EE5356 Digital Image Processing. Final Exam. 5/11/06 Thursday 1 1 :00 AM-1 :00 PM

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1 EE5356 Digital Image Processing Final Exam 5/11/06 Thursday 1 1 :00 AM-1 :00 PM I), Closed books and closed notes. 2), Problems carry weights as indicated. 3), Please print your name and last four digits of your ID. 4), For problems 1-16, circle the correct answer. Also show your work. 5), For part B, show all your work.

2 PART A: Multiple choices (4points for each question) l), What does the definition of entropy tell us? A, The average # of bits to encode a source without distortion. B, The upper bound to encode a source without distortion. C, The average # of bits to encode a source given a certain distortion. D, The lower bound to encode a source without distortion. 2), In Huffman coding, the size of the code book is L1, while the longest code word can have as many as L2 bits. What is the relationship between L1 and L2? A, Ll=L2 B, L1<L2 C, L1>L2 D, They do not have a certain relationship. 3), Which one of the following is a lossy coding? A, Run length coding B, Huffman coding C, Uniform quantizer D, Predictive coding without quantizer 4), There are two image compression systems: #l system can compress a 128x128 image into bits, and achieve PSNR=33dB; #2 system can compress the same image into 9900 bits, and achieve PSNR=29dB; Which system has more coding efficiency? A, #1 B, Cannot compare C, #2 D, Both are the same 5), In an image compression system, bits are used to represent a 256x256 image with 256 gray levels. What is the compression ratio for this system? A, 2.45 B, C, D, ), Which one of the following can not be adopted as a data compression system? A, Transform coding, followed by DPCM Coding B, Huffman coding, followed by transform coding. C, DPCM coding, followed by Huffman coding D, Transform coding, followed by uniform quantizer, followed by Huffman coding 7), 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 needs more bit rates. By The threshold coding mask gives a better choice of transmission samples. C, In threshold coding, the addresses of the transmitted samples have to be coded for every image block. D, Threshold coding has more distortion.

3 8), In DPCM codec, which of the following need to be quantized? A, The prediction value. B, The difference between prediction value and the original value. C, The reconstruction value. 1. D, The transform coefficient. 9), Baud rate is defined as the number of bits transmitted per second. Generally, transmission is accomplished in packets consisting a start bit, a byte (8 bits) of information, and a stop bit. Using these facts, how many minutes would it take to transmit a 5 12x5 12 image with 256 gray levels using a 28.8K baud modem? (1K=1024) lo), In run length coding, suppose the runs are coded in maximum lengths of M, then the probability distribution of the run lengths turns out to be the geometric distribution p(1-) OSlIM-1 dl) =, probability of a 'O'= p, probability of a ' 1 '= 1 - p. l=m Since a run length of 1 s M - 1 implies a sequence of 1'0's followed by a '1'. that is (1 + 1) symbols, the average number of symbols per run will be A, Cannot calculate. 1 I), 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 small, Wiener filter cannot give reconstruction while inverse filter can. B, When the ratio of spectrum N/H is small, both inverse filter and Wiener filter can give reconstruction. C, When the ratio of spectrum N/H is large, both inverse filter and Wiener filter cannot give reconstruction.

4 D, When the ratio of spectrum N/H is large, Wiener filter cannot give reconstruction while inverse filter can. 12), Given u = original object v = additive noise v = corrupted object h = detectionlrecorder impulse response li = reconstructed object Which one of the following comments of geometric mean filter (GMF) is not correct? A, For s>1/2, GMF tends more towards Wiener filter. By For s=o, GMF acts as an Wiener filter. - C, For s<1/2, GMF tends more towards Wiener filter. D, For s=l, GMF acts as an inverse filter. 13), In order to prove the power spectral density of the error of Wiener filter to be S, (o, 2, 02) = 1- GHI S,, + JG('s,,, what definition of power spectral density is applied? ( 3,, S,,, S,, = power spectral densities of reconstruction error, original object, and additive noise respectively. ) A, Power spectral density of the error is the Fourier transform of the autocorrelation function of the mean square error. By Power spectral density of the error is the Fourier transform of the error. C, Power spectral density of the error is the Fourier transform of autocorrelation function of the error. D, Power spectral density of the error is the Fourier transform of the power of the error in the spatial domain.

5 14), For Wiener filter, which one of the following about the mean square error 0: is not correct? S,, and S,, are PSDs of input signal u(m, n) and additive noise ~(m, n), respectively ( Given S, (o,,02) = 1- GHII S, + ~G/'S,, ) Given corrupted object object detector1 filter restored recorder object U, H, 7, V, G, fi are Fourier transforms of object u, detectorirecorder impulse response h, additive noise 7, corrupted object v, restoration filter impulse response g, and restored object ti respectively. 15), A simple nonlinear filter called root filter is defined as fi(w,, w2 ) = lvla exp( isv) where V(w,, w,) = I~(exp(j8~) For a <<I, the nonlinear filter acts as A, LPF B, BPF C, HPF D, none of the above

6 16), For a >>I, nonlinear filter acts as A, BPF B, LPF C, HPF D, none of the above

7 PART B: Computation problems (1 8points for each problem) I), Given Symbol S 0 S 1 S 2 S3 S4 what is the entropy,(h = -xpi log, pi), Draw Huffinan tree. 1 Find Huffrnan code and get its average code length and the redundancy. I Probability, pi ), The sequence 1 50,160,162,175,163,170 is to be predictively coded using the previous element prediction rule, i' (n) = u' (n - 1) for DPCM and ii(n) = u(n - 1) for the feedfonvard predictive coder. Assume a 2-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 feedfonvard predictive coder, whereas it tends to stabilize with the feedback loop of DPCM. Fig. 1 : DPCM codec Fig.2: Feedfonvard codec

8 Fig.3: Quantizer n 0 u(n) 150, ~ ii0(n) --- DPCM e(n) --- e'(n) --- u0(n) &(n) 0 u(n) pp-ppp- Feedforward Predictive Coder e(n) e'(n) u'(n) &(n) ~ LL

9 PART A: Multiple choices (4points for each question) I Problems I Answers I bits =14.46, bits Answer: C 512x512~8 bits+512x512x 2 bits 9. =1.48 min, Answer: D 28.8 x 1024 bits x 60 sec

10 PART B: Computation Problem (20points for each problem) 1) Symbol SO S 1 S2 Probability, Pi Codeword (Huffman Code) The entropy H = -xpi log, pi = - (0.3 x log2(0.3)+3 x 0.2 x log2(0.2)+ 0.1 x logz(o.l))= The average code length = 0.3 x x x x x 3=2.3 The redundancy = the average code length - the entropy = =