of the reader. The text itself is constructed in a logical order where every new idea is introduced with reference to the preceding notions and not to the following ones. Such a rule, compulsory when one writes a book, does not need to be respected by the readers. A person mainly interested in the algorithms and their experimental implementation may start with the first two chapters and jump directly to the four chapters on criteria. He can also leave out the theoretical sections included in these six chapters if he wishes (i.e. Chapter II, Section E; Chapter IX, Section D; Chapter X, Section F; Chapter XI, Sections B, C, D; Chapter XII, Sections B, G, H). The first reading will possibly inspire him to go further. He can then pursue with the more theoretical chapters, either those centred on probability or alternatively those on geometry. Should he decide to follow the way proposed for statisticians and probabilists, then the second level comprises Chapters V (parameters), VIII (sampling) and XIII (random sets). If he feels more tempted by geometrical methods, then we suggest a further step consisting of Chapters IV (convexity), VI and VII (digital morphology) and the theoretical complements left out in the first reading. Finally, Chapter III is a review of topological results needed practically everywhere in the book, and Chapter XIV, a nontechnical conclusion.