Chapter 2: Digital Image Fundamentals

1. Chapter 2: Digital Image Fundamentals Fall 2003, 劉震昌

2. Outline • Elements of Visual Perception • Image sensing and acquisition • Image sampling and quantization • Relationships between pixels

3. Understanding visual perception • Most image processing operations are based on math. and probability • Why understanding visual perception? • Human intuition plays an important role in the choice of processing technique

4. Structure of the Human eye 角膜 虹膜 水晶體 Diameter:20mm 網膜

5. 2 class of receptors: cones and rods • Distribution of cones and rods 1 cone -> 1 nerve Many rods -> 1 nerve

6. Discrete nature of human vision • Area of cones Cone density: 150,000 per mm 15mm

7. Image formation in the Eye

8. Image Sensing and Acquisition

9. Images? Illumination source scene reflection

10. Image sensors • Incoming energy is transformed into a voltage by the combination of input electrical power and sensor material (continuous)

11. Single sensor with motion

12. Sensor strips • Flat-bed scanner • aircraft

13. Sensor arrays • CCD arrays in digital camera

14. Image sampling and quantization

15. Image sampling and quantization • Sampling: digitize the coordinate values • Quantization: digitize the amplitude values • Why? Limited representation power in digital computers continuous data digital data discretize

17. Image sampling and quantization (cont.) • Sometimes, the sampling and quantization are done mechanically • Limitation on the sensing equipment sensor array

18. Sampling rule • How to determine the sampling rate? • Nyquist sampling theorem • If input is a band-limited signal with maximum frequency ΩN • The input can be uniquely determined if sampling rate ΩS > 2ΩN • Nyquist frequency : ΩN • Nyquist rate : ΩS

19. Sampling rule (cont.)

20. Representing digital images

21. Representing digital images (cont.) • Matrix form f(0,0) f(0,1) … f(0,N-1) f(1,0) f(0,1) … f(1,N-1) … … f(M-1,0) f(M-1,1) … f(M-1,N-1) MxN bits to store the image = M x N x k gray level = 2k

22. Representing digital images (cont.) • L = 2k gray levels, gray scales [0,…,L-1] • The dynamic range of an image • [min(image) max(image)] • If the dynamic range of an image spans a significant portion of the gray scale -> high contrast • Otherwise, low dynamic range results in a dull, washed out gray look

23. Spatial and gray-level resolution • L-level digital image of size MxN • = digital image having • a spatial resolution MxN pixels • a gray-level resolution of L levels • Spatial resolution in real-world space line width=W cm space width=W cm Resolution = 1/2W (line/cm)

24. Spatial and gray-level resolution (cont.) • Resolution of printer or screen • dpi(dot per inch) • pixel/unit of distance • When an digital image of size MxN is to be printed or viewed using devices with resolution k dpi, how large will be the output image?

25. Multi-rate image processing • Down-sampling • Up-sampling • neighboring pixel duplication • interpolation 2 2

26. Down-sampling operations

27. See the information loss due to down-sampling

28. Gray-level reduction

29. Gray-level reduction false contouring

30. Empirical study of resolutions • 2k-level digital image of size NxN • How K and N affect the image quality Increased details

31. Empirical study of resolutions(cont.) • iso-preference curses *shift up and right *A detailed image may need less gray levels

32. Zoom and Shrink • Operations applied to digital images • Zoom: up-sampling • Pixel duplication • Bi-linear interpolation • Shrink: down-sampling

33. Zoom and shrink: idea Idea: adjust the grid size over the original image

34. Zooming: example pixel duplication bilinear interpolation

35. Relationships Between Pixels

36. Neighbors of a pixel • 4-neighbors of p: N4(p) • Diagonal neighbors: ND(p) • 8-neighbors = 4-neighbors+diagonal neighbors : N8(p) p p

37. Adjacency, connectivity, regions, and boundaries • Connectivity of pixels • They are neighbors • Their gray levels satisfy a specified criterion of similarity • Concept about regions and boundaries • Adjacency • 4-adjacency: p and q with intensity from V and q is in N4(p) • 8-adjacency: p and q with intensity from V and q is in N8(p)

38. Connectivity and adjacency (cont.) • m-adjacency(mixed adjacency): p and q having intensity from V and • q is in N4(p), or • q is in ND(p) and N4(p) N4(q) has no pixels whose values are from V

39. Path • A path from p: (x,y) to q: (s,t) is a sequence of pixels: • Length = n • It’s a k-path if it is 4-, 8-, and m-adjacency (x,y), (x1,y1), (x2,y2),…, , (xn-1,yn-1),(s,t) consecutive pixels are adjacency

40. Growth of definitions adjacency path S connected component S connected set (region) S boundary

41. Summary • We need solid mathematical definitions to let the algorithm run on a computer

42. Distance measure • p: (x,y), q: (s,t) • Euclidean distance • De(p,q)=[(x-s)2+(y-t)2]1/2 • D4 distance • D4(p,q)=|x-s|+|y-t| • D8 distance • D8(p,q)=max(|x-s|,|y-t|) r 2 2 1 2 2 1 0 1 2 2 1 2 2 2 2 2 2 2 2 1 1 1 2 2 1 0 1 2 2 1 1 1 2 2 2 2 2 2

43. Pixel-wise operation • For example, how does image I divided by image M? • Division is carried out between corresponding pixels in the two images • Matlab: Q = I./M

44. Linear and non-linear operations • H be an operator whose input and output are images • H is linear if • H(af+bg) = aH(f)+bH(g) • Otherwise non-linear • We have well-understood theoretical and practical results about linear operators

45. Announcement !!! • There are solutions to the marked problems in the textbook • http://www.imageprocessingbook.com/teaching/problem_solutions.htm • HW#1