To simulate noise of different levels The most unbiased noise was taken as white Gaussian distributed one. Its variance a was chosen as its main parameter, because its mean value equaled zero. The ratio of ct to the maximum level of intensity on the projections  [c.117]

If the noise is assumed to be white with the Gaussian distribution  [c.331]

We give in the end of this section some simulation results in order to show the behaviour and the efficiency of the regularization criteria described before. The data are simulated using (2) considering the Born approximation. We have considered a test objet (Fig. 4a) (tluee closed flaws at the surface of the material). We added a white Gaussian noise to compute data to simulate measurement noise and modeling errors. We present successively the object function, the modulus of the simulated data, the least square solution, the reconstruction with the Beta law, the reconstruction with the weak membrane and finally the reconstruction with the compound criteria. We can conclude that the least square solution is characterized by its smootlmess ans its low contrast, the Beta law regularization improves the contrast, the weak membrane model tends to gather neighbouring pixels and the proposed joint regularizing function preserves details while building homogeneous patterns. This example leads to a perfect reconstruction.  [c.332]

Furthermore, the choice of the mother wavelet y/(t) is a factor of major importance for the quality of the representation. For CWT purposes, regular functions like the Morlet wavelet or derivative gaussian functions are usually chosen for their good time and frequency localization properties. It is usually admitted that wavelets having great resemblance with the defect signal to be detected give good analysis results. According to these remarks, in our case, the best choice for j/(t) should be the first derivative of gaussian function (fig 9). However, the Morlet wavelet expressed by  [c.362]

Finally, the band pass filters corresponding to the Morlet wavelet have a "quicker" decrease towards null frequencies than filters obtained with the first derivative of gaussian wavelet (fig. 9). As a result, they  [c.362]

Filter 1 Gaussian Filter Transform  [c.460]

L Smoothing of the image with a Gaussian filter  [c.526]

N. B. a has the inverse role of a in the first derivative of a Gaussian. Deriche proposes the following recursive implementation of the filter/in two dimensions. Deriche retains the same solution as Canny, that is  [c.527]

Operating on (4), after a rather long calculation and assuming the usual statistics for the surface of the wire (i.e. Gaussian distribution of the radii and also Gaussian correlation function) we obtain for two slightly different incident angles a and a + 5a the following expression  [c.664]

A fairly simple treatment, due to Guggenheim [80], is useful for the case of ideal or nearly ideal solutions. An abbreviated derivation begins with the free energy of a species  [c.65]

Guggenheim [5] extended his treatment to the case of regular solutions, that is, solutions for which  [c.66]

We now come to a very important topic, namely, the thermodynamic treatment of the variation of surface tension with composition. The treatment is due to Gibbs [35] (see Ref. 49 for an historical sketch) but has been amplified in a more conveniently readable way by Guggenheim and Adam [105].  [c.71]

An approach developed by Guggenheim [106] avoids the somewhat artificial concept of the Gibbs dividing surface by treating the surface region as a bulk phase whose upper and lower limits lie somewhere in the bulk phases not far from the interface.  [c.76]

R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, London, 1939.  [c.96]

E. A. Guggenheim, J. Chem. Phys., 13, 253 (1945).  [c.96]

E. A. Guggenheim, Trans. Faraday Soc., 41, 150 (1945).  [c.98]

E. A. Guggenheim, Trans. Faraday Soc., 36, 397 (1940).  [c.99]

R. Z. Guzman, R. G. Carbonell, and P. K. Kilpatrick, J. Colloid Interface Sci., 114, 536 (1986).  [c.167]

This approach, much used by Guggenheim [190], seems elaborate, but in the case of more complex situations than the above, it can be a very powerful one.  [c.210]

E. A. Guggenheim, Thermodynamies, Interscience, New York, 1949.  [c.217]

E. A. Guggenheim, Thermodynamics, Interscience, New York, 1949 J. Phys. Chem., 33, 842 (1929) 34, 1540, 1758 (1930).  [c.224]

Density functional theory from statistical mechanics is a means to describe the thermodynamics of the solid phase with information about the fluid [17-19]. In density functional theory, one makes an ansatz about the structure of the solid, usually describing the particle positions by Gaussian distributions around their lattice sites. The free  [c.334]

For most metals values are in the range of 10 to 100 kg/mm. Thus in a friction experiment with a load of 10 kg, the true contact area would indeed be about the 10 cm estimated from conductivity measurements. There are considerable uncertainties in the absolute values of A calculated in this way, since work hardening may increase at the contact points. Nevertheless, the relationship given by Eq. XII-1 should still apply. For very light loads, such that the elastic limit is not exceeded, a hemispherical rider on a flat surface will have an area of contact, A = k that is no longer directly proportional to the load. If there are numerous asperities following a Gaussian distribution, A is again proportional to W [1].  [c.434]

