By Jean Serra
ISBN-10: 012637242X
ISBN-13: 9780126372427
From the Preface
------------------
Mathematical morphology used to be born in 1964 while G. Matheron was once requested to enquire the relationships among the geometry of porous media and their permeabilities, and while while, i used to be requested to quantify the petrography of iron ores, as a way to are expecting their milling homes. This preliminary interval (1964-1968) has ended in a primary physique of theoretical notions (Hit or leave out modifications, openings and closings, Boolean models), and likewise within the first prototype of the feel analyser. It used to be additionally the time of the construction of the Centre de Morphologie Mathematique at the campus of the Paris college of Mines at Fontainebleau (France). certainly, the recent team had came across its personal variety, made up of a symbiosis among theoretical examine, purposes and layout of units.
These have the subsequent proposal in universal: the suggestion of a geometric constitution, or texture, isn't really basically aim. It doesn't exist within the phenomenon itself, nor within the observer, yet someplace in among the 2. Mathematical morphology quantifies this instinct via introducing the concept that of structuring components. selected through the morphologist, they have interaction with the article lower than research, enhancing its form and· decreasing it to a type of cartoon that is extra expressive than the particular preliminary phenomenon. the ability of the technique, but in addition its hassle, lies during this structural sorting. certainly, the necessity for a common thought for the principles of deformations seemed quickly. the strategy advanced due to an interchange among highbrow intuitions and sensible calls for coming from the functions. This ultimately bring about the content material of this ebook. at the approach, a number of researchers joined the preliminary crew and constituted what's now referred to as the "Fontainebleau School". between them, we will be able to 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 thought by no means looks by means of spontaneous iteration. It begins from a few preliminary wisdom and grows in a definite context. The genealogy of mathematical morphology basically contains the 2 branches of crucial geometry and geometrical percentages, plus a couple of collateral ancestors (harmonic research, stochastic techniques, algebraic topology). except mathematical morphology, 3 different parallel branches should be regarded as present descendants of a similar tree. they're stereology, element procedures and stochastic geometry as constructed by means of D. G. Kendall's institution at Cambridge. Stereology, not like the opposite , is orientated in the direction of purposes. The stereologists have succeeded in placing the foremost theorems of fundamental geometry into perform. certainly their society regroups biologists and experts of the fabric sciences whose mutual curiosity lies within the quantitative description of constructions, mostly on the microscopic scale.
The different and newer department of "picture processing" seemed within the usa at first of the Sixties due to the N.A.S.A. actions. this present day, its scope has prolonged to domain names except satellite tv for pc imagery, its viewers has develop into extra foreign and is now represented by way of clinical societies comparable to that of trend attractiveness. those scientists are regrouped extra via a typical category of difficulties (enhancement and segmentation of images, characteristic extraction, distant sensing) than via a selected method. right here, the theoretical instruments usually belong to the convolution and filtering tools (Fourier, Karhuhen-Loeve etc.); additionally they use a few algorithms of mathematical morphology with out connecting them with the final underlying notions. eventually, to a lesser quantity, they borrow their suggestions from syntactic and rest methods.
The final tree to which mathematical morphology belongs is that of photograph analysers. it all started in 1951, while J. Von Neumann proposed an automated method which in comparison every one pixel with its speedy neighbours. over the last two decades, approximately thirty prototypes of units were equipped for electronic photo research. one of the few of them that have been commercialized, we will be able to quote the quantimets, in accordance with classical stereology, and the Leitz texture analyser, which was once the best-selling photo analyser on the finish of the 1970s.
The necessity to build a tool that could simply practice morphological operations on genuine specimens seemed very early in my paintings. i needed to layout an an identical of the pc for geometry, the place the hit and miss transformation and its derivatives could substitute the fundamental algebraic operations cabled within the traditional desktops. I known as this invention the feel analyser, and with an expanding participation of J. C. Klein, I outfitted 4 prototypes among 1965 and 1975. The Wild-Leitz corporation obtained the licence in 1970 and presently produces this device, after having remodelled it for advertisement merchandising. even though the quasi-totality of the examples and of the pictures of this publication come from texture analysers, i've got systematically kept away from describing know-how and undefined.
