1. 電腦視覺 Computer and Robot Vision I Chapter2: Binary Machine Vision: Thresholding and Segmentation Instructor: Shih-Shinh Huang 1

2. Contents  Introduction  Thresholding  Connected Components Labeling  Signature Segmentation and Analysis 2

3. Computer and Robot Vision I 2.1 Introduction Introduction 3

4. Binary Machine Vision  Binary Image  Binary Value 1: Part of Object  Binary Value 0: Background Pixel  Definition of Binary Machine Vision  Generation and analysis of such a binary image 2.1 Introduction 4

5. Binary Machine Vision  Thresholding  It is the first step of binary machine vision  It is a labeling operation  Connected Components / Signature Analysis  They are multilevel vision grouping techniques.  They make a transformation from image pixels to more complex units. Regions Segments 2.1 Introduction 5

6. Computer and Robot Vision I 2.2 Thresholding Introduction 6

7.  What is Thresholding ?  It is a labeling operation.  It assigns a binary value to each pixel. Binary Value 1: pixels have higher intensity values Binary Value 0: pixels have higher intensity values 2.2 Thresholding 7

8. Introduction  Mathematical Formulation  : row and column  : gray-level intensity image  : intensity threshold  : binary intensity image 8 2.2 Thresholding

9. Introduction 9 2.2 Thresholding How to select an appropriate threshold ?

10. Introduction  Approaches  Global Thresholding: use a global value to make the pixel distinction in the image.  Local Thresholding: use spatial varying threshold to label the local pixels. 10 2.2 Thresholding Image

11. Histogram  Definition of Histogram  Histogram Probability 11 2.2 Thresholding number of elements m spans each gray level value e.g. 0 - 255

12. Histogram  Examples 12 2.2 Thresholding

13. Histogram 13 2.2 Thresholding

14. Histogram 14 2.2 Thresholding T=110T=130T=150T=170

15. Within-Group Variance  Observations  A group is a set of pixels with intensity homogeneity.  Homogeneity is measured by the use of variance High homogeneity group has low variance Low homogeneity group has high variance  Objective  Select a dividing score such that the weighted sum of the within-group variances is minimized. 15 2.2 Thresholding

16. Within-Group Variance  Definition: weighted sum of group variances  : probability for the group with values  : variance for the group with values 16 2.2 Thresholding

17. Within-Group Variance  Objective Formulation  Find a threshold which minimizes 17 2.2 Thresholding

18. Within-Group Variance  Implementation Issue  Step1: For t=0,…,255  Step2: Compute,,, and  Step3: Compute  Step4: If is less than the value in the previous iteration 18 2.2 Thresholding All variables should be re-compute at each iteration.

19. Within-Group Variance  Implementation Issue  Speed-Up Formulation 19 2.2 Thresholding

20. Within-Group Variance  Implementation Issue  Speed-Up Formulation 20 2.2 Thresholding

21. Within-Group Variance  Implementation Issue  Speed-Up Formulation 21 2.2 Thresholding

22. Within-Group Variance  Implementation Issue  Speed-Up Formulation 22 2.2 Thresholding

23. Within-Group Variance  Implementation Issue  Speed-Up Formulation 23 2.2 Thresholding constant minimizemaximize

24. Within-Group Variance  Implementation Issue  Speed-Up Formulation We have recursive form to compute optimal threshold. 24 2.2 Thresholding

25. Within-Group Variance  Example 25 2.2 Thresholding

26. Kullback Information Distance  Assumption  The observations come from a weighted mixture of two Gaussians distributions. Gaussian Distribution of Background Gaussian Distribution of Object 26 2.2 Thresholding

27. Kullback Information Distance 27 2.2 Thresholding Background Gaussian Distribution Object Gaussian Distribution

28. Kullback Information Distance  Objective Formulation T  Determine a threshold T that results in two Gaussian distributions which minimize Kullback divergence P(I) :P(I) : observed histogram distribution f(I) Tf(I) : a mixture of Gaussian distributions determined by T 28 2.2 Thresholding

29. Kullback Information Distance  Objective Formulation  Known Parameter: Observed Histogram  Unknown Parameter: Two Gaussian Distributions 29 2.2 Thresholding