Emulsion A has a droplet size distribution that obeys the ordinary Gaussian error curve. The most probable droplet size is 5 iim. Make a plot of p/p(max), where p(max) is the maximum probability, versus size if the width at p/p(max) = j corresponds to  [c.526]

The following derivation is modified from that of Fowler and Guggenheim [10,11]. The adsorbed molecules are considered to differ from gaseous ones in that their potential energy and local partition function (see Section XVI-4A) have been modified and that, instead of possessing normal translational motion, they are confined to localized sites without any interactions between adjacent molecules but with an adsorption energy Q.  [c.606]

One approach has been to build on the DR equation by adding a Gaussian [228] or gamma function-type [224] distribution of B values. Another approach makes use of a modified Fowler-Guggenheim equation (see Eq. XVII-53) [229]. A rather different method for obtaining a micropore size distribution was proposed by Mikhail, Brunauer, and Bodor [230], often known as the MP method. The method is an extension of the t-curve procedure for obtaining surface areas (Section XVII-9) a plot of cubic centimeters STP adsorbed per gram v versus the value of t for the corresponding P/F (as given, for example, by Table XVII-4) should, according to Eq. XVII-84, give a straight line of slope proportional to the specific surface area E. As illustrated in Fig. XVII-30, such plots may bend over. This is now interpreted not as a deviation from the characteristic isotherm principle but rather as an indication that progressive reduction in surface area is occurring as micropores fill. The proposal of Mikhail et al. was that the slope at each point gave a correct surface area for the P/P and v value. The drop in surface area between successive points then gives the volume of micropores that filled at the average P/P of the two points, and the average t value, the size of the pores that filled. In this way a pore size distribution can be obtained. Figure XVII-31a shows adsorption isotherms obtained for an adsorbent consisting of a-FeOOH dispersed on carbon fibers, and Fig. XVII-31b, the corresponding distribution of micropore diameters [231].  [c.670]

R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, England, 1952.  [c.676]

R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, England, 1952.  [c.677]

R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, England, 1952, p. 437.  [c.747]

After some preliminary tests with several edge detectors, the "Morphologie"- and the "Derivative of Gaussian"-edge detectors were chosen for this work.  [c.459]

The Derivative of Gaussian (DroG) operator is a classical example of a compound edge gradient. It combines a Gaussian shaped smoothing with a following differentiation and is described in [5].  [c.461]

Because of its similar characteristics, the evaluation of the images filtered with the DroG filter is guided by the feature extraction of the morphological filter. The Gaussian smoothing property of the filter results in an output profile which has even less extrema then the results of the morphologic filter. This eases feature extraction, which starts with detection of the local extrema in the signal. Afterwards the characteristic step in the profile is detected and its shape is analysed analogously to the evaluation of the filter before-mentioned.  [c.462]

Although certain potentials, such as the Galvani potential difference between two phases, are not experimentally well defined, changes in them may sometimes be related to a definite experimental quantity. Thus in the case of electrocapillarity, the imposition of a potential E on the phase boundary is taken to imply that a corresponding change in A occurs, that is, dE = d(A). It might also be noted that the practice of dividing the electrochemical potential of a charged species into a chemical and an electrostatic part is actually an arbitrary one not strictly necessary to thermodynamic treatments. It has been used by Br0nsted [189] and Guggenheim [190] as a useful way of separating out the feature common to charged species that their free energy does depend on the value of the electric field present. For further discussions of these various potentials, see Butler [191], Adam [192], and de Boer [193]. Case et al. [194] have reported on the determination of real potentials and on estimates of x.  [c.208]

It is assumed in the Langmuir model that while the adsorbed molecules occupy sites of energy Q they do not interact with each other. An approach due to Fowler and Guggenheim [10] allows provision for such interaction. The probability of a given site being occupied is N/S, and if each site has z neighbors, the probability of a neighbor site being occupied is zN/S, so the fraction of adsorbed molecules involved is zO/2, the factor one-half correcting for double counting. If the lateral interaction energy is o), the added energy of adsorption is Z036J2, and the added differential energy of adsorption is just zud.  [c.613]

See pages that mention the term Geissoschizine : [c.196]    [c.114]    [c.255]    [c.362]    [c.526]    [c.723]    [c.50]    [c.99]    [c.335]    [c.345]    [c.503]    [c.656]    [c.700]    [c.701]   
The logic of chemical synthesis (1989) -- [ c.397 ]