Sample Output from Algorithms

Color Constancy M. Ebner 2007 John Wiley Sons, Ltd 

White patch retinex algorithm, maximum value per channel. 

Gray world assumption, averaging over all pixels. 

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While different types of bioinformatics tools can be used to discriminate samples based on their source, the initial paper by Petricoin and Liotta used ProteomeQuest , a software tool developed by Correlogics of Bethesda, Maryland. This software combines elements from genetic algorithm methods and cluster analysis. For the analysis of mass-spectral data, each of the input files is composed of m/z values on the x axis along with their corresponding amplitudes on the y axis. The output of the algorithm is the most robust subset of amplitudes at dehned frequency values that best separates the preliminary data acquired from the samples obtained from either healthy or diseased patients [21]. 

An alternative form for the PI and PID control algorithms is the so-called velocity form. In this form, one does not compute the actual value of the controller output signal at the nth sampling instant, but its change from the preceding period. Thus consider the PID control action at the nth and (n - l)th sampling instants. From eq. (27.7) we take... 

Figure 4.10 Karplus-Strong synthesis uses a time-varying lookup table to simulate the behaviour of a vibrating medium. As samples are output from the right side of the array, they are processed according to a certain algorithm and the results are fed back to the left side...

Based on current knowledge of the process and its disturbance characteristics, one may know or choose a reasonable difference equation structure for the controller algorithm. Starting with some assumed initial parameter values in the controller equation, the controller can be implemented on the process as shown. The control algorithm is coupled with an on-line recursive estimation algorithm which receives information on the inputs and outputs at each sampling interval and uses this to recursively estimate the optimal controller parameters on-line and to update the controller accordingly. The idea is to use the data collected from the on-line control manipulations to tune the controller directly. 

In this chapter we present very briefly the basic algorithm for recursive least squares estimation and some of its variations for single input - single output systems. These techniques are routinely used for on-line parameter estimation in data acquisition systems. They are presented in this chapter without any proof for the sake of completeness and with the aim to provide the reader with a quick overview. For a thorough presentation of the material the reader may look at any of the following references Soderstrom et al. (1978), Ljung and Soderstrom (1983) Shanmugan and Breipohl, (1988), Wellstead and Zarrop (1991). The notation that will be used in this chapter is different from the one we have used up to now. Instead we shall follow the notation typically encountered in the analysis and control of sampled data systems. 

Cohen-Coon settings (see Section 16.5) From the process reaction curve we can estimate the process static gain K, the dominant time constant r, and the process dead time td Then, from eqs. (16.9) through (16.11c), we can compute the parameters Kc, r/, and rD of a P, PI, or PID control algorithm. The effect of the sampling period T has been accounted for by the nature of the experiment itself, because the reaction curve has been determined using sampled-values of the process output. 

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