摘要:

SUMMARYThe structures of primary concern in Part A are varieties—the generalization in higher dimensions of smooth curves and surfaces. Fixed orientation randoms‐sections (s‐dimensional flat sections) of a fixedt‐variety (t‐dimensional variety) inRd(d‐dimensional space) are considered in Section 2. Thet‐variety induces a density‐cum‐orientation distribution which is related to corresponding sectional quantities. The by now classical basic formula; of stereology are all special cases of the simple multi‐dimensional formula (2.16). Next (Section 3), statistics of the variety of intersection of several statistically homogeneous random varieties are related to the corresponding statistics of the parent varieties.Part B is concerned with the analysis by randoms‐sections of fixed aggregates oft‐dimensional opaque particles (i.e. varieties for 1 ≤t≤d— 1, domains fort=d) embedded within an opaque specimen. Fixed orientation random sections are considered in Section 5, and isotropically oriented ones in Sections 6–10. It is shown in Section 7 that the mean particle ‘caliper diameter’, a key quantity, may in theory be estimated by isotropic slice sectioning. The theory is particularly rich when the particles are convex, witness the arrays of useful formula; in Sections 8–10. Crofton's remarkable ‘second theorem’ comes into its own in Section 9, permitting simple estimates from isotropic test lines of mean area squared to mean perimeter (whend= 2) and mean volume squared to mean surface area (whend= 3); in fact, the formulæ of Sections 7–9 suggest estimates for both mean and variance of the areas (whend= 2) and volumes (whend= 3) of aggregates of embedded convex particles. Further results for aggregates of convex polytopes are given in Section 10. Certain general considerations and principles relating to estimation from random sections in the practical cases, i.e.d≤ 3, are included in the final Section 11.Equations which are the specializations of multi‐dimensional formulæ to the practical cases are asterisked. A feature is the attention given to the proper probabilistic specification of random sections through the specimen,

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03718.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA very general class ℛ of pointsets is introduced which is named rasterable.The term ‘rasterable’ designates the important property of these pointsets that they can be represented by the raster of those points of a lattice belonging to the pointset. This representation concerns the Minkowski measures and has to be interpreted in a statistical sense.It is shown that the directional Minkowski measures for rasterable pointsets can be interpreted as coefficients of the expansion of the corresponding correlation function. It follows that the well‐known Wiener spectrum of a two‐dimensional texture, which equals the Fourier transformation of a reduced correlation function, does not preserve the topological properties of the pointset.The described representability of a pointset by a point picture may clarify the property of the pointset to be ‘normal’ in the common sense of the word. If one knows the pathological appearances in the theory of pointsets this clarification is of spe

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03719.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYThe size of a set is defined without ambiguity as a ratio of homothety with an elementary set having the same shape. In order to generalize this, we compare the object studied with the elements of the family {λB} of the homothetics ofB.The size λ of a particular elementBis going to act as a measure of the object.If the latter is made up of individualized elements, we can calculate the size of each one and construct the size histogram, assuming for example that the size of a connex componentCaccording toBis the size of the largestBincluded inC.(Examples: inscribed circle radius, maximum intercept.) For any object (alveolar lung space, pore system), the size at each pointxis defined as the largest λBincluded in the object and containingx.The set of pointsxof a given size λ is related to the opening with respect to λB.This geometrical transformation of opening has mathematical properties similar to those of the sieving process, and is the basis of the size distribution concept as generalized by mathematical morphology.In the plane, the texture analyser allows the above measurem

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03720.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA major problem in dealing with complex structures is to identify simple parameters which will summarize significant information. For crystal structures the simplest measure is volume per atom. The Voronoi polyhedron (or Dirichlet region) about each atom can be calculated exactly or statistically. This has been done for a number of structures with unexpected results.Algorithms for examining the local atomic configurations by the calculation ofN‐dimensional volumes are described. Other proposals for the statistical examination of known crystal structures are put forward. Crystals are significant in themselves and in that they provide model structures which can be handled exactly.Formulæ, convenient for handling the packing of spheres and polyhedra inNdimensions, are list

