Scaling input values

Color Constancy M. Ebner 2007 John Wiley Sons, Ltd 

USING LOCAL SPACE AVERAGE COLOR FOR COLOR CONSTANCY 

After we have estimated the illuminant, we can use this information to calculate the reflectances of the objects in view. In Chapter 3 we have seen that, for the given assumptions, pixel intensity c is given by the product of a geometry factor G, the object reflectance R, and the illuminant L. For a nonuniform illuminant, we obtain 

Therefore, the product between the geometry factor G and the reflectances can be calculated 

By integrating such a color constancy algorithm directly into the imaging chip, we would obtain a color corrected image before the data is stored in memory. No external processor would be required. Efforts to create artificial retina chips have already tried to include functions such as edge detection, elimination of noise, and pattern matching directly into the image acquisition chip (Dudek and Hicks 2001 Kyuma et al. 1997). 

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This methodology can be used for the calculation of local reaction rates and effectiveness factors in dependence on gas components concentrations, temperature and porous catalytic layer structure (cf. Fig. 9). The results can then be used as input values for simulations at a larger scale, e.g. the effective reaction rates averaged over the studied washcoat section can be employed as local reaction rates in the ID model of monolith channel. 

Optimization techniques are used to find either the best possible quantitative formula for a product or the best possible set of experimental conditions (input values) needed to run the process. Optimization techniques may be employed in the laboratory stage to develop the most stable, least sensitive formula, or in the qualification and validation stages of scale-up in order to develop the most sta-... 

Figure 11.1 Implementation of color constancy algorithm that uses local space average color to scale the input values. Data from surrounding pixels is iteratively averaged. Input values are divided by twice the local space average color.

Figure 11.14 (a) Original data points. The filled diamond marks the average of the data points, (b) Input data points. All points were scaled by 0.3. (c) Result of scaling algorithm (d) Result of subtract scale algorithm, (e)-(g) same as (b)-(d) except that a bias was applied to the input values. 

A local intake line (from the case study of Lachlan, Australia) is drawn in Fig. 12.4, along with point X, representing a sample that was found to contain 530 x 107 atoms 36C1/1, accompanied by 3180 mg Cl/1. The corresponding point Y on the local intake line reveals the initial 36C1 input value of 950 x 107 atoms/1. Hence, P36 = (530/950) x 100 = 55.8%. Applying this value to the decay curve of Fig. 12.1, point O is obtained, and an age of 2.9 x 105 years is read on the lower scale of the horizontal axis. 

In words, the bias input unit is given an input signal of value -1 the second unit, -.25 the third unit value. 50 and the fourth unit, 1.0. Note that although theoretically any range of numbers may be used, for a number of practical reasons to be discussed later, the input vectors are usually scaled to have elements with absolute value between 0.0 and 1.0. Note that the bias term unit in Figure 2.7, which has a constant input value of -1.0, is symbolized as a square, rather than a circle, to distinguish it from ordinary input nodes with variable inputs. 

Figure 17.6 Effective CPE coefficient defined by equation (17.7), scaled by the input value of the double-layer CPE coefficient, as a function of frequency with a as a parameter for the Randles circuit presented as Figure 17.1(a). (Taken from Orazem et al. and reproduced with permission of The Electrochemical Society.)...

The performance of the robust estimators has been tested on the same CSTR used by Liebman et al (1992) where the four variables in the system were assumed to be measured. The two input variables are the feed concentration and temperature while the two state variables are the output concentration and temperature. Measurements for both state and input variables were simulated at time steps of 1 (scaled time value corresponding to 2.5 s) adding Gaussian noise with a standard deviation of 5% of the reference values (see Liebman et al, 1992) to the true values obtained from the numerical integration of the reactor dynamic model. Same outliers and a bias were added to the simulated measurements. The simulation was initialized at a scaled steady state operation point (feed concentration = 6.5, feed temperature = 3.5, output concentration = 0.1531 and output temperature = 4.6091). At time step 30 the feed concentration was stepped to 7.5. 

Procedures for steels having CEs up to 0.70 for use with scales C, D and E. Heat input values in the welding diagrams and tables based on 100% arc efficiency, instead of 80% (i.e. the value appropriate to MMA welding, as discussed in Chapter 3 under Heat input and in BS 5135). 

It is assumed that each input variable is nominally at the midpoint of its range and is expressed in perturbation variable form, and scaled by dividing by its nominal value. For example, if Fj is an inlet flow rate, nominally at 500 Ibmol/hr, its operating range is 0 Fj < 1,000 Ibmol/hr, in perturbation variable form, —500 F, < 500, and in scaled form, -1 < F, < 1. Thus, F ir and F 5) are scaled by multiplying the gains in each column by the nominal value of the appropriate input variable. As a result, all of the scaled inputs vary over the same range [—1, 1]. Note, however, that the RGA is scale independent, whereas the DC is input scale dependent. 

VoM is presented as determined from the slope of the best linear fit using the geometric mean to the simulated data for the RAFT mediated MA polymerization. Various chain lengths for the macroRAFT species, and input values for the scaling... 

The model was subjected to a total of eight earthquakes during two flights. The earthquakes were pseudo-harmonic wavelets except for the last earthquake fired during the first flight that was a sine sweep. This signal is actually a sine wave of decreasing acceleration amplitude and frequency. The main characteristics of the input motions are tabulated in Table 22.3 both in model and prototype scale (bracketed values), while the time histories are depicted in Fig. 22.5. 

Figure 3.27 Termination rate coefficient versus chain length for the Smoluchowski termination model including Poisson broadening variation of the scaling factor V. Line represents the input values of the simulation.

Figure 2.9. Simulation based on mechanism (2.113) for the catalytic reaction between A and B. with competitive equilibrium adsorption of A and B, a rate-limiting irreversible surface reaction between Aads and B ds and a kinetically insignificant irreversible desorption of the product AB. Dashed lines represent the high temperature limits. Input values A// =-94kJ/mol, A// = -lOOkJ/mol, /r [A] = 10" = 2 10 the reaction rates have been scaled to unity at maximum.

The present chapter is not exhaustive. The emphasis is on the third and fourth point. The outcome of simple models, which can be applied for the second point, is included, since it can provide input values for contact analyses. In contrast, REV and fracture mechanics simulations, suited to address the first and second point, provide at present material properties or failure criteria. This situation is expected to change in a near fumre, since the implementation of the knowledge of the failure mechanisms at the stack scale, gained by refined experiments and dedicated models, will require integrated modelling approaches. 

The superposition integral (1) corresponds to a division of the input signal u(x) into a lot of Dirac impulses 5 x). which are scaled to the belonging value of the input. The output of each impulse 5fx) is known as the impulse response g(x). That means, the output y(x) is got by addition of a lot of local shifted and scaled impulse responses. 

The remainder of the input file gives the basis set. The line, 1 0, specifies the atom center 1 (the only atom in this case) and is terminated by 0. The next line contains a shell type, S for the Is orbital, tells the system that there is 1 primitive Gaussian, and gives the scale factor as 1.0 (unsealed). The next line gives Y = 0.282942 for the Gaussian function and a contiaction coefficient. This is the value of Y, the Gaussian exponential parameter that we found in Computer Project 6-1, Part B. [The precise value for y comes from the closed solution for this problem S/Oir (McWeeny, 1979).] There is only one function, so the contiaction coefficient is 1.0. The line of asterisks tells the system that the input is complete. 

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