052009 dr pierre elbischger mip1isapss09 e14 32 the

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Unformatted text preview: stogram Equalization (3) 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 E14 32 The variance of summed random variables Assuming N is arbitrarily distributed and statistically independent random variables with mean µk = E{xk} and variance σk2 = E{(xk-µk)2}, the variance σy2:=E{(y-µy)2} of their sum is given by: For the variance of the sum of N independent RVs xk with equal variances σk = σx | k=1…N follows: For the variance of the mean of N independent and RVs xk with equal variances σk = σx | k=1…N follows: The variance of the mean is decreased as the number of samples used to estimate the mean is increased. 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 33 Noise sources Counting statistics → due to a small number of incident particles (photons, electrons, etc.) Instability in the light source or detector during the time required to scan or digitize an image. Thermal noise that increases the dark current – cooling can reduce this effect. Infrared cameras must be cooled more than a visible light camera. Quantization noise Salt & pepper noise (defect pixels) Readout noise Additional sources of noise from the other associated electronics: clock signals, wiring from the camera to the digitizer, pickup of electrical signals from the computer itself, ... 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 34 Visualize the noise by image differencing Two images of the same view, acquired as sequential video frames, Difference between the two images. 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 35 Poisson distribution The Poisson distribution expresses the probability of a number of events k occurring in a fixed period of time if these events occur with a known average rate and are independent of the time since the last event. e−λ λ k f (k ; λ ) = k! = λ, σ 2 λ µ= f (k ; λ ) λ is a positive real number, equal to the expected number of occurrences that occur during the given interval. Example For instance, if the events occur on average every 4 minutes, and you are interested in the number of events occurring in a 10 minute interval, you wou...
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This note was uploaded on 07/09/2009 for the course MEDIT 1 taught by Professor Pierreelschbinger during the Spring '09 term at Carinthia University of Applied Sciences.

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