ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03706.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03707.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYIn order to study objects forming a sub‐setAof euclidean space, mathematical morphology uses structuring figuresBand notes the frequency of events such as ‘BhitsA’, ‘Bis included intoA’etc. Thus, a probabilistic formalism is associated with this experimental technique and facilitates its interpretation. IfAis considered as a closed set, we obtain a random closed‐sets theory, closely connected with integral geometry. The functionalsTdefined byT(K) =P(A∩K≠ Ø) forKcompact are characterized as alternating capacities of infinite order. Interesting classes of functionalsTare obtained ifAis indefinitely divisible or semi‐markovian. At last, the mathematical notion of granulometry (size distribution) is studied by using a

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03708.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA generalized, geometrical approach is adopted in reviewing the basic relationships of projected structures. Projections of features from a plane to a projection line, and from a three‐dimensional foil to a projection plane are considered briefly. The relationships that apply to apparent and total projections are next assembled for lines, surfaces and bounded regions. The properties of convex bodies, the geometrical attributes, and the related projected quantities are enumerated. The inter‐relationships of important microstructural parameters are expressed for convex bodies in space, in sections, and in the projection plane.Based on the important concept of total projection, expressions are obtained that correct for truncation and overlap of particles in foils. Approximations to the total projection are developed for lines obscured by surfaces, and for points hidden by surfaces in space. Finally methods for determining size distributions of particles in thin foils are reviewed and recent modifications to the original procedures are discus

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03709.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYScanning electron microscopy (SEM) provides a considerably greater depth of field than optical microscopy at the same magnification. It is therefore particularly suitable for the examination of specimens with irregular surfaces.This review of procedures for quantitative measurements on SEM images falls into two parts. The first deals with mensuration; that is, with the determination of the lengths, dihedral angles and other properties of specific features in the image. Particular emphasis is given to means of correcting for non‐linearity and other distortions caused by instrumental defects. The second part considers the analysis for bulk properties such as volume fraction and boundary area per unit volume. In the case where observations are made on a planar section, these properties can be determined by use of the standard stereological relationships after making a computable correction (where necessary) for the tilt of the specimen and non‐linearities in the scan. However, for irregular surfaces (for example, those produced by fracture) rigorous estimations are not possible without certain assumptions which, unfortunately, are in many cases unrealis

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03710.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYMistakes are often made and perpetuated in the three‐dimensional interpretation of single sections. Such errors can be avoided and corrected if the observer considers carefully what kind of three‐dimensional shape has the greatest probability of yielding profiles such as are seen in the microscope; and if he does not take certain published or verbal statements at their face va

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03711.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYProcedures have been developed whereby the topological properties of single‐phase cell structures, and two‐phase structures, may be estimated from a series of closely spaced microsections. In both cases, the analysis is straightforward but tedious. However, because the topological properties abstract a description of the basic skeleton or framework of the structure from details of shape and size, their quantitative knowledge provides insights into microstructural behaviour that may be obtained in no other way. These combined factors make it likely that the application of these procedures will be limited to very select problems, but that where they are applied the results will significantly affect the thinking in the fi

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03712.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYAn object's quantitative analysis is not purely objective. On the contrary, it results from the interaction of a structuring element chosen by the observer, with the object to be analysed. After defining this relation in a quantitative way (hit‐or‐miss transformation), and recalling its probabilistic interpretation (Matheron, 1971) some examples of structuring elements are given:The couple of points which measures the covariances matrix. It allows harmonic analysis and the solving of sample problems.The segment which measures the chord distribution, and leads to the stereo‐logical parameter ‘the star’.The parallel segments doublet, which measures curvature radius distribution and the number of particles in the two‐dimensional space.The hexagon, which measures bi‐dimensional granulometries, etc.These measurements have been made on the texture analyser, built by us especially for that purpose. As a conclusion, we give an application of structuring elements to clustering

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03713.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA general survey has been made of the present utility of computing equipment and automatic devices for common problems in stereology and morphometry. Three situations have been evaluated:(1) Commonly available computer facilities permit easy and rapid prediction of two‐dimensional measurement distributions characteristic of any mathematically defined spatial structure. Tabulated predictions can be computed by direct simulation of sampling processes and random perturbations may be introduced if desired. Resort to formal mathematical solutions is not normally required.(2) For purposes of controlling the quality of useful solid materials, the materials engineer can be satisfied by description of a Gestalt which characterizes the material as a whole and which can reasonably be presumed to control the behaviour of the material in service. Six stereologically valid parameters are sufficient to describe such a Gestalt. These are: volume fraction (Vv), mean free path in the matrix (l̄α), mean intercept width of particles (l̄β) and measures of material variability, general anistropy, and degree of patternness. Practical measurements of the latter parameters have been defined. Current scanner models are intrinsically suitable for these measurements but will benefit from standardized data outputs and improvements to increase measuring accuracy.(3) While Gestalt measurements may perhaps be applicable to some biological problems, many problems in this field are specifically concerned with the micro‐architecture of individual objects or cells. Micro‐architectural observations such as counting and measuring, or identifying, individual object sections are inefficiently performed in ordinary computers. Large programming effort is required for limited machine intelligence and the operating speeds are unsatisfactory. These machine operations are not yet competitive with human observers. A partnership combining human identification with machine measurement of identified objects is practical and equipment is presently available. There is reason to presume that computer methods of object identification which have been employed are not similar to the methods actually employed by humans. New hardware systems appear to be necessary either to obtain satisfactory operating speeds by known processes or, if possible, to economically simulate human processes of image re

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03714.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYAmong the examples reviewed are volume‐fraction measurements in phase diagram and kinetic studies, properties dependent upon internal surface area, the characterization of phase arrangements by contiguity, proximity and dihedral‐angle measurements. The use of grain boundary and particle spacings in studies of mechanical properties is discussed in relation to current theories of strengthening mechanisms. Applications of size‐distribution analysis in kinetic studies and in the assessment of inclusion contents in steels are sur

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03715.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY