COMP 9517 Computer Vision

1. COMP 9517 Computer Vision Binary Image Analysis COMP 9517 S2, 2009

2. Binary Image Analysis • How to do this? ? COMP 9517 S2, 2009

3. Binary Image Analysis • How to obtain binary images from scale-level images? • How to extract connected groups of pixels (components)? • How to process the separate components? • How to extract properties of components for use in high-level tasks? COMP 9517 S2, 2009

4. Binary Image • Definition: A binary image is a digital image with all pixel values 0 or 1 • Foreground: a subset of image pixels that are of interest in an image analysis task • Background: the rest of the image • A binary image B can be obtained from a gray-scale image or colour image through a selection operator: • Thresholding: subset of gray tones or colour space • Classification, segmentation, etc COMP 9517 S2, 2009

5. Binary Image Example • A gray-scale image contains the character “C” • Threshold t=200 to obtain a binary image • 1s denote foreground pixels, 0s background pixels COMP 9517 S2, 2009

6. Binary Image Analysis • Thresholding: convert gray scale image to binary image • Labelling: connected component labelling • Counting: object counting • Thinning & Thickening: join and/or separate components • Component Properties: extract features for higher level processes COMP 9517 S2, 2009

7. Applications • Document analysis • Industrial machine vision • Counting, recognition, localisation and inspection tasks COMP 9517 S2, 2009

8. Thresholding • Binary image can be obtained from gray-scale images by thresholding • Choose foreground and background based on the distribution of gray tones • Types of thresholding: • threshold above: p ≥ the threshold t • threshold below: p < t • threshold inside: t1 ≤ p < t2 • threshold outside: p < t1 or p ≥ t2 COMP 9517 S2, 2009

9. How to choose the thresholds • The basis for choosing a threshold is the histogram of the gray-tone image • The histogram h of gray-tone image I is defined by Where m spans the gray-level values. COMP 9517 S2, 2009

10. Compute A Histogram • Compute the histogram H of gray-scale image I Procedure histogram(I,H) { //Initialise the bins of the histogram to zero. for i=0 to MaxVal H[i] = 0; //Compute values by accumulation. for r=0 to MaxRow for c=0 to MaxCol { grayval = I[r,c]; H[grayval] = H[grayval] + 1; } } COMP 9517 S2, 2009

11. Threshold from Histogram • Bimodal: • one mode corresponding to dark pixels • the other one corresponding to light pixels • choose any value in the valley between two modes • Overlapped modes – more difficult t t COMP 9517 S2, 2009

12. Pixel and Neighbourhoods • Not only the value of a pixel but also its neighbours are used • 4-neighbours and 8-neighbours • N4[r,c]: {[r-1,c],[r+1,c],[r,c-1], and [r,c+1]} • N8[r,c]: N4[r,c] + {[r-1,c-1], [r-1,c+1], [r+1, c-1], and [r+1,c-1]} • A pixel [r’,c’] neighbours a pixel [r,c] if [r’,c’] lies in the selected type of neighbourhood of [r,c] COMP 9517 S2, 2009

13. Masks • Mask: a set of pixel positions and corresponding values called weights • Origin of a mask: usually the centre of the mask COMP 9517 S2, 2009

14. Applying a Mask • Convolution: apply a mask to an image • yields same size output image • for each pixel, place the mask on the image with the mask origin on that pixel • value of pixel under the mask multiplied by the corresponding mask weight • summed up to a single output value for the pixel COMP 9517 S2, 2009

15. Example of Applying a Mask the sum of the weights COMP 9517 S2, 2009

16. Example of Applying a Mask COMP 9517 S2, 2009

17. Connected Component Labelling • Definition: a connected component labelling of a binary image B is a labelled image LB in which the value of each pixel is the label of its connected component. COMP 9517 S2, 2009

18. Recursive Labelling • B is the original binary image; • LB will be the labelled connected component image. • Recursive_connected_components(B, LB) { • LB = negate(B); • label = 0; • Find_components(LB, label); • } • Find_components(LB,label){ • for (r=0 to MaxRow) • for (c=0 to MaxCol) • if (LB[r, c]==-1){ • label = label + 1; • Search(LB, label, r, c); • } • } • Search(LB, label, r, c) { • LB[r, c] = label; • Nset = neighbours(r, c); • for ([r’, c’] in Nset) • if (LB[r’, c’]==-1) Search(LB, label, r, c); • } COMP 9517 S2, 2009

