1. 4 - 0 4.1. Levels of Image Data Representation 4.2. Traditional Image Data Structures 4.3. Hierarchical Data Structures Chapter 4 – Data structures for image analysis

2. 4 - 1 4.1. Levels of Image Data Representation (i) Pixel-level representation Intensity image Range image

3. 4 - 2 Color image Indexed (or palette) color image

4. 4 - 3 (ii) Region-level representation Image Segmentation

5. 4 - 4 (iii) Abstract level representation Region adjacency graphs Semantic nets Segmented Image Binary Image

6. 4 - 5 4.2. Traditional Image Data Structures 4.2.1. Matrices Matrices, chains, graphs, tables (i) Ratio image – removes the effect of illumination variation Image model:

7. 4 - 6 Brightness ratio between adjacent pixels: or Grayscale image Ratio image

8. 4 - 7 Local binary pattern (LBP) (ii) Local binary coding (LBC) image For 4-neighbor, the range of LBC is 0 - 15 For 8-neighbor, the range of LBC is 0 - 255 4-neighbor LBC8-neighbor LBC

9. 4 - 8 Intrinsic Image Extraction

10. Interference Reflection Separation 4 - 9

11. 4 - 10 Dichromatic Reflection Decomposition

12. Dehaze

13. 4 - 12 Integral image ii Input image f (iii) Integral image

14. 4 - 13

15. 4 - 14 Application: Face location

16. 4 - 15

17. 4 - 16

18. Adaboost (learning) algorithm (10.6) n training samples: : data space, : label space m positive samples: l negative samples: 4 - 17 Feature set: Classifier set associated with F: Sample’s distribution at time t :

19. For 1. Normalization 4 - 18 2. For each classifier Classification error: Choose the classifier with the smallest Remove from H Initially,

20. Construct the strong classifier where Extension: Cascaded adaboost algorithm 4 - 19 3. Update where

21. 4 - 20 Positive Samples

22. 4 - 21 Negative Samples

23. 4 - 22 (iv) Co-occurrence matrix (or Spatial gray-level dependence matrix) Texture analysis Texture: closely interwoven elements

24. 4 - 23 r = (orientation, distance)

25. Example r = (orientation, distance) Image: r = (0, 1), C (0, 1) = r = (135, 1), C (135, 1) = 4 - 24

26. 4 - 25 Potential features calculated from co-occurrence matrices Energy: Entropy: Correlation: Homogeneity:

27. 4 - 26 Inertia: where

28. 4 - 27 Feature vector formed from features e.g., Different relations

29. 4 - 28 4.2.2. Chains (i)Chain code: for description of object borders

30. 4 - 29 (ii) Attributed strings

31. 4 - 30 String matching Scene string: Model string: Types of edition: insert, delete, change Calculate the cost of transforming to String transformation through editions The larger the cost the larger the difference between the two strings, and in turn the larger the difference between the two shapes described by the strings.

32. 4 - 31 Define the cost functions of editions The total cost of string transformation Object recognition by

33. 4 - 32 (iii) Run length code: to represent strings of symbols in an image (e.g., for transmission) Binary images: (Row#, (beginning col., end col.).... (beginning col., end col.)) ……………………………………… (Row#, (beginning col., end col.).... (beginning col., end col.)) Gray level images: (Row#, (beginning col., end col., brightness).... (beginning col., end col., brightness)) …………....…………………. (Row#, (beginning col., end col., brightness).... (beginning col., end col., brightness))

34. 4 - 33 4.2.3. Graphs -- Topological data structures Graph: G(V, E), where V: set of nodes, E: set of arcs Attributed (or weighted) graph: values are assigned to nodes, arcs, or both.

35. 4 - 34 Region adjacency graphs Semantic nets Images are described as a set of elements and their relations.

36. 4 - 35 4.2.4. Tables -- Relational structures Table

37. 4 - 36 4.3. Hierarchical data structures 4.3.1. Pyramids Matrix pyramid: a sequence of images is derived from by reducing the resolution by 1/2 corresponds to one pixel only Multigrid processing

38. 4 - 37 the set of nodes at level k Let : the size of an image Tree pyramid:

39. 4 - 38 Z: a set of brightness levels mapping the nodes in to those in Leaf nodes have pixel brightness values defines the values of nodes, e.g., average, maximum, minimum div: whole-number division(?)

40. 4 - 39 e.g., From k = 1,

41. 4 - 40 k = 2, e.g., From

42. 4 - 41 4.3.2. Quadtrees

43. 4 - 42 4.3.3. Other pyramidal structures Criteria: reduction window, window overlapping, reduction rate, regularity