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03721.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYThe stereological analysis of volume and surface of sarcoplasmic reticulum tubules in muscle cells meets with particular problems because these structures are (a) highly oriented in the longitudinal direction of the muscle cells, (b) lined up in parallel, (c) periodically arranged in relation to sarcomeres and (d) internally symmetrical in analogy to sarcomere symmetry. On the whole this system may be characterized as a parallel linear array of units with translational‐reflexive symmetry. On the basis of a simple model it is demonstrated that the problems of sampling and stereological measurement can be overcome if a combination of oblique and transverse sections are used. The procedure can be simplified to operate exclusively with oblique sections only slightly inclined to the transverse plane if a small systematic error can be accepte

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03722.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYWhen particles of randomly varied sizes and shapes within limits are aggregated, the expectation is that their disorder will increase as particles are added. But, depending on how disorder is measured, this is not necessarily so. It is shown mathematically that a maximum to the degree of disorder exists, and moreover, that this maximum can only be maintained by highly specialized sequences of particles thereafter. Consequently, it is probable that the degree of disorder, having first increased, will then decrease. As the degree of disorder falls, it becomes more probable that it will increase, so that the expectation is for the degree of disorder to oscillate as particles are added. If sampling sections pass through these more ordered regions the impression can arise that the structure is ordered, whereas the structure may in fact be random.

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03723.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYSerial histological sections may be graphically reconstructed in the form of paired ‘stereo‐maps’ for observation with a stereoscope. Comfortable stereo‐vision is obtained if the contour lines which produces grades are laterally parallaxed to an appropriate degree. Since the technique is advantageous and its procedures are simple in practice, it will be applied in a number of investigations. The basis of the technique is that the parallax is achieved by staggering one of the half‐maps with a micrometer at the rate of one‐tenth the section interval, which gives rise to perspective in the stereo‐vision. Some fundamental conditions, involved in procedures as well as observation, were investigated in order to consider the nature of the final image. Thus, it has proved to be a satisfactory representation. Other than the primary reconstruction, which is observed at right angles to the sectional plane, a method to convert the viewing direction, or the profile cartography, has been developed, so that we are able to observe sectioned structures practically from

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03724.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYThe standard projection methods of dendritic field analysis have revealed that dendritic density decays exponentially with increasing distance from the centre of the perikaryon and present ideas about dendritic connectivity are largely based on this theory. However, inherent in the projection method are a series of errors which have not hitherto been defined and which indicate that much of the data obtained by the projection technique may be an artefact of the method itself. However, it is possible, given the projection data from a sample of neurons, to extrapolate the three‐dimensional array of dendritic fields by employing a computer technique.In this technique the perikaryon is enclosed in concentric spheres set 20 mμ apart and dendritic endings (E) and branching nodes (B) are positioned within the volume of the total sphere according to known distributions. The number of dendritic intersections (I) at the surface of thenth concentric sphere can be calculated given the number of primary dendrites from the relationship;I(n− 1)+Bn—En. These numbers may then be corrected for the distortion due to projection and sectioning. Comparison of these corrected data with those obtained from conventional histological methods suggests that the distribution of dendritic parameters may be quite different from the conventionally held view and that the decay of dendritic density is not expon

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03725.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA scanning procedure is described by which means morphometric parameters of dendrite tree structures may be collected with low operator interaction. The system requires a small computer with 4K core and interfacing to A/D and D/A converters, a scanning oscilloscope, a standard microscope and a photo‐multiplier tube. Modular, or local pattern information is sampled on a circular scan raster, and standardized patterns specified in terms of the number of dendrite processes scanned. These modular patterns are linked together to map a chord approximation of the object. Branches out of focus are recognized and the stage adjusted by remote control of a stepping motor. The paper records a pilot study, performed at the Department of Anatomy, University of Rochester, N.

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03726.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY

摘要:

SUMMARYA computerized flying‐spot scanning device has been used to count the number of synaptic contacts in neural tissue stained with ethanolic phosphotungstic acid (E‐PTA). The ability of the computer to idealize the irregular synaptic contacts as solid disks by modifying the information gleaned from scanning the preparation allows the stereological principle of Weibel&Gomez to be used to calculate the number of E‐PTA stained synaptic contacts per unit volume of tissue. This technique represents a significant improvement over the time necessary for making similar quantitative determinations man

ISSN:0022-2720    

DOI:10.1111/j.1365-2818.1972.tb03727.x

出版商:Blackwell Publishing Ltd    

年代:1972

数据来源: WILEY