Stereology and image analysis

A common problem in microscopy is that three dimensional information on microstructure is required, but the objects (sections or surfaces) and their images are two dimensional. 

Stereology is the field that provides the mathematical methods which allow one to go from two to three dimensions [102, 103]. The mathematical methods are quite complex. A simple example of the problem is a material containing spheres dispersed in a matrix. If the spheres are of uniform diameter, an image of a thin section will contain circular structures of varying diameter. If the spheres are of a range of sizes, a thin section will appear much the same. Analysis of the size distribution of the circles is needed to distinguish the two cases. 

Image analysis is the discipline which involves making the kinds of measurements which are used in stereology [104-106]. Image analysis is the measurement of geometric features in images, and it can be done with a ruler, time and patience. The state of the art today has automated, quantitative instruments available to conduct such 

The parameters that are commonly measured include particle numbers, diameters, areas, perimeters and ferets. A flexible system can be programmed to measure anything, such as arc lengths in diffraction patterns. In the example described above, an image of circular structures of varying diameters, image analysis methods are used to measure a statistical number of these structures. Stereological formulas provide the size distribution of the spheres. 

Image analysis is the discipline that involves making the kinds of measurements used in stereology [126-128]. In a simplistic sense, image 

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Riss, J., Gentler, S., Genter, A. 2001. Granitic core cross section numerical modelling. Proceedings of the 8 International Symposium for Stereology and Image Analysis. 

The first detailed book to describe the practice and theory of stereology was assembled by two Americans, DeHoff and Rhines (1968) both these men were famous practitioners in their day. There has been a steady stream of books since then a fine, concise and very clear overview is that by Exner (1996). In the last few years, a specialised form of microstructural analysis, entirely dependent on computerised image analysis, has emerged - fractal analysis, a form of measurement of roughness in two or three dimensions. Most of the voluminous literature of fractals, initiated by a mathematician, Benoit Mandelbrot at IBM, is irrelevant to materials science, but there is a sub-parepisteme of fractal analysis which relates the fractal dimension to fracture toughness one example of this has been analysed, together with an explanation of the meaning of fractal dimension , by Cahn (1989). 

Morphometric and stereological research methods are valuable quantitative tools for toxicological studies. However, these methods can be very labour intensive and therefore are infrequently used for toxicity evaluation studies. Computerized image analysis may solve some of these problems in the fiiture. Other automated quantitative methods, such as flow cytometry, have also been used (Kangasniemi et al., 1990 Toppari et al., 1990). However, these are not routine techniques and are not incorporated in any testing guidelines at present. 

Shea K, Stewart S and Rouse R (2014) Assessment standards comparing histopathology, digital image analysis, and stereology for early detection of experimental cisplatin-induced kidney injury in rats. Toxicol Pathol. 42(6) 1004-15. 

Thiedmann, R. (2011) New approaches to stochastic image segmentation and modeling of complex microstructures -application to the analysis of advanced materials, PhD thesis, Ulm University. Baddeley, A.J. and Cruz-Orive, LM. (1995) The Rao-Blackwell theorem in stereology and some counterexamples. Adv. Appl. Probab., 27, 2-19. 

A material s structure is observed on polished cross-sections or lateral faces of elements and specimens. Thin layers sawn out of specimens may be subjected to x-ray analysis and very thin layers are transparent enough to enable observation and structural analysis. The data on volume fractions of particular constituents, their spatial distribution and orientation, may be deduced from 2D images using stereological methods. 

It should be obvious that the size of object features derived from image analysis and stereology depends on knowing the actual magnification. Image analysis, whether done by ruler or by computer, depends totally on knowing the relation between linear measurements on the micrograph and in the object. 

In addition to the problem of defining pore shape, probably the best approach to data for obtaining a realistic measure of pore size distribution is through computer-assisted analysis of thin sections of core samples impregnated with resin or Wood s metal. The problem of analysing two-dimensional images, presented by thin sections, to obtain three-dimensional properties is known as stereology and is discussed in detail by Underwood (1970). Specific consideration of analysis of pore structure has been made by Dullien and Dhawan (1974) and Dullien (1979). These workers provide fairly reliable estimates of pore size distribution, but results have been presented for only a few samples. 

A complete stereological concept is nowadays available for quantitative image analysis of section or projection images of SFRC specimens. Actual reinforcement ratio s can be determined in this way. Generally, anisometry and segregation will also be detected by this approach the fibre distribution will be found to deviate from the conventionally assumed uniform randomness. 

The issue of ICC quantification is a complex one and has been widely addressed in the recent past. Useful information can be found in [93-102]. In brief, major benefits have been obtained from the development of dedicated software that, broadly speaking, allow a more reliable, unbiased, and rapid analysis than in the past. In several instances, the use of proper sampling approaches and stereology has also significantly improved the possibility of reliably quantifying ICC reactions at both LM and EM levels. Computer-assisted image analysis has been in use since the 1980s and has proved superior to the semiquantitative method, especially in terms of accuracy. These methods undoubtedly represent the... 

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