Question 2
Test 2 Solution
(a) (8 marks) Fig. (i) shows an image degraded by noise. Inverse filter is used to recover the image, producing the result shown in Fig. (ii). Explain mathematically why the degraded image cannot be recovered by the inverse filter.
(b) (9 marks) What can be done to the inverse filter to improve the result? Express your modification mathematically.
(c) (8 marks) Given that the power spectrums of the noise and the undegraded image are not known, can the Wiener filter still be used to recover the degraded image in Fig. 1(i)? If so, describe the workflow of the image recovery process. If not, provide your justification.
Solution:
(a) ,= , =,+ , , ,
The noise is enhanced when , is close to zero.
(b) Inverse filter can be improved by filtering only at low frequencies:
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(c) Yes, the ratio between the spectrums of the undegraded image and noise can be approximated by a constant denoted by SNR. The Wiener filter becomes:
SNR is tuned empirically for the optimum result.
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Question 3
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Question 4
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(a) (11 marks) Find the closing of the binary image F, shown in Fig. (i), by the structural element H, shown in Fig. (ii). Draw the intermediate and final results.
(b) (13 marks) Find the grayscale opening of the function f sketched in Fig. (iii) with the structural element h shown in Fig. (iv). Sketch the immediate and final results.
(c) (13 marks) Given the function f and the structural element h in Part b, identify an algorithm that outputs the function shown in Fig. (v). What is this algorithm called? List an application of this algorithm.
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(a)
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