211A_1_Midterm2010Solutions

211A_1_Midterm2010Solutions - EE211A Digital Image...

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Unformatted text preview: EE211A Digital Image Processing I Fall Quarter, 2010 Page 1 Midterm Solutions Note that 1. 2D Convolution and Autocorrelation (25 points) Consider the continuous 2D function f(x,y) given below, which has value 1 where the dark regions are located and 0 elsewhere. (a) (15 points) Make a sketch showing the boundaries of non-zero regions of the function g(x,y) , where g(x,y) = f(x,y) * f(x,y) . Be sure to place your sketch on a set of marked axis such that relevant dimensions and positions of features of g(x,y) are clearly indicated. Answer: EE211A Digital Image Processing I Fall Quarter, 2010 Page 2 (b) (10 points) Make a sketch showing the boundaries of non-zero regions of the autocorrelation of f(x,y) . Again, your answer must be clearly indicated for you to receive credit. Answer: EE211A Digital Image Processing I Fall Quarter, 2010 Page 3 2. Summation (25 points) Use the Fourier transform relationships given in the problem statement below to evaluate the following summation: You may find the following information useful for this problem. For a discrete, aperiodic function , the Fourier transform relationship is where will be continuous and periodic with period . The inverse transform equation is: The relationship between the energy in the two domains is: The relationship between multiplication in the input domain and convolution in the transform domain is: Given and then: Also, given a constant W , the following transform relationship holds: Answer: Let The FT of is EE211A Digital Image Processing I Fall Quarter, 2010 Page 4 Let , which is the argument of the summation given in the problem statement. , which is the argument of the summation given in the problem statement....
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This note was uploaded on 12/27/2011 for the course EE211A 211A taught by Professor Villasenor during the Spring '11 term at UCLA.

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211A_1_Midterm2010Solutions - EE211A Digital Image...

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