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Unformatted text preview: 1 Image Processing : 6. Linear Filters 6. Linear Filters Aleix M. Martinez aleix@ece.osu.edu Convolution Represent these weights as an image, H . H is usually called the kernel. The operation is called a convolution : Notice order of indices all examples can be put in this form its a result of the derivation expressing any shift invariant linear operator as a convolution. R ij H i u , j v F uv u , v Example: Smoothing by Averaging Smoothing with a Gaussian Smoothing with an average actually doesnt compare at all well with a defocussed lens Most obvious difference is that a single point of light viewed in a defocussed lens looks like a fuzzy blob; but the averaging process would give a little square. A Gaussian gives a good model of a fuzzy blob exp x 2 y 2 2 2 An Isotropic Gaussian Smoothing with a Gaussian 2 Differentiation and convolution Recall This is linear and shift invariant, so must be the result of a convolution. We could approximate this as: f x lim f x , y f x , y f x f x n 1 , y f x n , y x Finite differences Finite differences responding to noise Increasing noise => (this is zero mean additive gaussian noise)....
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This note was uploaded on 10/21/2010 for the course ECE 707 taught by Professor Martinez during the Fall '10 term at Ohio State.
 Fall '10
 Martinez
 Image processing

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