Image_Processing1 - Basic Image Processing January 26, 30...

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Basic Image Processing January 26, 30 and February 1
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Last week, we mentioned the important fact: Mathematically, every linear, shift-invariant system S is given by a convolution. The idea is to define a function called the point-spread function (of the system) h (x, y), which are the system’s outputs of the delta functions Formally, given a signal (2D signal, image) f (x, y), we can write
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The linearity implies that the system’s output commutes with the integral to give Its turns out every 2D linear shift-invariant system has the following functions as its eigenfunctions S
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Recall that The imaginary and real parts can be interpreted as waves S H (u, v) is called the modulation-transfer function.
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Fourier Transform Analogous to expanding a function in the “Dirac” basis: We can expand the function in the “Fourier” basis The “coefficient function” is given by the Fourier transform of f (x, y)
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We have H(u , v) is the modulation-transfer function of the system. What does it do?
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Image_Processing1 - Basic Image Processing January 26, 30...

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