19. Recursive Labelling COMP 9517 S2, 2009

20. Binary Image Morphology • Morphology refers to form, structure and the shape of a region in computer vision • Mathematical morphology: set operations • Structuring element: a shape presented by a binary image, any size and arbitrary structure • Common structuring element: Box, Disk & Ring COMP 9517 S2, 2009

21. Basic Morphology Operations • Dilation: enlarges a region • Erosion: makes a region smaller • Closing: closes up internal holes and eliminate bays on boundaries • Opening: gets rid of juts COMP 9517 S2, 2009

22. Dilation • Definition: the dilation of a binary image B by structuring element S is denoted by and is defined by • S is swept over B • When the origin of S touches 1 in B, S is ORed to the output image COMP 9517 S2, 2009

23. Dilation S B COMP 9517 S2, 2009

24. Erosion • Definition: the erosion of a binary image B by structuring element S is denoted by B S and is defined by B S • S is swept over B • When every element of S covers a 1-pixel in B, the pixel in B corresponding to the origin of S is ORed to the output image COMP 9517 S2, 2009

25. Erosion S B COMP 9517 S2, 2009

26. Closing • Definition: The closing of a binary image B by structuring element S is denote by and is defined by S B COMP 9517 S2, 2009

27. Opening • Definition: the opening of a binary image B by structuring element S is denoted by and is defined by S B COMP 9517 S2, 2009

28. Conditional Dilation • Remove noise by erosion, but want to keep entire components • Definition: give an original binary image B, a processed binary image C and a structuring element S, let and . The conditional dilation of C by S with respect to B is defined by where the index m is the smallest index satisfy COMP 9517 S2, 2009

29. Conditional Dilation • C is repeatedly dilated by S, and each result is reduce to only the pixels that were 1s in B V S B C AND COMP 9517 S2, 2009

30. Other Morphological Algorithms • Boundary extraction COMP 9517 S2, 2009

31. Basic Morphological Algorithms • Region Filling COMP 9517 S2, 2009

32. Applications of Morphology • Opening & closing to separate components and remove holes Thresholding Opening + Closing COMP 9517 S2, 2009

33. Applications of Morphology • Industrial inspection – identify defects • hole_ring, hole_mask, gear_body, sampling_ring_spacer, sampling_ring_width, tip_spacing , defect_cue a b c d f g h e COMP 9517 S2, 2009

34. Applications of Morphology • Feature extraction • Extract shape corners Original image B Resultant opening R Corner image C=B-R COMP 9517 S2, 2009

35. Region Properties • Properties of the regions as input to higher- level procedures for decision making • Area: • Centroid: • Perimeter COMP 9517 S2, 2009

36. Region Properties • Perimeter length • Circularity • Mean radial distance • Standard deviation of radial distance COMP 9517 S2, 2009

37. Region Properties • Bounding box and extremal points • Extremal axis length COMP 9517 S2, 2009

38. Region Properties • Second-order row moment • Second-order column moment • Second-order mixed moment COMP 9517 S2, 2009

39. Region Adjacency Graphs • Definition: a region adjacency graph(RAG) is a graph in which each node represents a region of the image, and an edge connects two nodes if the two regions are adjacent. 1 -1 0 2 -3 3 -2 COMP 9517 S2, 2009

40. References • Shaoo, P.K., and others. 1988. A survey of thresholding techniques. Compu. Vision, Graphics, and Image Proc. V.41:233-260. • Rosefeld,A., and J.L. Pfaltz, 1966. Sequential operations in digital picture processing. Journal of the Association for Computing Machinery, Vol. 13: 471-494. • Serra, J. 1982. Image Analysis and Mathematical Morphology. Academic Press, New York. COMP 9517 S2, 2009

41. Acknowledgement • Some material, including images and tables, were drawn from the textbook and Digital Image Processing by Gonzalesz and Woods. COMP 9517 S2, 2009