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Chapter 4 – Data structures for image analysis

Chapter 4 – Data structures for image analysis. 4.1. Levels of Image Data Representation 4.2. Traditional Image Data Structures 4.3. Hierarchical Data Structures. 4.1. Levels of Image Data Representation. (i) Pixel-level representation. Intensity image. Range

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Chapter 4 – Data structures for image analysis

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

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

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

  4. (ii) Region-level representation Image Segmentation

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

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

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

  8. 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 LBC 8-neighbor LBC 4 -7

  9. Integral image ii (iii) Integral image Input image f 4 -8

  10. 4 -9

  11. Application: Face location 4 -10

  12. 4 -11

  13. 4 -12

  14. Adaboost (learning) algorithm (10.6) n training samples: : label space : data space, m positive samples: l negative samples: Feature set: Classifier set associated with F: Sample’s distribution at time t : 4 -13

  15. Initially, For 1. Normalization 2. For each classifier Calculate classification error: Choose the classifier with the smallest Remove from H 4 -14

  16. 3. If , then stop; 4. Update where Construct the strong classifier where Extension: Cascaded adaboost algorithm 4 -15

  17. Positive Samples 4 -16

  18. Negative Samples 4 -17

  19. (iv) Co-occurrence matrix (or Spatial gray-level dependence matrix) Texture analysis Texture: closely interwoven elements 4 -18

  20. r = (orientation, distance) 4 -19

  21. Example: r = (orientation, distance) Image: C(0, 1)= r = (0, 1), C(135, 1)= r = (135, 1), 4 -20

  22. Potential features calculated from co-occurrence matrices Entropy: Energy: Correlation: Homogeneity: 4 -21

  23. Inertia: where 4 -22

  24. Feature vector formed from features e.g., Different relations 4 -23

  25. 4.2.2. Chains • Chain code: for description of object borders

  26. (ii) Attributed strings 4 -25

  27. String matching Scene string: Model string: Calculate the cost of transforming to 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. String transformation through editions Types of edition: insert, delete, change 4 -26

  28. Define the cost functions of editions The total cost of string transformation Object recognition by 4 -27

  29. (iii) Run length code: For binary images: (Row#, (begin col., end col.) .... (begin col., end col.)) ……………………………………………………. (Row#, (begin col., end col.) .... (begin col., end col.)) Example: ((11144) (214) (52355)) 4 -28

  30. Gray level images: (Row#, (begin col., end col., brightness) ................ (begin col., end col., brightness)) …………....………………….. ………………….. (Row#, (begin col., end col., brightness) ................. (begin col., end col., brightness)) 4 -29

  31. 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.

  32. Images are described as a set of elements and their relations. Region adjacency graphs Semantic nets 4 -31

  33. 4.2.4. Tables -- Relational structures Table 4 -32

  34. 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 4.3. Hierarchical data structures Multigrid processing

  35. Tree pyramid: Let : the size of an image the set of nodes at level k e.g., k = 1,

  36. mapping the nodes in to those in e.g., 4 -35

  37. defines the values of nodes, e.g., average, maximum, minimum Z: a set of brightness levels Leaf nodes have pixel brightness values 4 -36

  38. 4.3.2. Quadtrees 4 -37

  39. 4.3.3. Other pyramidal structures Criteria: reduction window, window overlapping, reduction rate, regularity

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