DIGITAL IMAGE PROCESSING

1. Chapter 9 – Morphological Image Processing DIGITAL IMAGE PROCESSING J. Shanbehzadeh, M. Mahdijo Shanbehzadeh@gmail.com Khwarizmi University of Tehran

2. Table of Contents

3. Preview • Morphology : form and structure • Extracting image components for: representation and description of region shape • From Image processing methods Input: Image Output: Image • To Image processing methods Input: Image Output: Attributes

4. 9.1 Preliminaries • Reflection and Translation: • Translation : (B)z = {c | c = b + z, for b є B}

5. 9.1 Preliminaries • Structuring Elements:

6. 9.1 Preliminaries • Structuring Elements:

7. 9.2 Erosion and Dilation • Erosion (B)z = {c | c = b + z, for b є B}

8. 9.2 Erosion and Dilation

9. Computing the Erosion of a Binary Image • For each foreground pixel, we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates. • If for every pixel in the structuring element, the corresponding pixel in the image underneath is • a foreground pixel, then the input pixel is left as it is. • Otherwise, it is set to background value.

10. The effect of Erosion • removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness). • Such pixels must lie at the edges of white regions, and so the practical upshot is that foreground regions shrink (and holes inside a region grow).

11. Effect of Erosion Using a 3×3 Square Structuring Element

12. 9.2 Erosion

13. 9.2 Erosion • Erosion (More examples):

14. 9.2 Erosion • Erosion (More examples):

15. Erosion in removing salt noise 14 14

16. 9.2 Dilation (B)z = {c | c = b + z, for b є B} • Dilation

17. 9.2 Dilation

18. 9.2 Dilation

19. Dilation • The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels. • Thus areas of foreground pixels grow in size while holes within those regions become smaller

20. Dilation: Example

22. Gray level erosion /dilation 􀂄 Erosion: 􀂄 Chose the local minimum over the region defined by the structure element 􀂄 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed

24. Dilation in noise reduction

25. Dilation in edge detection

26. 9.2 Erosion and Dilation • Duality • Proof:

27. 9.3 Opening and Closing Opening Closing

28. Closing Opening Dilation Erosion

29. Isthmus An isthmus (/ˈɪsθməs/ or /ˈɪsməs/; plural: isthmuses; from Ancient Greek:ἰσθμόςisthmos “neck”) is a narrow strip of land connecting two larger land areas, usually with water on either side.[1] A tombolo is an isthmus where the strip of land consists of a spit or bar. The Suez Canal goes across the western side of the Sinai Peninsula The Isthmus of Panama

30. pro·trude  (prō-tro̅o̅d′)v.pro·trud·ed, pro·trud·ing, pro·trudespro·trude  (prō-tro̅o̅d′)v.pro·trud·ed, pro·trud·ing, pro·trudes v.tr.To push or thrust outward. v.intr.To jut out; project. See Synonyms at bulge. Example sentences The air-conditioner does not protrude  into the alley. They are large-bodied and display a mouthful ofsharp teeth that protrude  in  Samantha's face and paws protrude  from thecutout door. Scrub the mussels, and use a paring knife toremove any beards that protrude 

31. 9.3 Opening and Closing • Opening: • smoothes the contour of an object , breaks narrow isthmuses, and eliminates thin protrusions. Erosion Dilation • Opening is defined as an erosion followed by a dilation using the same structuring element for both operations.

32. Opening • Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels. • Opening is less destructive than erosion in general. • The exact operation is determined by a structuring element.

33. Opening • The effect of the operator is: • to preserve foreground regions that • have a similar shape to this structuring element, • or can completely contain the structuring element, • Eliminating all other regions of foreground pixels.

34. Opening Effect of opening using a 3×3 square structuring element

35. Opening • opening can be very useful for separating out particularly shaped objects from the background, • opening is far from being a universal 2-D object recognizer/segmenter. • E.g. if we use a long thin structuring element to locate a pencils in our image, any one such element will only find pencils at a particular orientation.

36. Opening • If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation. • It is also necessary to be very careful that the structuring element chosen does not eliminate • too many desirable objects, or • retain too many undesirable ones, and • sometimes this can be a delicate or even impossible balance

37. 9.3 Opening Opening:

38. 9.3 Opening Opening: Separate out the circles from the lines, so that they can be counted.Opening with a disk shaped structuring element 11 pixels in diameter gives

39. 9.3 Opening Opening: Extracting the horizontal and vertical linesThe results of an Openingwith a 3×9 vertically and 9x3 horizontally oriented structuring elementis shown.

40. 9.3 Opening and Closing Opening in removing salt noise:

41. 9.3 Opening and Closing Opening in removing pepper noise:

42. 9.3 Closing 41 • Closing: • Smooth sections of contours, but as opposed to Opening, it generally fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour Dilation Erosion

43. Closing • Closing is opening performed in reverse. • Closing is the dual of opening, • i.e. closing the foreground pixels with a particular structuring element, is equivalent to closing the background with the same element. • a dilation followed by an erosion using the same structuring element for both operations. • The closing operator requires two inputs: • an image to be closed • a structuring element.

44. Closing Effect of closing using a 3×3 square structuring element

45. 9.3 Closing Closing:

46. 9.3 Closing: exapmles Removing the small holes while retaining the large holes Closingwitha 22 pixel diameter disk • Closing with a disk-shaped structuring element with a diameter larger than the smaller holes

47. 9.3 Closing: examples Enhance binary images of objects obtained from thresholding

48. 9.3 Closing Closing for pepper noise:

49. 9.3 Closing Closing for salt noise:

50. 9.3 Opening and Closing