Anyway, this actual approach, like any machine elements, will quickly turn into out of date. The applied sciences will swap, convinced particular workouts can be pre-programmed by means of microprocessors, the interior constitution can be made extra parallel, or extra pipelined, however the inspiration of the feel analyser will stay a similar. the reason is,, through the elemental morphological operations, it hyperlinks the particular experiments to very basic must haves of the experimentation of geometrical structures.
Schematically, forty% of the fabric of this booklet has no longer been released earlier than, one other forty% comes from works of the Fontainebleau institution yet isn't really consistently renowned, and the remainder comes from different assets. i've got set the extent of the ebook on the interface of purposes and conception, and feature emphasised the hyperlinks among modes of operation and normal underlying techniques. A accomplished set of natural mathematical effects are available in G. Matheron (I 975). I quote, with no proofs, his most vital theorems.
This publication is directed to the triple viewers of the clients of the strategy (biologists, metallographers, geologists, geographers of aerial imagery ... ), the experts of photo processing and the theoreticians (probabilists, statisticians). those diversified different types of readers usually are not used to an identical formalism, neither do they formulate their techniques in a typical language. for this reason, I needed to discover a universal floor for the 3, which isn't a simple activity. i am hoping the reader will excuse me if i have never thoroughly succeeded. for instance, i've got kept away from utilizing programming languages or even stream charts, who prefer to offer the morphological notions in the extra normal framework of set geometry. unusual phrases corresponding to "idempotence" or "antiextensivity" tend to surprise many naturalists; i do know this, yet their geometrical interpretations are so intuitive that each experimenter will quickly grab their meaning.
Apart from the language of mathematical morphology, its methodological deductions might bewilder the reader used to a different conceptual history. might be this trouble might be lessened if I make a number of reviews at the subject.
Mathematical morphology offers with units in Euclidean or electronic areas, and considers the services outlined in an n-dimensional area as specific units of measurement n + l (classically, in photograph processing, the functionality is the first concept and the set is a selected case). To invert the concern among units and features leads us to stress the non-linear operations of sup and inf to the detriment of addition and subtraction.
Basically, the gadgets below learn are regarded as being embedded within the traditional Euclidean area; afterwards they're digitalized (in distinction to this, photograph processing is basically digital). compatible topologies then enable the robustness of the morphological operations to be studied. this could be most unlikely in a natural electronic framework, the place the reference of the Euclidean house is lacking. i do know that common topology isn't really normal to nearly all of the readers, however it is the fee we need to pay for analysing the steadiness, the standard, i.e. ultimately the that means of all of the useful algorithms.
As we've seen, the most aim of morphology is to bare the constitution of the gadgets through reworking the units which version them (such a function generalizes that of necessary geometry and of stereology, which is composed of reworking bounded units into major numbers). in spite of the fact that, ready changes will not be on the comparable point. Algorithms are ruled by means of extra basic standards, which in tum fulfill a couple of common constraints. an individual wishing to grasp mathematical morphology needs to assimilate this vertical hierarchy (picture processing is incomparably extra "horizontal"). therefore, we didn't layout the e-book based on quite a few difficulties corresponding to photo enhancement, filtering, or segmentation, yet on a category in keeping with standards and similar questions. each morphological criterion can assist to phase a picture, based upon the kind of photo and the preliminary wisdom of it that we own. it really is accurately this data which orients us in the direction of one or one other form of criteria.
A powerful counterpoint interlaces standards to versions. It more often than not brings set types into play, however the advent of probabilistic notions opens the door to the extra particular classification of random set versions. this offers upward push to the 4 major components of the booklet: theoretical instruments, partial wisdom, standards, random models.
