Morphological descriptors

The morphological descriptors described above will be examined later for their physical Interpretation. But first their very Interesting relationship to the statistical properties of the particle profile radial distribution will be considered. 

In order to do this the points of the image have to be incorporated into the analysis in the form of invariant descriptors. The interpretation of the textural morphology features depends upon the physics of the situation (for example, the gray level may be related to altitude or in another case to the chemical analysis from point to point. The interpretation also depends upon the mathematical relationships between the various morphological descriptors used. There are three major types of morphological texture descriptors. These are statistical terms, symmetry operations, and Invariant texture morphology descriptors (ITMD s). 

Once a spatially 2D or 3D image of the multiphase medium of interest has been obtained, it is desirable to characterize the image by a set of morphological descriptors, which can then be correlated with effective properties of the medium or their evolution followed in time when a structure-transformation process (e.g., dissolution) takes place in the medium. Let us now review some morphological descriptors most commonly used for the characterization of porous and multiphase media. 

Molecular descriptors here considered include allele frequencies at enzyme loci and DNA-DNA hybridization data. Morphological descriptors include morphometric variables describing the external morphology, the shape of the epiphallus (i.e. male copulatory structure), and the patterns of egg chorion ultrastructure as well. Other character sets utilized for comparative purposes were related to the ecology and life cycle of populations studied. 

Computed tomography (CT) certainly is the key imaging modality used for the evaluation of mesothelioma. This applies to both the clinical assessment of mesothelioma and the staging of mesothelioma for therapeutic or epidemiological purposes. The morphological descriptors and criteria for the tumor node metastasis staging of mesothelioma are summarized in Tables 9.1-9.3. 

The parameters mentioned above for shape analysis are straightforward to obtain. As computing technology has advanced, so have the descriptors that have been used to describe particles. Kaye proposed the use of fractal dimensions in describing particulate solids.27 Leurkins proposed the application of the morphological variational principle to describe particle shape that states 25... 

Many materials used for food and beverage packaging have characteristic odors or sensory active compounds (Torri et ah, 2008). The intensity and description of the odor may be affected by the number and type of volatile compounds that are released under environmental conditions at the time of evaluation. Chemical composition of the material and polymer morphology may play a role in the sensory characterization. Sensory descriptors do not define a specific chemical compound but may be related to different compounds, a blend of compounds, and even a limited concentration range of a compound or class of compounds. For example, frans-2-nonenal in water changes in sensory (taste) description from "plastic (0.2 gg/1) to "woody" (0.4-2.0 p.g/1), "fatty" (8-40 pg/1), and "cucumber" (1000 gg/1) (Piringer and Ruter, 2000). Such terms are descriptive of the sensation and perception by human response to the chemical stimuli (Table 2.1). 

Fig. 3 shows the theoretical descriptors S2(r) and p(r) and their recalculations from construct B depicted in Fig. 1. RES A shows high angularity, and the deviation of the computed and the theoretical p(r) at low r reflects the difficulty of constructing the shape of contacting and sUghtly penetrating spheres precisely. However, the principal character of the morphology is recovered. A complete agreement between target and spatial reconstruction was observed at no time [29,30,34,35]. The construction was fairly successful with respect to the geometrical parameters, as the comparison of the data in the third row in Table 1 with the theoretical data in the first row shows.

At this time, a sufficiently wide sample of populations belonging to different species, and a reasonably diversified array of descriptors have become available to compare, (a) patterns of variation at the micro- and macro-geographic scale from different sets of descriptors and, (b) trees for an assumed monophyletic sample of five species resulting from either molecular or morphological data sets. 

Let us now look at the geographic variation of allozyme descriptors in Dolichopoda from a broader window. Twentyfive populations belonging to five morphologically inferred species from Central-Southern Italy (1 population of D.aegi 1 ion, 3 of D.baccettii, 6 of D.schiavazzii, 6 of D.laetitiae, and 9 of D.geniculata) have been electrophoretically studied for 15 gene loci (Sbordoni et al., 1985). 

ATm values for single copy DNA data, Euclidean distances for morphological data, and complements of simple matching coefficients for population and habitat descriptors. 

The (i-band center model has been used extensively to describe experimentally measured catalytic activities, as a descriptor of catalyst behavior. Most computations have been performed on flat surfaces or surfaces with steps and kinks [7, 24,46 9]. The electronic stmcture of nanoparticles is expected to be deeply affected by the characteristic particle size and morphology. Particle size is therefore a critical parameter. The surface science studies that involve the reactions on a uniform single crystal surfaces and introduce the complexity characteristic to real nanoparticles by involving the defects, kinks, and steps in the models may not be sufficient to model the catalytic behavior at nanoscale. Such model does not take into account an inherent particle property sensitively dependent on structural parameters such as the particle size, strain, and local surface morphology. 

The QRS complex takes on many morphologies as it twists around this imaginary axis, leading to the descriptor polymorphic. 

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