1. Digital Image Fundamentals Faculty of Science Silpakorn University

2. Overviews  Elements of Visual Perception  Term of image  Sampling and Quantization

3. Term of image  Pixel  Resolution  Neighbor of pixels  Space and Frequency  Vector

4. PIXEL  Pixel is a smallest component of digital image  Pixel is a color point of digital image  An image should be comprised of many Pixels.

5. PIXEL

6. RESOLUTION  How quality of image  With the same size of picture –If high resolution, high memory is required to store data –If low resolution, less memory is required to store data  Its unit is call “point per inch”

7. RESOLUTION 72 18 36 9

8. Digital Image Representation x y f(x,y)

9. Neighbors of a pixel  Neighbors of pixel are the pixels that are adjacent pixels of an identified pixel.  Each pixel is a unit distance from the particular pixel.  Some of the neighbors of pixel lie outside the digital image if its position is on the border of the image.

10. Pixel at coordinate (column x, row y) can be represented by f(x,y) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Pixel at the 7 th column and 4 th row is yellow color Zoom 1600%

11. 4-neighbors of pixel  4-neighbors of pixel is denoted by N 4 (p)  It is set of horizontal and vertical neighbors f(x,y) is a yellow circle f(x,y-1) is top one f(x-1,y) is left one f(x+1,y) is right one f(x,y+1) is bottom one (x-1) (y-1) (y+1) (x+1)(x) (y)

12. Diagonal neighbors of pixel  Diagonal neighbors of pixel is denoted by N D (p)  It is set of diagonal neighbors f(x,y) is a yellow circle f(x-1,y-1) is top-left one f(x+1,y-1) is top-right one f(x-1,y+1) is bottom-left one f(x+1,y+1) is bottom-right one (x-1) (y-1) (y+1) (x+1)(x) (y)

13. 8-neighbors of pixel  8-neighbors of pixel is denoted by N 8 (p)  4-neighbors and Diagonal neighbors of pixel f(x,y) is a yellow circle (x-1,y-1), (x,y-1),(x+1,y-1), (x-1,y), (x,y), (x+1,y), (x-1,y+1),(x,y+1), (x+1,y+1) (x-1) (y-1) (y+1) (x+1)(x) (y)

14. Connectivity  Establishing boundaries of objects and components of regions in an image.  Group the same region by assumption that the pixels being the same color or equal intensity will are the same region

15. Connectivity  Let C is the set of colors used to define  There are three type of connectivity:  4-Connectivity : 2 pixels (p and q) with value in C are 4-connectivity if q is in the set N 4 (p)  8-Connectivity : 2 pixels (p and q) with value in C are 8-connectivity if q is in the set N 8 (p)  M-Connectivity : 2 pixels (p and q) with value in C are 8-connectivity if (i)Q is in N 4 (p), or (ii)Q is in N D (p) and the set N 4 (p) ∩ N 4 (q) is empty

16. Binary Image Represent 0000000000 0000110000 0011111100 0001001000 0001001000 0001001000 0001111000 0111001110 0000000000

17. Example 4-Connectivity  Set of color consists of color 1 ; C ={1} 11 1 0 1 0 0 00 1 11

18. Example 8-Connectivity  Set of color consists of color 1 ; C ={1} 11 1 0 1 0 0 00 1 11

19. Example M-Connectivity  Set of color consists of color 1 ; C ={1} 11 1 0 1 0 0 00 1 11

20. Distance Measure  For pixels p, q, and z, with coordinates (x,y), (s,t) and (u,v) respectively, D is a distance function or metric if (a)D(p,q) ≥ 0 and (b)D(p,q) = 0 iff p = q and (c)D(p,q) = D(q,p) and (d)D(p,z) ≤ D(p,q) + D(q,z)

21. The D 4 Distance  Also called city-block distance  Calculate between p and q is defined as D 4 (p,q) = | p x - q x | + | p y - q y | 1 11 1 2 22 22 22 2 0

22. The D 8 Distance  Also called city-block distance  Calculate between p and q is defined as D 8 (p,q) = max(| p x - q x |,| p y - q y |) 1 11 1 2 11 22 11 2 0 2 2 222 2 22 22 22

23. Labeling of connected Components  Scan an image pixel by pixel from left to right and top to bottom  There are 2 types of connectivity interested  4-connectivity  8-connectivity  Equivalent labeling

24. Step: 4-connected components  P is pixel scanned process  If pixel p is color value 0 move on the next scaning  If pixel p is color value 1 examine pixel top and left –If top and left were 0, assign a new label to p –If only one of them’re 1, assign its label to p –If both of them’re 1 and have the same number, assign their label to p Different number, assign label of top to p and make note that two label is equivalent  Sort all pairs of equivalent labels and assign each equivalent to be same type

25. Example 4-connected components 11 1 0 1 0 0 00 1 11 1 1 2 1 3 4 3 12 34 Equivalent Table

26. Step: 8-connected components  Steps are same as 4-connected components  But the pixel that are consider is 4 previous pixels ( top-left, top, top-right, and left )

27. Example 8-connected components 11 1 0 1 0 0 00 1 11 1 1 1 1 1 1 1

28. Multi-Color Labeling  Well define the group of color clearly and independency.  Then label each group independency.

29. Example Multi-Color labeling แทน 0 แทน 1 แทน 2 แทน 3 Group of color 1 st Group consists of 1 2 nd Group consists of 2 3 rd Group consists of 3

30. Color Labeling 1 st Group 1 1 1 1 111 11 1 1 2 22222 22 2 222 22 22 2 2 2 2 2 2 2 2

31. Color Labeling 2 st Group 111 111 111 555 555 2 333 333 333 333 3 3 4

32. Color Labeling 3 st Group 111 111 111 111 111 111 2 42 42 333 3333 3 3 4 5555 555 55 6

33. Exercise  If we want to label red and yellow is the same group.  How many label we can get?