1. CSE340/540 Lecture 12 Slides prepared from various sources … including my understanding of IA

2. Q1. Write the expression of 2D continuous convolution in Fourier Domain. (1 m) Q2. Give a single intensity transformation function for spreading the intensities of an image so the lowest intensity is 0 and highest is L-1. (2 m) Q3. Given a noisy binary image (character L), what methodology you would use to remove the noise without too much damage to the character? Using the empty images (as many as you think is needed), explain and perform the operations you think are suitable and draw the result.(2 m) Q4. Show the proof of properties of Fourier transform (2+2 m) ( ⊃ represents conversion from spatial to Fourier relationship and vice versa – e.g. I(x,y) ⊃ F(u,v)) (a) If g(x) ⊃ G(s) and h(x) ⊃ H(s), where and a and b are some scalars, then (a)ag(x) + bh(x) ⊃ aG(s) + bH(s). (b) If g(x) ⊃ G(s) and h(x) ⊃ H(s), then g(x) ∗ h(x) ⊃ G(s)H(s). ( ∗ represents convolution in spatial domain) Q5. Explain (1+2 m) (a) the process and filter involved in the two examples. (b) Can you give associated filters in Spatial domain? If yes, provide details Of the filters; if no, explain why not. QUIZ 2 – PART 1 (25 MINS)

3. Q6. (8 marks) An archaeological expedition in the heart of the Australian desert has just returned with a very interesting discovery. Buried in the middle of nowhere, they found strangely carved metallic boxes, with inside them paper rolls written in a cryptic language. The quantity of these rolls is considerable, and it would take decades to decipher them by hand. But the language seems rather simple, consisting only of series of zeros and ones. It has been decided to automate the process, and let computers process the data. As the image processing specialist, your goal is to extract the "message" on the rolls (i.e. digitize the scanned image). This is an example of the data you are studying: Describe and illustrate an image processing system that would solve this problem. Include your hypotheses, a mathematical description of the method used, and a discussion about possible results. The following elements should be included in your discussion: a) Image acquisition (Discuss the needs for resolution, lighting, etc.). b) Image enhancement. c) Shape description. QUIZ 2 – PART 2 (15 MINS)

4. Three common suggestions 1.Course pace is fast 1.This year, we are slowest 2.Pre-reqs are not covered in detail 1.They are pre-reqs. 2.Homework/assignments and quizzes are less 3.OK, we will have more quizzes and assignments LET US QUICKLY GO OVER THE COURSE FEEDBACK

5. From your textbook: I will send some questions via email. WRITTEN HW

6. LETS START THE NEXT TOPIC

7. Where does blur come from? Optical blur: camera is out-of-focus Motion blur: camera or object is moving Why do we need deblurring? Visually annoying Bad for analysis Numerous applications IMAGE RESTORATION

8. The Story of Hubble Space Telescope (HST) HST Cost at Launch (1990): $1.5 billion Main mirror imperfections due to human errors “The error was well characterized and stable, enabling astronomers to optimize the results obtained using sophisticated image processing techniques such as deconvolution”. Got repaired in 1993 APPLICATION (I): ASTRONOMICAL IMAGING

9. RESTORATION OF HST IMAGES

10. ANOTHER EXAMPLE

11. THE REAL (OPTICAL) SOLUTION Before the repair After the repair

12. APPLICATION (II): LAW ENFORCEMENT Motion-blurred license plate image

13. RESTORATION EXAMPLE

14. APPLICATION: BIOMETRICS out-of-focus iris image

15. This ww2 photo is given here in its original form. From a human eye point of view – it has a good enough quality. Pay attention : some surfaces, like the runway’s asphalt or the roofs of the buildings, do not have a smooth texture… (pacific us navy airbase, ww2)

16. Now, pass the airbase photo through an edge detecting filter (sobel). Result: along with the “correct” edges, this product photo contains many false edges. This is not a good enough edge-marking product.

17. If we smooth the image, we can expect a lot less noise… Smoothing the original with Gaussian 5x5…

18. Running edge detection… Many of the false edges were smoothed. Unfortunately, so were the true edges.

19. Linear Blur Model h(m,n) blurring filter x(m,n)y(m,n) Gaussian blurmotion blur Spatial domain

20. H(u,v) blurring filter X(u,v)Y(u,v) Gaussian blurmotion blur Frequency (2D-DFT) domain Linear Blur Model

21. Blurring Effect Gaussian blur motion blur From [Gonzalez & Woods]

22. Image Restoration: Deblurring/Deconvolution h(m,n) blurring filter g(m,n) x(m,n)y(m,n) deblurring/ deconvolution filter x(m,n) ^ Non-blind deblurring/deconvolution Given: observation y(m,n) and blurring function h(m,n) Design: g(m,n), such that the distortion between x(m,n) and is minimized Blind deblurring/deconvolution Given: observation y(m,n) Design: g(m,n), such that the distortion between x(m,n) and is minimized x(m,n) ^ ^

23. Deblurring: Inverse Filtering h(m,n) blurring filter g(m,n) x(m,n)y(m,n) inverse filter x(m,n) ^ X(u,v) H(u,v) = Y(u,v) X(u,v) = Y(u,v) H(u,v) 1 =Y(u,v) G(u,v) = 1 H(u,v) Exact recovery!

24. Deblurring: Pseudo-Inverse Filtering h(m,n) blurring filter g(m,n) x(m,n)y(m,n) deblur filter x(m,n) ^ G(u,v) = 1 H(u,v) Inverse filter: What if at some (u,v), H(u,v) is 0 (or very close to 0) ? Pseudo-inverse filter: small threshold

25. More on restoration Weiner Filter NEXT CLASS