Download e-book for iPad: Image Processing for Computer Graphics by Jonas Gomes

By Jonas Gomes

Picture processing is anxious with the research and manipulation of pictures through computing device. the focal point of this publication is to supply an intensive remedy of picture processing with an emphasis on these elements so much utilized in special effects. all through, the authors be aware of describing and examining the underlying innovations instead of on providing algorithms or pseudocode. As befits a latest advent to this subject, an outstanding stability is struck among discussing the underlying arithmetic of the topic and the most subject matters lined: sign processing, info discretization, the speculation of color and varied color structures, operations in pictures, dithering and half-toning, warping and morphing, and picture processing.

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SIAM Books, Philadelphia. Oppenheim, A. , Willsky, A. , and Young, I. T. (1983). Signals and Systems. Prentice-Hall, Englewood Cliffs, NJ. Van Loan, C. (1986). Computational Frameworks for the Fast Fourier Transform. SIAM, Philadelphia. Weaver,]. ( 1989). Theory of Discrete and Continuous Fourier Analysis. John Wiley & Sons, New York. Wolberg, G. ( 1990). Digital Image Wmping. IEEE Computer Society Press, Los Alamitos, CA. Zayed, A. ( 1993). Advances in Shannon's Sampling Theory. CRC Press, Boca Raton, FL.

14) we obtain +oo f(t) = L 206t f(kM)S(t- k6t) *sine (2n0t). 15) we obtain +oo f(t)= L 20Mf(k6t)sinc(2nO(t-Ut)). 17) is precisely the expression of the exact reconstruction of the signal f from its samples f(k6t), fork E Z. 17) converges absolutely, and the convergence is uniform on compact parts of the domain. In fact, one can show that, by normalizing the elements of the set {sinc(2nO(t- Ut))}, fork E Z, one obtains a complete orthonormal basis in an appropriate signal space. This is called the Shannon basis.

In this convention, if t represents time or space, the variable s of the transformed signal indeed represents the frequency with no scale factor. All these considerations generalize to m-dimensional signals. The Fourier transform of a signal f : JRm -t lR is defined by t(U) = { } Rm f(X)e-Z1ti(X ,U) dX, where U = (u1, Uz, ... , Urn), X = (x1, xz, ... , Xm), (X, U) = and dX = dx1 dx2 ... dxm. :1 XiUi, Other Frequency Models There are other frequency-variable functional models for signals in addition to the one based on the Fourier transform.

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