# gaussian - Gaussian Filters A common tool for filtering...

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Gaussian Filters A common tool for filtering images is the Gaussian Filter. This is a filter that uses a Gaussian function to create a two-dimensional filter kernel. But, instead of leaping right into a 2D filter, we’ll start by examining the use of a Gaussian filter in only one dimension. The one-dimensional Gaussian is defined as: 2 2 2 / 2 1 σ π i i e h = 1 The parameter sigma determines the amount of smoothing the filter will perform. A larger value will cause greater smoothing. We can do a Gaussian filter on the rows of an image using a one-dimensional filter. Example 1 – A =2 row filter Suppose you want to create a Gaussian filter on the rows of an image with σ =2. We have to decide how big we want that filter to be. A good rule thumb is that σ should be about 70% of the size of the filter neighborhood, the range to the left and right of the pixel we are looking at. So, we want a neighborhood n such that σ =0.7n. n=2.8, but neighborhoods are always integers, and need to contain the range, so I’ll round this number up to 3. This means the filter kernel size needs to be 7. One (1) for the pixel itself and three (3) on each size. I can compute the filter coefficients using Equation 1: 064 . 0 , 121 . 0 , 176 . 0 , 199 . 0 , 176 . 0 , 121 . 0 , 064 . 0 3 2 1 0 1 2 3 = = = = = = = h h h h h h h We can express this as a matrix: H=[0.064 0.121 0.176 0.199 0.176 0.121 0.064]. Now we can consider the indices into this matrix as -3, -2, -1, 0, 1, 2, 3, but that’s not really what a compiler will like, so we’ll consider the matrix to start at zero. So, h -3 is location 0. Any h k will be location k+3 in the matrix. To compute the color at pixel r,c in our image, we compute the following equation:

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## This note was uploaded on 07/25/2008 for the course CSE 471 taught by Professor Owen during the Fall '07 term at Michigan State University.

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gaussian - Gaussian Filters A common tool for filtering...

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