Transcription of Gaussian Filtering - Auckland
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Gaussian Filtering - Auckland
5/25/2010. Gaussian Filtering Gaussian Filtering g is used to blur images g and remove noise and detail. In one dimension, the Gaussian function is: x2. 1 . G ( x) = e 2 2. 2 2. Where is the standard deviation of the distribution. distribution The distribution is assumed to have a mean of 0. Shown graphically, we see the familiar bell shaped Gaussian distribution. Gaussian distribution with mean 0 and = 1. 18. 1. 5/25/2010. Gaussian Filtering Significant values x 0 1 2 3 4. 2 2/ 2 9/4 2 8/ 2. * G ( x ) / 1 e e e e 2 2/ 2 9/4 2 8/ 2. G ( x ) / G (0) 1 e e e e For =1: x 0 1 2. G ( x) G ( x ) / G (0) 1 19. 2. 5/25/2010. Gaussian Filtering Standard Deviation Th Standard The St d d deviation d i ti off the th Gaussian G i ffunction ti plays l an iimportant t t role in its behaviour. The values located between +/- account for 68% of the set, while two standard deviations from the mean (blue and brown) account for 95%, and three standard deviations (blue, brown and green).
This means we can normally limit the kernel size to contain only values within three standard deviations of the mean. 5/25/2010 7 ... This is a common first step in edge detectionThis is a common first step in edge detection. The images below have been processed with a …
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