Geometric classification

The group could be a geometrical group such as the group of all translations, rotations, scalings, etc. The desired classification of pattern is invariant under the action of the group, i.e. 

The aim of this work which enter in a research project on NDT, is to conceive a system of aid for interpretation and taking decisions, on imperfections in metallic fusion welds, we have studied and tested several segmentation techniques based on the two approaches ( contour and regions ). A quantitative analysis will be applied to extract some relatives geometricals parameters. To the sight of these characteristics, a first classification will be possible. 

A quantitative analysis to extract some relative geometrical parameters will be applied. To the sight of these characteristics, a first classification will be possible. We proceed as follow ... 

The geometrical measurements previously extracted help the making decision system to decide for example whether the defect is linear or not. This defect discrimination into two categories is considered as a first attempt for defect classification. To this end, we define a linearity ratio (Ri) Rl =Length / width. If Rl is equal or near to "1", the defect is volumic, otherwise it is a linear defect. 

The classification as a carcinogen need not apply to fibres with a length weighted geometric mean diameter less two standard errors greater than 6 pm Sodium dichromate Sodium dichromate dihydrate... 

A distinction between a solid and liquid is often made in terms of the presence of a crystalline or noncrystalline state. Crystals have definite lines of cleavage and an orderly geometric structure. Thus, diamond is crystalline and solid, while glass is not. The hardness of the substance does not determine the physical state. Soft crystals such as sodium metal, naphthalene, and ice are solid while supercooled glycerine or supercooled quartz are not crystalline and are better considered to be supercooled liquids. Intermediate between the solid and liquid are liquid crystals, which have orderly structures in one or two dimensions,4 but not all three. These demonstrate that science is never as simple as we try to make it through our classification schemes. We will see that thermodynamics handles such exceptions with ease. 

It must be emphasized that the duodectet rule (4.6) initially has no structural connotation, but is based on composition only. Indeed, the compositional regularity expressed by (4.6) encompasses both molecular species (such as the metal alkyls) and extended lattices (such as the oxides and halides) and therefore appears to transcend important structural classifications. Nevertheless, we expect (following Lewis) that such a rule of 12 may be associated with specific electronic configurations, bond connectivities, and geometrical propensities (perhaps quite different from those of octet-rule-conforming main-group atoms) that provide a useful qualitative model of the chemical and structural properties of transition metals. 

Correspondingly, the values of nF characterize the connectivity of the lattice of particles or skeleton of a PS and the values of Zc characterize the interconnectivity of the lattice of pores of the same PS. Connectivity of PS is the major topological attribute, which in the general case does not depend on the shape and size of the PS s individual supramolecular elements, although the latter characterize the major geometrical properties of PS [8], Appropriately, the classification of PSs by the degree of interconnectivity with allocation of various types of integrity is possible. 

Only one class modeling method is conmonly applied to analytical data and this is the SIMCA method ( ) of pattern recognition. In this method the class structure (cluster) is approximated by a point, line, plane, or hyperplane. Distances around these geometric functions can be used to define volumes where the classes are located in variable space, and these volumes are the basis for the classification of unknowns. This method allows the development of information beyond class assignment ( ). 

Since SIMCA is a class modeling method, class assignment is based on fit of the unknowns to the class models. This assignment allows the classification result that the unknown is none of the described classes, and has the advantage of providing the relative geometric portion of the newly classified object. This makes it possible to assess or quantitate the test sample in terms of external variables that are available for the training sets. 

Brakoulias A, Jackson RM (2004) Towards a structural classification of phosphate binding sites in protein-nucleotide complexes an automated all-against-all structural comparison using geometric matching. Proteins Struct Funct Bioinformatics 56 250-260... 

Petitjean, M. (1992) Applications of the radius-diameter diagram to the classification of topological and geometrical shapes of chemical compounds. J. Chem. Inf. Comput. Sci. 32, 331-337. 

Although these room-temperature CW-EPR spectra can be useful for making a rough classification of the types of ligations occurring at the Cr(V) center,10-20 they do not allow derivation of a full geometric model. As illustrated in Fig. 1, the method... 

JIFor a different kind of classification of photochemical reactions, sec Dauben Salem Turro Acc. Chem. Res. 1975,. 41. For reviews of photochemical reactions where the molecules are geometrically constrained, see Rama-murlhy Tetrahedron 1986, 42. 5753-5839 Ramamurlhy Eaton Acc. Chem. Res. 1988, 21. 300-306 Turro Cox Paczkowski Top. Curr. Chem. 1985, 129. 57-97. 

As to the first of these, I have elsewhere [10] discussed the classification of the ionic hydrates, which can best be taken on a geometrical basis according to the way the water molecules are grouped, In the first group the water molecules occur singly or in clusters they may be... 

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