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Digital Image Processing CP-7008 Lecture # 09 Morphological Image Processing

Digital Image Processing CP-7008 Lecture # 09 Morphological Image Processing. Fall 2011. Agenda. Image Morphology Erosion Dilation Opening Closing Hit-Miss Transformation Misc. Morphological Operations. Introduction.

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Digital Image Processing CP-7008 Lecture # 09 Morphological Image Processing

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  1. Digital Image ProcessingCP-7008Lecture # 09Morphological Image Processing Fall 2011

  2. Agenda • Image Morphology • Erosion • Dilation • Opening • Closing • Hit-Miss Transformation • Misc. Morphological Operations

  3. Introduction • Morphology: a branch of biology that deals with the form and structure of animals and plants • Morphological image processing is used to extract image components for representation and description of region shape, such as boundaries, skeletons, and the convex hull

  4. Mathematic Morphology mathematical framework used for: pre-processing noise filtering, shape simplification, ... enhancing object structure skeletonization, convex hull... quantitative description area, perimeter, ...

  5. Basic Set Theory

  6. Preliminaries (1) • Reflection • Translation

  7. Example: Reflection and Translation

  8. Preliminaries (2) • Structure elements (SE) Small sets or sub-images used to probe an image under study for properties of interest

  9. Examples: Structuring Elements (1) origin

  10. Examples: Structuring Elements (2) Accommodate the entire structuring elements when its origin is on the border of the original set A Origin of B visits every element of A At each location of the origin of B, if B is completely contained in A, then the location is a member of the new set, otherwise it is not a member of the new set.

  11. Erosion

  12. Example of Erosion (1)

  13. Erosion Example Original Image Processed Image With Eroded Pixels Structuring Element

  14. Erosion Example Original Image Processed Image Structuring Element

  15. Erosion Example 2 Watch out: In these examples a 1 refers to a black pixel! Original image Erosion by 3*3 square structuring element Erosion by 5*5 square structuring element

  16. Erosion Example 3 After erosion with a disc of radius 10 Original image After erosion with a disc of radius 5 After erosion with a disc of radius 20

  17. What Is Erosion For? Erosion can split apart joined objects Erosion can strip away extrusions Watch out: Erosion shrinks objects

  18. Dilation

  19. Examples of Dilation (1)

  20. Dilation Example Original Image Processed Image Structuring Element

  21. Dilation Example Original Image Processed Image With Dilated Pixels Structuring Element

  22. Dilation Example 2 Dilation by 3*3 square structuring element Dilation by 5*5 square structuring element Original image Watch out: In these examples a 1 refers to a black pixel!

  23. Examples of Dilation (3)

  24. What Is Dilation For? Dilation can repair breaks Dilation can repair intrusions Watch out: Dilation enlarges objects

  25. Duality • Erosion and dilation are duals of each other with respect to set complementation and reflection

  26. Duality • Erosion and dilation are duals of each other with respect to set complementation and reflection

  27. Duality • Erosion and dilation are duals of each other with respect to set complementation and reflection

  28. Opening and Closing • Opening generally smoothes the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions • Closing tends to smooth sections of contours but it generates fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour

  29. Opening and Closing

  30. Opening

  31. Opening Example Original Image Image After Opening

  32. Closing Example Original Image Image After Closing

  33. Duality of Opening and Closing • Opening and closing are duals of each other with respect to set complementation and reflection

  34. The Properties of Opening and Closing • Properties of Opening • Properties of Closing

  35. The Hit-or-Miss Transformation

  36. Some Basic Morphological Algorithms (1) • Boundary Extraction The boundary of a set A, can be obtained by first eroding A by B and then performing the set difference between A and its erosion.

  37. Example 1

  38. Example 2

  39. Some Basic Morphological Algorithms (2) • Hole Filling A hole may be defined as a background region surrounded by a connected border of foreground pixels. Let A denote a set whose elements are 8-connected boundaries, each boundary enclosing a background region (i.e., a hole). Given a point in each hole, the objective is to fill all the holes with 1s.

  40. Some Basic Morphological Algorithms (2) • Hole Filling 1. Forming an array X0 of 0s (the same size as the array containing A), except the locations in X0 corresponding to the given point in each hole, which we set to 1. 2. Xk = (Xk-1 + B) Ac k=1,2,3,… Stop the iteration if Xk = Xk-1

  41. Example

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