Test-Problems0 - (image – not the power spectrum will be...

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CSCE 5225 DIP Exam Review Problems There will be between 4 and 6 problems on the test. You will be given two sets of three problems. One problem from each set will be on the test. (That is, you will see two of the problems that will actually be on the test.) The first set of three problems is: 1. Prove the following two Fourier transform properties: a. f(-x,-y) = F --1 {F * (u,v)} if f(-x,-y) is real b. f * (x,y) = F --1 {F * (-u,-v)} if f(x,y) is imaginary 2. Prove the following: a. The DFT of the discrete function f(x,y) = 1 is b. The DFT of the discrete function f(x,y) = sin (2 π u 0 x+2 π v 0 y) is 3. Given an image of size M x N , imagine performing an experiment that consists of repeatedly lowpass filtering the image using a Gaussian lowpass filter with a given cutoff frequency D 0 . Ignore computational round-off error. Let c min denote the smallest positive number representable in the machine in which the imagined experiment will be conducted. a. Let K denote the number of applications of the filter. Can you predict what the result
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Unformatted text preview: (image – not the power spectrum) will be for a sufficiently large value of K ? (What is the result?) b. Derive an expression for the minimum value of K that will guarantee the result in part (a). The second set of three problems is: 1. Suppose that a digital image is subjected to histogram equalization. Show that a second pass of histogram equalization (on a histogram-equalized image) will produce exactly the same result as the first pass. 2. Two images, f(x,y) and g(x,y) , have histograms h f and h g . Give conditions under which you can determine the histograms of a. f(x,y) + g(x,y) b. f(x,y) – g(x,y) 3. Discuss the limiting effect of repeatedly applying a 3 x 3 lowpass (averaging) spatial filter to a digital image. Ignore the border effects. (Compare with problem 3 in the first set, remembering that not the same filter is used here.)...
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