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Morphological Image Processing

Morphological Image Processing. More on Hit-and-Miss Transform. Hit-and-Miss Transform. hit-and-miss: selects corner points, isolated points, border points hit-and-miss: performs template matching, thinning, thickening, centering hit-and-miss: intersection of erosions J,K kernels satisfy

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Morphological Image Processing

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  1. Morphological Image Processing

  2. More on Hit-and-Miss Transform

  3. Hit-and-Miss Transform • hit-and-miss: selects corner points, isolated points, border points • hit-and-miss: performs template matching, thinning, thickening, centering • hit-and-miss: intersection of erosions • J,K kernels satisfy • hit-and-miss of set A by (J,K) • hit-and-miss: to find upper right-hand corner

  4. Hit-and-Miss Transform (cont’)

  5. Hit-and-Miss Transform (cont’) • J locates all pixels with south, west neighbors part of A • K locates all pixels of Ac with south, west neighbors in Ac • J and K displaced from one another • Hit-and-miss: locate particular spatial patterns

  6. Hit-and-Miss Transform (cont’) • hit-and-miss: to compute genus of a binary image

  7. Hit-and-Miss Transform (cont’)

  8. 5.2.3 Hit-and-Miss Transform (cont’) • hit-and-miss: thickening and thinning • hit-and-miss: counting • hit-and-miss: template matching DC & CV Lab. CSIE NTU

  9. 5.2.3 Hit-and-Miss Transform (cont’) • hit-and-miss: thickening and thinning • hit-and-miss: counting • hit-and-miss: template matching DC & CV Lab. CSIE NTU

  10. 5.7 Bounding Second Derivatives • opening or closing a gray scale image simplifies the image complexity

  11. 5.8 Distance Transform and Recursive Morphology

  12. 5.9 Generalized Distance Transform

  13. Distance Transform and Recursive Morphology

  14. Distance • Applies to binary images • For each pixel in a region • distance = minimum path to outside

  15. Distance Transform and Recursive Morphology (cont’) • Fig 5.39 (b) fire burns from outside but burns only downward and right-ward

  16. Distance Transform and Recursive Morphology

  17. Generalized Distance Transform

  18. Distance Transform and Recursive Morphology (cont’) • Fig 5.39 (b) fire burns from outside but burns only downward and right-ward

  19. Medial Axis

  20. Medial Axis • medial axis transform medial axis with distance function

  21. Processing grey scale images • Same methods can be applied to greyscale images • Slight redefinition

  22. Computation • Use erosion • Label removed pixel with iteration number • Use relationship operator • f(i,j) are neighbours of f(x,y)

  23. Skeleton • Reduces regions of a binary image to lines one pixel thick • Preserves • Shape • Continuity • How? Uses?

  24. Algorithms • Thinning • Repeatedly thin image • Retain end points and connections • Distance Transform • Skeleton lies along discontinuities • Sort of local maxima or ridges

  25. Applications • Shape representation, maintaining topology • Character recognition

  26. Medial Axis and Morphological Skeleton • morphological skeleton of a set A by kernel K ,where

  27. Medial Axis and Morphological Skeleton (cont’) DC & CV Lab. CSIE NTU

  28. Medial Axis and Morphological Skeleton (cont’) K A DC & CV Lab. CSIE NTU

  29. Medial Axis and Morphological Skeleton (cont’)

  30. Morphological Sampling Theorem • Before sets are sampled for morphological processing, they must be morphologically simplified by an opening or a closing . • Such sampled sets can be reconstructed in two ways: by either a closing or a dilation.

  31. Morphological Shape Feature Extraction • morphological pattern spectrum: shape-size histogram [Maragos 1987]

  32. Fast Dilations and Erosions • decompose kernels to make dilations and erosions fast

  33. Connectivity • morphology and connectivity: close relation

  34. Separation Relation • S separation if and only if S symmetric, exclusive, hereditary, extensive

  35. Morphological Noise Cleaning and Connectivity • images perturbed by noise can be morphologically filtered to remove some noise

  36. Openings Holes and Connectivity • opening can create holes in a connected set that is being opened

  37. Conditional Dilation • select connected components of image that have nonempty erosion conditional dilation J , • defined iteratively J0= J • J are points in the regions we want to select • conditional dilation J =Jm • where m is the smallest index Jm=Jm-1

  38. DC & CV Lab. CSIE NTU

  39. Generalized Openings and Closings • generalized opening: any increasing, antiextensive, idempotent operation • generalized closing: any increasing. extensive, idempotent operation

  40. Hit and Miss (cont’) • hit-and-miss: thickening and thinning • hit-and-miss: template matching

  41. Hit and Miss (cont’) • hit-and-miss: thickening

  42. 450 convex hull Hit and Miss (cont’)

  43. Hit and Miss (cont’) Octagonal skeleton DC & CV Lab. CSIE NTU

  44. Hit and Miss (cont’) • hit-and-miss: thinning

  45. Hit and Miss (cont’) • hit-and-miss: template matching

  46. Openings Closings and Medians • median filter: most common nonlinear noise-smoothing filter • median filter: for each pixel, the new value is the median of a window • median filter: robust to outlier pixel values leaves, edges sharp • median root images: images remain unchanged after median filter

  47. Hit-or-Miss Transformation

  48. Hit-or-Miss Transformation

  49. Morphological edge detection

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