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Figure 11.9 shows the typical Sobel kernel for determining vertical edges (ydirection), and Figure 11.10 shows the kernel used for determining horizontal edges (x-direction). Each of these kernels is placed over every pixel in the image. Let P be the grayscale version of the input image. Grayscale images are determined from RGB color images by taking a weighted sampling of the red, green, and blue color spaces. The value of each pixel in a grayscale image was found by considering its corresponding color input intensities, and applying the following formula: 0.212671 R + 0.715160 G + 0.072169 B, which is a built in function in OpenCV, which was used in the implementation. Let P(x, y) represent the value of the pixel at point (x, y) and I(x, y) is a 3 3 matrix of pixels centered at (x, y). Let X and Y represent output edge orientation images in the x and y directions, respectively. X and Y are computed as follows: X(i, j) = hx I(i, j) = Y (i, j) = hy I(i, j) = P(i 1, j 1) + P(i + 1, j 1) 2P(i 1, j) +2P(i + 1, j) P(i 1, j + 1) + P(i + 1, j + 1), P(i 1, j 1) 2P(i, j 1) P(i + 1, j 1) +P(i 1, j + 1) + 2P(i, j + 1) + P(i + 1, j + 1)



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Bazaraa, M. S., Jarvis, J. J., and Sherali, H. D., Linear Programming and Network Flows, John Wiley and Sons, Hoboken, New Jersey, 2005 Bergen, A. R., Power Systems Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1986 Boyle, G. (editor), Renewable Energy, 2nd edition, Oxford University Press, Oxford, 2004 Brealy, R. A., and Myers, S. C., Principles of Corporate Finance, McGraw-Hill, New York, 1996 Casazza, J., Delea, F., Understanding Electric Power Systems: An Overview of Technology and the Marketplace, John Wiley and Sons, Hoboken, New Jersey, 2003 Crew, M. A., and Kleindorfer, P. R., The Economics of Public Utility Regulation, MIT Press, Cambridge, Massachusetts, 1986 Crosno, D. C., Fundamentals of Electromechanical Conversion, Harcourt, Brace and World, New York, 1968 Cusatis, P., Hedging Instruments and Risk Management, McGraw-Hill, New York, 2005 Dash, J. W., Quantitative Finance and Risk Management: a Physicist s Approach, World Scienti c, River Edge, New Jersey, 2004 Duffie, D., Dynamic Asset Pricing Theory, Princeton University Press, Princeton, New Jersey, 2001





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Many transparent crystals and minerals such as quartz, calcite, rutile, tourmaline, and others are optically anisotropic and exhibit a property known as double refraction. When letters on a printed page are viewed through a calcite crystal, remarkably each letter appears double (Figure 8-6). Calcite is therefore said to be doubly refracting, or birefringent. Birefringent materials split an incident ray into two components that traverse different paths through the crystal and emerge as two separate rays. This occurs because atoms in crystals are ordered in a precise geometric arrangement causing directiondependent differences in the refractive index. In contrast, a sheet of glass, such as a microscope slide, which is an amorphous mixture of silicates, is usually optically isotropic and does not exhibit double refraction. When a ray of light is incident on a birefringent crystal, it usually becomes split into two rays that follow separate paths. One ray, the ordinary ray or O ray, observes the laws of normal refraction, while the other ray, the extraordinary ray or E ray, travels along a different path. Thus, for every ray entering the crystal there is a pair of O and E rays that

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In this section we identify the roles and responsibilities of the market participants and ISO from day-ahead setting of the dispatch schedule to real-time delivery. This section focuses on physical transactions, transactions that result in physical power ows. The short-term networking and planning activities required to ensure power delivery in traditionally regulated markets are presented in s 3 and 4. The presentation culminates in a list given in Section 4.1. All these activities are necessary in a market environment as well. Aside from those activities, additional activities are necessary to coordinate balancing between market players through the ISO. The activities follow.

The presentation layer implementation of an object-oriented middleware implements the transport of complex request parameters and results and the resolution of heterogeneous data representation We discussed the main activities of the development process for distributed objects These include the interface definition, the generation of client and server stubs, the coding of client and server objects and the registration of the server object The interface is defined using an interface definition language that is an essential part of most object-oriented middleware The middleware provides a compiler that checks interfaces on syntactic and static semantic consistency and produces client and server stubs C lient and server stubs contribute to achieving type safety of request On the client side, this is concerned with ensuring that the client only requests operations that are declared in the interface and that the client passes correct actual parameters.

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