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Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C.

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Presentation on theme: "Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C."— Presentation transcript:

1 Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C. Computer and Robot Vision I Chapter 2 Binary Machine Vision: Thresholding and Segmentation Presented by: 傅楸善 & 翁丞世 0925070510 mob5566@gmail.com mob5566@gmail.com 指導教授 : 傅楸善 博士

2 DC & CV Lab. CSIE NTU 2.1 Introduction to detect the objects, the input image is often simplified binary value 1: considered part of object binary value 0: background pixel binary machine vision: generation and analysis of binary image

3 DC & CV Lab. CSIE NTU 2.2 Thresholding if r: row, c: column I: grayscale intensity, B: binary intensity T: intensity threshold

4 DC & CV Lab. CSIE NTU 2.2 Thresholding

5 DC & CV Lab. CSIE NTU 2.2 Thresholding

6 DC & CV Lab. CSIE NTU 2.2 Thresholding

7 DC & CV Lab. CSIE NTU 2.2 Thresholding The question of thresholding is a question of the automatic determination of the threshold value.

8 DC & CV Lab. CSIE NTU 2.2 Thresholding histogram m spans each gray level value e.g. 0 - 255 #: operator counts the number of elements in a set

9 2.2 Thresholding DC & CV Lab. CSIE NTU 02233 10011 12301 01101 11233 2-bits source image histogram of left image

10 DC & CV Lab. CSIE NTU 2.2 Thresholding

11 DC & CV Lab. CSIE NTU 2.2 Thresholding

12 DC & CV Lab. CSIE NTU 2.2 Thresholding

13 DC & CV Lab. CSIE NTU 2.2 Thresholding

14 DC & CV Lab. CSIE NTU 2.2 Thresholding

15 DC & CV Lab. CSIE NTU 2.2 Thresholding Minimizes a criterion function Minimize the within-group variance Minimize the Kullback information distance

16 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance : histogram probabilities of gray values : the spatial domain of the image

17 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance Given threshold t, divide histogram into two parts. Part 1 is the left hand side of the histogram. Part 2 is the right hand side of the histogram.

18 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance Within-group variance : weighted sum of group variances find which minimizes

19 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance

20 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance

21 DC & CV Lab. CSIE NTU find which maximizes constant minimize

22 DC & CV Lab. CSIE NTU 2.2 Thresholding

23 DC & CV Lab. CSIE NTU 2.2.1 Minimizing Within-Group Variance

24 2.2.2 Minimizing Kullback Information Distance DC & CV Lab. CSIE NTU Gaussian distribution

25 DC & CV Lab. CSIE NTU 2.2.2 Minimizing Kullback Information Distance : mean of distribution

26 DC & CV Lab. CSIE NTU 2.2.2 Minimizing Kullback Information Distance minimize the Kullback directed divergence mixture distribution of the two Gaussians in histogram:

27 2.2.2 Minimizing Kullback Information Distance DC & CV Lab. CSIE NTU minimize constant

28 2.2.2 Minimizing Kullback Information Distance DC & CV Lab. CSIE NTU

29 2.2.2 Minimizing Kullback Information Distance DC & CV Lab. CSIE NTU find the *t the minimize H

30 DC & CV Lab. CSIE NTU 2.2.2 Minimizing Kullback Information Distance

31 DC & CV Lab. CSIE NTU 2.2.2 Minimizing Kullback Information Distance Left dark line: Otsu Right dark line: Kittler-Illingworth

32 DC & CV Lab. CSIE NTU 2.3 Connected Components Labeling Connected Components labeling is a grouping operation. Connected Component labeling is one image-processing technique that can make a unit change from pixel to region.

