This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 nonzero 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 nonzero 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....
View
Full
Document
This note was uploaded on 12/27/2011 for the course EE211A 211A taught by Professor Villasenor during the Spring '11 term at UCLA.
 Spring '11
 Villasenor

Click to edit the document details