Image Processing

1. Image Processing Introduction and Overview Instructor: Juyong Zhang juyong@ustc.edu.cn http://staff.ustc.edu.cn/~juyong . 1. %. {. . {. . . . . . . .

2. Introduction and Overview This presentation is an overview of some of the ideas and techniques to be covered during the course.

3. Topics 1. Image formation 2. Point processing and equalization 3. The Fourier transform 4. Convolution 5. Spatial filtering 6. Image restoration 7.Advanced topics (sparse fft, total variation, non-local mean, compressed sensing, graph cut, image inpainting…)

4. References • Rafael C. Gonzalez, Richard E. Woods, Digital Image Processing • G. Sapiro, Geometric Partial Differential Equations and Image Analysis • IEEE Trans On Image Processing • Siam Journal On Image Science

5. Grades • Small projects: 25% • Paper Reading: 25% • Big project: 50%

6. Projects and paper reading • Small project: basic image operation • Big project: select one paper in recent years (ICCP, Siggraph, Siggraph Asia, Eurographics) • Paper Reading: A short presentation/report

7. lens object image plane Image Formation

8. light source Image Formation

9. Image Formation projection through lens image of object

10. Image Formation projection onto discrete sensor array. digital camera

11. Image Formation sampled image

12. Image Formation discrete real-valued image

13. Digital Image Formation: Quantization discrete color output continuous colors mapped to a finite, discrete set of colors. continuous color input

14. Digital Image Color images have 3 values per pixel; monochrome images have 1 value per pixel. a grid of squares, each of which contains a single color each square is called a pixel (for picture element)

15. Are constructed from three intensity maps. Each intensity map is pro-jected through a color filter (e.g., red, green, or blue, or cyan, magenta, or yellow) to create a monochrome image. The intensity maps are overlaid to create a color image. Each pixel in a color image is a three element vector. Color Images

16. Point Processing

17. - gamma - brightness original + brightness + gamma histogram mod - contrast original + contrast histogram EQ Point Processing

18. Color Sensing / Color Perception The eye has 3 types of photoreceptors: sensitive to red, green, or blue light. luminance hue saturation The brain transforms RGB into separate brightness and color channels (e.g., LHS). brain photo receptors

19. these complex exponentials are 2D sinusoids. The 2D Fourier Transform of a Digital Image Let I(r,c) be a single-band (intensity) digital image with R rows and C columns. Then, I(r,c) has Fourier representation where are the R x C Fourier coefficients.

20. 2D Sinusoids: ... are plane waves with grayscale amplitudes, periods in terms of lengths, ... A

21. The Fourier Transform of an Image magnitude phase Ð[F{I}] I |F{I}|

22. sFFT DFT: O(n*n) FFT: O(n*logn) sFFT: O(k*logn), if signal is k-sparse

23. Convolution Sums of shifted and weighted copies of images or Fourier transforms. Sum times 1/5

24. Convolution Property of the Fourier Transform The Fourier Transform of a product equals the convolution of the Fourier Transforms. Similarly, the Fourier Transform of a convolution is the product of the Fourier Transforms

25. Frequency Domain (FD) Filtering Power Spectrum Original Image

26. FD Filtering: Lowpass Image size: 512x512 SD filter sigma = 8 Filtered Image Filtered Power Spectrum Original Image

27. FD Filtering: Highpass Image size: 512x512 FD notch sigma = 8 Filtered Image Filtered Power Spectrum Original Image

28. Spatial Filtering blurred original sharpened

29. Spatial Filtering Bandpass filter original

30. Motion Blur regional vertical original rotational zoom

31. Motion deblur Input Output

32. High dynamic range imaging • A greater dynamic range between the lightest and darkest areas of an image than current standard digital image methods

33. HDR Image

34. Image Compression Original image is 5244w x 4716h @ 1200 ppi: 127MBytes

35. Image Compression: JPEG File size in bytes JPEG quality level

36. Image Compositing • Combine parts from separate images to form a new image. • It’s difficult to do well. • Requires relative positions, orientations, and scales to be correct. • Lighting of objects must be consistent within the separate images. • Brightness, contrast, color balance, and saturation must match. • Noise color, amplitude, and patterns must be seamless.

37. Image Compositing Example Prof. Peters in his home office. Needs a better shirt.

38. Image Compositing Example This shirt demands a monogram.

39. Image Compositing Example He needs some more color.

40. Image Compositing Example Nice. Now for the way he’d wear his hair if he had any.

41. Image Compositing Example He can’t stay in the office like this.

42. Image Compositing Example Where’s a hepcat Daddy-O like this belong?

43. Image Compositing Example Collar this jive, Jackson. Like crazy, Man ! In the studio!

44. PDE in Image Processing

45. Outline 1. Non linear PDEs 2. Variational Methods 3. Geometrical Schemes

46. Noisy image Denoised image

47. Total variation model input output

48. Image smoothing

49. Medical image segmentation Initial contour Final contour

50. Thanks!