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Morphological Image Processing

Morphological Image Processing. Spring 2006, Jen-Chang Liu. Preview. Morphology 形態學 About the form and structure of animals and plants Mathematical morphology Using set theory Extract image component Representation and description of region shape. Preview (cont.).

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Morphological Image Processing

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  1. Morphological Image Processing Spring 2006, Jen-Chang Liu

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

  3. Preview (cont.) • Sets in mathematical morphology represent objects in an image • Example • Binary image: the elements of a set is the coordinate (x,y) of the pixels, in Z2 • Gray-level image: the element of a set is the triple, (x, y, gray-value), in Z3

  4. Outline • Preliminaries – set theory • Dilation and erosion • Opening and closing • Hit-or-miss transformation • Some basic morphological algorithms • Extensions to gray-scale images Binary images

  5. Preliminaries – set theory • A be a set in Z2. • a = (a1, a2) is an element of A. • a is not an element of A • Null (empty) set: 

  6. Set theory (cont.) • Explicit expression of a set • Example: 1 2

  7. Set operations • A is a subset of B: every element of A is an element of another set B • Union 聯集 • Intersection 交集 • Mutually exclusive 

  8. Graphical examples

  9. Graphical examples (cont.)

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

  11. Special set operationsfor morphology translation reflection

  12. Outline • Preliminaries • Dilation(擴張) and erosion(侵蝕) • Opening and closing • Hit-or-miss transformation • Some basic morphological algorithms • Extensions to gray-scale images

  13. Dilation (擴張)  B:structuring element

  14. Dilation: another formulation

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

  16. Erosion 侵蝕 z: displacement B:structuring element

  17. Erosion (cont.)

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

  19. Dilation and erosion are duals   

  20. Application: Boundary extraction • Extract boundary of a set A: • First erode A (make A smaller) • A – erode(A) =

  21. Application: boundary extraction original image Using 5x5 structuring element

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

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

  24. Opening (cont.)

  25. Opening (cont.) Find contour Fill in contour Smooth the contour of an image, breaks narrow isthmuses, eliminates thin protrusions 切除窄接線 消去小凸起

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

  27. 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 連接小斷點，消除小空洞，填補空隙

  28. Properties of opening and closing • Opening • Closing Open後變小 重複做open等於做一次open close後變大 重複做close等於做一次close

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

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

  31. Hit-or-miss transformation • Find the location of certain shape X erosion Find the set of pixels that contain shape X 如何只找到相符形狀中心點？

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

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

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

  35. 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

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

  37. Region filling (cont.) stop

  38. Application: region filling The first filled region Fill all regions Original image

  39. Extraction of connected components • 找到連通部分 • Idea: start from a point in the connected component, and dilate it iteratively Until

  40. Extraction of connected components (cont.)

  41. original 雞肉 thresholding erosion 去除小雜訊

  42. Skeletons 骨架 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!

  43. Skeleton • Idea: 不斷的erosion Erosion k 次 直到空集合

  44. Problem • The scanned image is not adjusted well • How to detection the direction of lines? • How to rotate?

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