finalterm2009

# finalterm2009 - Department of Electrical Engineering,...

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1 Department of Electrical Engineering, Polytechnic University, Brooklyn Fall’ 00 EL5123 --- DIGITAL IMAGE PROCESSING (I) Y. Wang Final Exam 12/22/2009, 1PM-4PM Your Name: _______________________________________________ ID Number: _______________________________________________ Closed book. One sheet of notes (double sided) permitted. Write your solutions in the space provided next to the questions (use both sides if necessary). If you need extra space, you are probably on the wrong track! PROBLEM NO. FULL POINTS YOUR POINTS 1 10 2 15 3 15 4 10 5 10 6 20 7 20 8 (bonus) 10 Total Points 110

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2 1. (15pt) (a) Find the opening of the binary image, F, in Fig. (a) by the structuring element H in Fig. (b). You can use the grids in Fig. (c) and Fig. (d) to draw the intermediate and the final results. (b) Find the gray scale closing of the function sketched in Fig. (e) with the structural element in Fig. (f). Sketch the intermediate and final result in Figs. (g) and (h). Comment on the effect of closing and grayscale opening. Origin H b ) ( F a ) ( h f ) ( f e ) ( -3 1 2 1 1 0 2 -2 ) ( c ) ( c
3 2. (15pt) Consider a 2D image f(x,y)=sin(4 π x-6 π y). a) (3pt) Determine its Fourier transform F(u,v) and illustrate the spectrum (i.e., the impulses in the transform) in Fig. (a). Indicate the magnitude of each impulse. b) (3pt) Suppose this signal is sampled uniformly with sampling intervals Δ x= Δ y= Δ =1/5. Draw the spectrum of the sampled signal in Fig. (b). c) (4 pt) Suppose the sampled signal is interpolated by an ideal low-pass filter h 1 (x,y) with frequency response otherwise f v u f v u H s s 0 , 2 / , 2 / ) , ( 2 1 where f s =1/ Δ . Draw the spectrum of the reconstructed signal in Fig. (c). Give the spatial representation of the reconstructed signal f r1 (x,y).

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## This note was uploaded on 01/22/2012 for the course EL 5123 taught by Professor Yaowang during the Fall '07 term at NYU Poly.

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finalterm2009 - Department of Electrical Engineering,...

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