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Unformatted text preview: of samples kn (often called the frequency) that fall in each of these bins. The estimated probability is proportional to that count. Choosing Gaussian distribution results in the following estimates of the underlying n=1000, #bins=100 n=100, #bins=10 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 18 Histograms of noisy images I The original image had only three distinct gray levels. 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 19 Histograms of noisy images II 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 E16 20 Sample moments Assuming a sample {x1, x2, …, xN} with N observations, the sample moments are defined as: r’th sample raw moment m1 represents the mean of the distribution r’th sample central moment s2 represents the variance of the distribution 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 21 Other statistical parameters Order statistics The sample set is ordered. Often they are used as robust estimates for: •the mean (e.g., median) and •standard deviation (3σ -> 99-th percentile). p-th percentile 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 22 Gray-level transformation (1) Changes the gray value independent of the pixel location in the image Is often used to improve the visual appearance to a human The gray value of each pixel in the input image f(x,y) is replaced by the gray value determined by the gray-level transformation function T(.) resulting in the output image g(x,y). T(.) relates the gray-level of an input pixel r to a gray-level of an output pixel s. In the case where the image consists of discrete values, the transformation can efficiently be implemented using a lookup table. s brighter r1 r2 r brighter 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 23 Gray-level transformation (2) r negative image 19.05.2009 s s s r1 r2 r contrast enhancement Dr. Pierre Elbischger - MIP1/ISAP'SS09 c r binary threshold 24 Gray-level transformation (3) s r negative image of a mammogram 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 25 Gamma correction (1) A pixel value may represent the amount of light falling onto a sensor element in a camera, the photographic density of film, the amount of light to be emitted by a monitor, the number of toner particles to be deposited by a printer, o...
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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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