33 DC & CV Lab. CSIE NTU 2.3.1 Connected Components Operators

34 DC & CV Lab. CSIE NTU 2.3.1 Connected Components Operators Two 1-pixels and belong to the same connected component if there is a sequence of 1-pixels of where and is a neighbor of for

35 DC & CV Lab. CSIE NTU 2.3.1 Connected Components Operators 00100 11101 00011 10010 11010 00100 11102 00022 30020 33020 00100 11101 00011 20010 22010 source binary image Connected components labeling with 4-adjacency Connected components labeling with 8-adjacency

36 DC & CV Lab. CSIE NTU 2.3.2 Connected Components Algorithms All the algorithms process a row of the image at a time All the algorithms assign new labels to the first pixel of each component and attempt to propagate the label of a pixel to right or below neighbors

37 DC & CV Lab. CSIE NTU 2.3.2 Connected Components Algorithms What label should be assigned to pixel A? How to keep track of the equivalence of two or more labels? How to use the equivalence information to complete processing?

38 DC & CV Lab. CSIE NTU 2.3.2 Connected Components Algorithms An Iterative Algorithm The Classical Algorithm A Space-Efficient Two-Pass Algorithm with a Local Equivalence Table *An Efficient Run-Length Implementation of the Local Table Method

39 DC & CV Lab. CSIE NTU 2.3.3 An Iterative Algorithm Step 1. initialization of each pixel to a unique label Step 2. iteration of top-down followed by bottom-up passes Step3. repeat step 2 until no change

40 DC & CV Lab. CSIE NTU 2.3.3 An Iterative Algorithm

41 DC & CV Lab. CSIE NTU 2.3.4 The Classical Algorithm performs label propagation as above when two different labels propagate to the same pixel, the smaller label propagates and equivalence entered into table resolve equivalence classes by DFS (Depth-First Search) second pass performs a translation

42 DC & CV Lab. CSIE NTU 2.3.4 The Classical Algorithm

43 DC & CV Lab. CSIE NTU

44 DC & CV Lab. CSIE NTU 2.3.4 The Classical Algorithm main problem: global equivalence table may be too large for memory

45 DC & CV Lab. CSIE NTU 2.3.5 A Space-Efficient Two-Pass Algorithm That Uses a Local Equivalence Table Small table stores only equivalences from current preceding line Relabel each line with equivalence labels when equivalence detected

46 DC & CV Lab. CSIE NTU 2.3.5 A Space-Efficient Two-Pass Algorithm That Uses a Local Equivalence Table

47 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method A run-length encoding of a binary image is a list of contiguous typically horizontal runs of 1-pixels.

48 DC & CV Lab. CSIE NTU run 1run 2 run 7 run number

49 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method

50 DC & CV Lab. CSIE NTU

51 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method

52 DC & CV Lab. CSIE NTU

53 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method

54 DC & CV Lab. CSIE NTU

55 DC & CV Lab. CSIE NTU

56 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method

57 DC & CV Lab. CSIE NTU

58 DC & CV Lab. CSIE NTU 2.3.6 An Efficient Run-Length Implementation of the Local Table Method

59 DC & CV Lab. CSIE NTU

60 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis Signature analysis perform a unit change from the pixel to the region or segment. Signature: histogram of the nonzero pixels of the resulting masked image projections can be vertical, horizontal, diagonal, circular…

61 DC & CV Lab. CSIE NTU

62 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis vertical projection of a segment: column between horizontal projection: row between vertical and horizontal projection define a rectangle and

63 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis

64 DC & CV Lab. CSIE NTU

65 DC & CV Lab. CSIE NTU

66 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis 1. segment the vertical and horizontal projections 2. treat each rectangular subimage as the image

67 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis OCR: Optical Character Recognition MICR: Magnetic Ink Character Recognition

68 DC & CV Lab. CSIE NTU 2.4 Signature Segmentation and Analysis Diagonal projections: : from upper left to lower right : from upper right to lower left object area: sum of all the projections values in the segment

69 DC & CV Lab. CSIE NTU

70 DC & CV Lab. CSIE NTU 2.5 Summary Create binary image by thresholding. Find out connected component on binary image. Generate signature segmentation by projection.

71 DC & CV Lab. CSIE NTU Project due Oct. 6 Write a program to generate: a binary image (threshold at 128) a histogram connected components (regions with + at centroid, bounding box)

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