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Chapter 9

Chapter 9. Morphological Image Processing. Preview. Morphology About the form and structure of animals and plants Mathematical morphology Using set theory Extract image component Representation and description of region shape. Z 2 and Z 3.

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Chapter 9

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  1. Chapter 9 Morphological Image Processing

  2. Preview • Morphology • About the form and structure of animals and plants • Mathematical morphology • Using set theory • Extract image component • Representation and descriptionof region shape

  3. Z2 and Z3 set in mathematic morphology represent objects in an image binary image (0 = white, 1 = black) : the element of the set is the coordinates (x,y) of pixel belong to the object  Z2 gray-scaled image : the element of the set is the coordinates (x,y) of pixel belong to the object and the gray levels  Z3 3

  4. Graphical examples (cont.)

  5. Logic operations on binary images • Functionally complete operations • AND, OR, NOT

  6. Special set operationsfor morphology translation reflection

  7. Structuring element (SE) • small set to probe the image under study • for each SE, define origin. • shape and size must be adapted to geometric • properties for the objects 7

  8. Structuring element (SE)

  9. Outline • erosion and Dilation • Opening and closing • Hit-or-miss transformation • Some basic morphological algorithms • Extensions to gray-scale images

  10. Erosion Does the structuring element fit the set? erosion of a set A by structuring element B: all z in A such that B is in A when origin of B=z shrink the object 10

  11. Erosion

  12. Erosion

  13. Dilation Does the structuring element hit the set? dilation of a set A by structuring element B: all z in A such that B hits A when origin of B=z grow the object 13

  14. Dilation

  15. Application of dilation: bridging gaps in images Structuring element Effects: increase size, fill gap max. gap=2 pixels

  16. Application of erosion: eliminate irrelevant detail Squares of size 1,3,5,7,9,15 pels Erode with 13x13 square original image erosion dilation

  17. Dilation and erosion are duals   

  18. Outline • Preliminaries • Dilation and erosion • Opening and closing • Hit-or-miss transformation • Some basic morphological algorithms • Extensions to gray-scale images

  19. Opening • Dilation: expands image w.r.t structuring elements • Erosion: shrink image • erosion+dilation = original image ? • Opening= erosion + dilation

  20. Opening (cont.)

  21. Opening (cont.) Find contour Fill in contour Smooth the contour of an image, breaks narrow isthmuses, eliminates thin protrusions

  22. Closing • Dilation+erosion = erosion + dilation ? • Closing = dilation + erosion

  23. Closing (cont.) Find contour Fill in contour Smooth the object contour, fuse narrow breaks and long thin gulfs, eliminate small holes, and fill in gaps

  24. Closing (cont.)

  25. Properties of opening and closing • Opening • Closing

  26. Noisy image Remove outer noise opening closing Remove inner noise

  27. Outline • Preliminaries • Dilation and erosion • Opening and closing • Hit-or-miss transformation • Some basic morphological algorithms • Extensions to gray-scale images

  28. Hit-or-miss transformation • Find the location of certain shape X erosion Find the set of pixels that contain shape X

  29. Hit-or-miss transformation Detect object via background Erosion with (W-X)

  30. Hit-or-miss transformation • Eliminate un-necessary parts AND

  31. Hit-or-miss transformation

  32. Basic morphological algorithms • Extract image components that are useful in the representation and description of shape • Boundary extraction • Region filling • Extract of connected components • Convex hull • Thinning • Thickening • Skeleton • Pruning

  33. Boundary extraction

  34. Boundary extraction

  35. Region filling • How? • Idea: place a point inside the region, then dilate that point iteratively Until Bound the growth

  36. Region filling (cont.) stop

  37. Application: region filling

  38. Extraction of connected components • Idea: start from a point in the connected component, and dilate it iteratively Until

  39. Extraction of connected components (cont.)

  40. original thresholding erosion

  41. Convex hull A set A is said to be convex if the straight line segment joining any two points in A lies entirely within A. The convex hull of a set A is the smallest convex set containing A. 41

  42. Convex hull 42

  43. Thinning 43

  44. Thickening 2. Ac 1. A 4. complement the result in 3 3. Thinning Ac 44

  45. Skeletons How to define a Skeletons? Maximum disk Set A 1. The largest disk Centered at a pixel 2. Touch the boundary of A at two or more places Recall: Balls of erosion!

  46. Skeletons 46

  47. Skeletons

  48. Skeleton

  49. Pruning H = 3x3 structuring element of 1’s 50

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