EE5356 Digital Image Processing

Transcription

1 EE5356 Digital Image Processing INSTRUCTOR: Dr KR Rao Spring 007, Final Thursday, 10 April :00 AM 1:00 PM ( hours) (Room 111 NH) INSTRUCTIONS: 1 Closed books and closed notes All problems carry weights as indicated 3 Please print your name and ID 4 For problem 1 15, put the correct answer in the answer box 5 For Part B, show all your work 6 No cheating, no talking Name Student ID

2 PART A: MULTIPLE CHOICES (4 POINTS FOR EACH QUESTION) (Q1) Which one of the following is a lossy coding? A Huffman coding B Run-length coding C Predictive coding without quantizer D Optimum mean square quantizer (Q) In an image compression system, 65,536 bits are used to represent a image with 56 gray levels What is the compression ratio for this system? A 30 B 196 C 1446 D None of above (Q3) There are two image compression systems: #1 system can compress a image into 4,000 bits, and achieve PSNR=3dB; # system can compress the same image into 19,000 bits, and achieve PSNR=33dB; Which system has more coding efficiency? A #1 B # C Cannot compare D Both are the same

3 (Q4) In Huffman coding, the size of the codebook is L1, while the longest codeword can have as many as L bits What is the relationship between L1 and L? A L1<L B L1=L C L1>L D They do not have a certain relationship (Q5) Which one of the following cannot be adopted as a data compression system? A DPCM coding, followed by Huffman coding B Transform coding, followed by DPCM coding C Huffman coding, followed by transform coding D Transform coding, followed by uniform quantizer, followed by Huffman coding (Q6) What does the definition of entropy tell us? A The lower bound (bpp) to encode a source for an arbitrarily small distortion B The upper bound (bpp) to encode a source without distortion C The average number of bits to encode a source without distortion D The average number of bits to encode a source for a specified distortion (Q7) Comparing geometrical zonal coding with threshold coding, for the same number of transmitted samples, which one of the following is NOT correct? A Threshold coding has more distortion B Threshold coding needs more bit rates C The threshold coding mask gives a better choice of transmission samples D In threshold coding, the addresses of the transmitted samples have to be coded for every image block 3

4 (Q8) In DPCM codec, which of the following need to be quantized? A The prediction value B The transform coefficient C The reconstruction value D The difference between prediction value and the original value, ie, prediction error (Q9) In run-length coding, suppose the runs are coded in maximum length of M, and the probability distribution of the run-lengths turns out to be the geometric distribution, l p ( 1 p), 0 l M gl () = M p, l = M 1, Probability of a 0 =p, probability of a 1 =1 p Since a run-length of l M 1 implies a sequence of l 0 s followed by a 1, that is, ( l 1) symbols, the average number of symbols per run will be, A B C μ = μ = μ = M ( 1 p 1 ) 1 p M ( 1 p ) 1 p M ( 1 p ) 1 p D None of the above 4

5 (Q10) A simple nonlinear filter called root filter is defined as, U ˆ ( ω, 1 ω) = V α exp ( j θ ), where V ( ω ) ( ) V 1, ω = V exp jθv Degraded image v m,n Nonlinear filter Restored image ^ u m,n V(ω 1,ω ) g m,n G(ω 1,ω ) ^ U(ω 1,ω ) Figure 1, g, and u are in D-spatial domain v mn, mn, ˆm, n V ( ω1, ω ), G ( ω 1, ω ), and U ˆ ( ω, 1 ω ) are in D-frequency domain For α 1, the nonlinear filter acts as, A BPF B HPF C LPF D None of the above (Q11) From (Q10), for α 1, the nonlinear filter acts as, A BPF B HPF C LPF D None of the above 5

6 (Q1) Which comment is correct according to inverse filter and Wiener filter? (Cannot give reconstruction means, does not yield useful reconstructed images) (N = Fourier transform of additive noise, H = Fourier transform of imaging system) A When the ratio of spectrum N/H is large, Wiener filter cannot give reconstruction while inverse filter can B When the ratio of spectrum N/H is small, Wiener filter cannot give reconstruction while inverse filter can C When the ratio of spectrum N/H is large, both inverse filter and Wiener filter cannot give reconstruction D When the ratio of spectrum N/H is small, both inverse filter and Wiener filter can give reconstruction (Q13) Given u v u^ h G s η Figure u is original object, η is additive noise, v is corrupted object h is detector/recorder impulse response, û is reconstructed object, 1 s * s HS Gs = ( H ), 0 s 1 H S S ηη s = ( Pseudo inverse filter) ( Wiener filter) 1 s Which one of the following comments of geometric mean filter (GMF) is correct? A For s < 1/, GMF tends more towards pseudo inverse filter B For s > 1/, GMF tends more towards Wiener filter C For s = 0, GMF acts as a pseudo inverse filter D None of the above 6

7 (Q14) For Wiener filter, which one of the following about the mean square error is NOT correct? Given S and S ηη are PSDs of input signal umn) (, and additive noise η ( mn, ), respectively Given S ( ω, ω ) = 1 GH S G S ηη e 1 σ e A π 1 σe Sηηdωd 4 π = ω π π π π π π π π π π 1 1 B σ = e S e(, ω ) dωdω 4 ω C σe = ( 1 GH S G Sηη) dω 1d ω 4π π π D {[ ( ) ( )] σe = E u m, n uˆ m, n } = E e ( m, n) (Q15) In order to prove the power spectral density of the error of Wiener filter to be ( ω, ω ) = 1 G S, what definition of power spectral density is Se 1 GH S ηη applied? (Given S, S, are power spectral densities of reconstruction error, original e S ηη object, and additive noise, respectively) A Power spectral density of the error is the Fourier transform of the power of the error in the spatial domain B Power spectral density of the error is the Fourier transform of autocorrelation function of the error C Power spectral density of the error is the Fourier transform of the autocorrelation function of the mean square error D Power spectral density of the error is the Fourier transform of the error 7

8 PART B: COMPUTATION PROBLEMS (0 POINTS FOR EACH PROBLEM) (Q16) Show that the Wiener filter does not restore the power spectral density of the 1 object, whereas the geometric mean filter does, when s =, (Derive that S S for Wiener filter and S = S for GMF) Hint: ˆˆ ˆˆ vv S = G S for any filter G ˆˆ u H v G u^ (Object) Detector Recorder η Filter Figure 3 η is stationary additive noise uncorrelated with u Also u and v are zero mean random sequence (Q17) The sequence 150, 160, 16, 175, 163, 170 is to be predictively coded using the previous element prediction rule, u ( n) = u ( n 1) for DPCM and u( n) = u( n 1) for the feedforward predictive coder Assume a -bit quantizer shown on the next page is used, except the first sample is quantized separately by a 7-bit uniform quantizer, giving u ( 0) = u( 0) = 150 Please fill up the form on the next page showing that reconstruction error builds up with a feedforward predictive coder, whereas it tends to stabilize with the feedback loop of DPCM (Figures and Table are in the next page) 8

9 _ - Q P - P Figure 4: DPCM codec P Q _ - - P Figure 5: Feedforward codec Figure 6: Quantizer n ( ) u n u( n) DPCM Feedforward predictive coder en ( ) ( ) ( ) δ ( ) ( ) en u n u n u n ( ) en ( ) ( ) ( ) en u n δ u n δ u( n) = u( n) u ( n) END OF TEST QUESTIONS 9