30. Kullback Information Distance  Solution Derivation 30 2.2 Thresholding Constant

31. Kullback Information Distance  Solution Derivation  Assumption: The modes are well separated. 31 2.2 Thresholding

32. Kullback Information Distance  Solution Derivation 32 2.2 Thresholding

33. Kullback Information Distance  Implementation Issue  Step1: For t=0,…,255  Step2: Compute,,, and  Step3: Compute  Step4: If is less than the value in the previous iteration 33 2.2 Thresholding

34. Kullback Information Distance  Example 34 2.2 Thresholding

35. Kullback Information Distance 35 2.2 Thresholding Within Group Variance (Otsu) Kullback Information (Kittler-Illingworth)

36. Computer and Robot Vision I 2.3 Connected Component Labeling Introduction 36

37. Introduction  Description  Connected Components labeling is a grouping operation.  It performs the unit change from pixel to region or segment.  All pixels are given the same identifier Have value binary 1 Connect to each other 37 2.3 Connected Component Labeling

38. Introduction  Terminology  label: unique name or index of the region  connected components labeling: a grouping operation  pixel property: position, gray level or brightness level  region property: shape, bounding box, position, intensity statistics 38 2.3 Connected Component Labeling

39. Connected Component Operators  Definition of Connected Component  Two pixels and belong to the same connected component if there is a sequence of 1-pixels, where are neighbor 39 2.3 Connected Component Labeling

40. Connected Component Operators  Neighborhood Types 40 2.3 Connected Component Labeling 4-connected 8-connected Original ImageConnected Components

41. Connected Component Algorithms  Common Features  Process a row of image at a time  Assign a new labels to the first pixel of each component.  Propagate the label of a pixel to its neighbors to the right or below it. 41 2.3 Connected Component Labeling

42. Connected Component Algorithms  Common Features 42 2.3 Connected Component Labeling What label should be assigned to A How does the algorithm keep track of the equivalence of two labels How does the algorithm use the equivalence information to complete the processing

43. Algorithm1: Iterative Algorithm  Algorithm Steps  Step1 (Initialization): Assign an unique label to each pixel.  Step2 (Iteration) : Perform a sequence of top- down and bottom-up label propagation. 43 2.3 Connected Component Labeling Use no auxiliary storage Computational Expensive

44. Algorithm2: Classic Algorithm  Two-Pass Algorithm  Pass 1: Perform label assignment and label propagation Construct the equivalence relations between labels when two different labels propagate to the same pixel. Apply resolve function to find the transitive closure of all equivalence relations.  Pass 2: Perform label translation. 44 2.3 Connected Component Labeling

45. Algorithm2: Classic Algorithm  Example: 45 2.3 Connected Component Labeling {2=4} {3=5} {1=5}

46. Algorithm2: Classic Algorithm  Example:  Resolve Function 46 2.3 Connected Component Labeling {2=4}{3=5}{1=5}{2=4}{1=3=5} Computational Efficiency Need a lot of space to store equivalence

47. Computer and Robot Vision I 2.4 Signature Segmentation and Analysis Introduction 47

48. Introduction  Description  Signature analysis perform unit change from the pixel to the segment.  It was firstly used in character recognition  Definition of Signature  The signature, which is a projection, is the histogram of the non-zero pixels of the masked image. 48 2.4 Signature Segmentation and Analysis

49. Introduction  General Signatures  Vertical Projection  Horizontal Projection  Diagonal Projection 49 2.4 Signature Segmentation and Analysis

50. Signature Segmentation  Steps  Thresholding : generate the binary image.  Projection Computation: compute the vertical, horizontal, or diagonal projections.  Projection Segmentation: divide the image into several segments or regions according to the signatures. 50 2.4 Signature Segmentation and Analysis

51. Signature Segmentation 51 2.4 Signature Segmentation and Analysis

52. Signature Segmentation 52 2.4 Signature Segmentation and Analysis

53. Signature Segmentation 53 2.4 Signature Segmentation and Analysis OCR: Optical Character Recognition MICR: Magnetic Ink Character Recognition

54. The End Computer and Robot Vision I