This publication might be learn in numerous alternative ways, based upon the sector of curiosity of the reader. The textual content itself is built in a logical order the place each new inspiration is brought just about the previous notions and never to the next ones. this type of rule, obligatory whilst one writes a publication, doesn't must be revered by way of the readers. somebody in general attracted to the algorithms and their experimental implementation may well commence with the 1st chapters and bounce on to the 4 chapters on standards. He may also omit the theoretical sections incorporated in those six chapters if he needs (i.e. bankruptcy II, part E; bankruptcy IX, part D; bankruptcy X, part F; bankruptcy XI, Sections B, C, D; bankruptcy XII, Sections B, G, H). the 1st interpreting will potentially motivate him to move extra. He can then pursue with the extra theoretical chapters, both these concentrated on chance or on the other hand these on geometry. should still he choose to keep on with the way in which proposed for statisticians and probabilists, then the second one point includes Chapters V (parameters), VIII (sampling) and XIII (random sets). If he feels extra tempted by means of geometrical tools, then we propose one other step including Chapters IV (convexity), VI and VII (digital morphology) and the theoretical enhances ignored within the first analyzing. eventually, bankruptcy III is a assessment of topological effects wanted essentially all over the ebook, and bankruptcy XIV, a nontechnical end.
Read or Download Image Analysis and Mathematical Morphology, Volume 1 PDF
Similar imaging systems books
Investigations of Field Dynamics in Laser Plasmas with Proton Imaging
Laser-driven proton beams are nonetheless of their infancy yet have already got a few notable attributes in comparison to these produced in traditional accelerators. One such characteristic is the more often than not low beam emittance. this enables first-class solution in imaging functions like proton radiography. This thesis describes a singular imaging approach - the proton streak digital camera - that the writer built and primary used to degree either the spatial and temporal evolution of ultra-strong electric fields in laser-driven plasmas.
Mathematical morphology in image processing
Education structuring components in morphological networks / Stephen S. Wilson -- effective layout ideas for the optimum binary electronic morphological clear out: percentages, constraints, and structuring-element libraries / Edward R. Dougherty and Robert P. Loce -- Statistical homes of discrete morphological filters / Jaakko Astola, Lasse Koskinen, and Yrjö Neuvo -- Morphological research of pavement floor situation / Chakravarthy Bhagvati, Dimitri A.
The foreign Acoustical Imaging Symposium has been held continually because 1968 as a distinct discussion board for complicated learn, selling the sharing of expertise, advancements, tools and idea between all components of acoustics. The interdisciplinary nature of the Symposium and the vast foreign participation are of its major strengths.
Digital Processing: Optical Transmission and Coherent Receiving Techniques
With coherent blending within the optical area and processing within the electronic area, complex receiving options using ultra-high pace sampling premiums have stepped forward vastly during the last few years. those advances have introduced coherent reception structures for lightwave-carried info to the subsequent level, leading to ultra-high ability international internetworking.
Extra info for Image Analysis and Mathematical Morphology, Volume 1
Example text
Any further impact acts on all three of the descendant particles in the same way, independently of the preceding impact; the direction of each impact is assumed uniformly distributed on the unit sphere. 11 a photograph of a simulation of the model. It is a very nice image, but not realistic because in practice, each of the three particles after being split, do not stay together but move around in the crusher. 11 separated from each other and displayed in an arbitrary order. Only then do we have an idea of what the human eye sees on a polished section.
Granulometry) of the milled product obtained after time t? To look at this question, Ph. Cauwe 28 IMAGE ANALYSIS AND MATHEMATICAL MORPHOLOGY (1973) studied two very different types of rocks: firstly, a Cu-Pb-Zn ore with a complex multi phase texture, and secondly a concentrate of very homogeneous magnetite. He milled them under thirty different operational conditions, and analysed on polished sections the morphology of the resulting fragments. These experiments led to a surprising result. e. of the texture of the initial rocks (crystal size, pores, contacts between phases, directions of cleavage), but depended mainly on the working conditions of the crusher.
Their role is to "grip" the object by a series of operational constraints that become more and more restrictive. By construction, they are not verifiable. Their use is analogous to the use the human body makes of its five senses, or to the use a tradesman makes of his panoply of tools. The decision to use the variogram in preference to the opening for the description of wood anatomy, is similar to the choice of pliers instead of the head of a hammer for extracting a nail. The second movement happens when the pieces of information extracted by the criteria induce a certain interpretation of the object, opening the door to a universe of canonical patterns, models, each with their own logical structure.