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Morphological Image Processing

Morphological Image Processing. Morphology. Morphology The branch of biology that deals with the form and structure of organisms without consideration of function Mathematical Morphology Mathematical tool for processing shapes in image, including boundaries, skeletons, convex hulls, etc.

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Morphological Image Processing

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  1. Morphological Image Processing

  2. Morphology • Morphology • The branch of biology that deals with the form and structure of organisms without consideration of function • Mathematical Morphology • Mathematical tool for processing shapes in image, including boundaries, skeletons, convex hulls, etc. • Use of set theoretical approach (c) 2003-2006 by Yu Hen Hu

  3. SET () A collection of objects (elements) membership () If  is an element (member) of a set , we write    Subset () Let A, B are two sets. If for every a  A, we also have a  B, then the set A is a subset of B, that is, A  B If A  B and B  A, then A = B. Empty set () Complement set If A  , then its complement set Ac = {|   , and A} Union () A B = {|  A or  B} Intersection () A  B = {|  A and  B} Set difference (-) B\A = B Ac Note that B-A A-B Disjoint sets A and B are disjoint (mutually exclusive) if A  B=  Set Theory: Definitions and Notations (c) 2003-2006 by Yu Hen Hu

  4. Set Relations (c) 2003-2006 by Yu Hen Hu

  5. Translation (A)z = { c| c = a + z, for a A } Reflection: Translation and Reflection (c) 2003-2006 by Yu Hen Hu

  6. Logic Operations Between Binary Images (c) 2003-2006 by Yu Hen Hu

  7. Dilation B: structure element Erosion AB = {z | (B)z A} Relations (AB)c = Dilation and Erosion (c) 2003-2006 by Yu Hen Hu

  8. Example of Dilation (c) 2003-2006 by Yu Hen Hu

  9. Example of Erosion (c) 2003-2006 by Yu Hen Hu

  10. Opening A B = (AB) B (c) 2003-2006 by Yu Hen Hu

  11. Closing A B = (AB) B (c) 2003-2006 by Yu Hen Hu

  12. Example: Opening & Closing (c) 2003-2006 by Yu Hen Hu

  13. Finger Print Processing using Opening and Closing (c) 2003-2006 by Yu Hen Hu

  14. Hit-or-Miss Transformation for shape detection (e) (d) Figure 9.12 (a) Set A, (b) A window W and the local Background of X w.r.t. W, W-X. (c) Ac. (d) AX Intersection of (d) and (e) shows the location of the origin of X, as desired. (c) 2003-2006 by Yu Hen Hu

  15. Hit-or-Miss Transform • Denote B1: object, B2: local background of B1, then, or • Reason to have a local background: • Two or more objects are distinct only if they form disjoint (disconnected) sets. This is guaranteed by requiring that each object have at least a one-pixel-thick background around it. (c) 2003-2006 by Yu Hen Hu

  16. Previous example does not contain don’t care entries. In structure element 1 – foreground 0 – background X – don’t care Output is 1 if exact match of both foreground and background pixels. Hitnmiss.m +1: foreground -1: background 0: don’t care Hit-or-Miss Transform Hitnmiss.m (c) 2003-2006 by Yu Hen Hu

  17. Morphological Boundary Extraction (A) = A− (A  B) (9.5-1) (c) 2003-2006 by Yu Hen Hu

  18. Example of Boundary Extraction (c) 2003-2006 by Yu Hen Hu

  19. Region Filling Fig915.m (c) 2003-2006 by Yu Hen Hu

  20. Region Filling Example (c) 2003-2006 by Yu Hen Hu

  21. Y: connected component in set A, p: a known point in Y Connected Component Extraction Fig915.m (c) 2003-2006 by Yu Hen Hu

  22. Thinning Thinning is often accomplished using a sequence of rotated structuring elements (a). Given a set A (b), results of thinning with first element is shown in (c), and the next 7 elements (d) – (i). There is no change between 7th and 8th elements, and no change after first 3 elements. Then it converges to a m-connectivity. Fig921.m (c) 2003-2006 by Yu Hen Hu

  23. Thickening AB = A hitnmiss(A,B) A{B} =((…(AB1) B2) … Bn) Thickening is the dual of thinning operation. Usually, thickening a set A is accomplished by thinning Ac, and then complement the result. Then a post-processing prunning process is applied to remove disconnected points as shown to the left. (c) 2003-2006 by Yu Hen Hu

  24. A skeleton of a set A consists of points z that is the center of a maximum disk A maximum disk is a circle in A that can not be enclosed by another circle that is also in A. Figure 9.23. (a) set A, (b), (c) sets of possible maximum disks. (d) dotted line is the skeleton. Skeleton (c) 2003-2006 by Yu Hen Hu

  25. Skeleton Equations • Define k consecutive erosions of A as: AkB = ( …(AB)B) …)B) (9.5-13) Sk(A) = (AkB) − (AkB)B (9.5-12) • Let K = max{k | (AkB) } (9.5-14) Then the skeleton can be found as: (c) 2003-2006 by Yu Hen Hu

  26. Illustration of Skeleton Computation Figure 9.24 Implementation of eq. (9.5-11)-(9.5-15). The original set is at the top left and its morphological skeleton is at the bottom of the 4th column. The reconstructed set is at the bottom of the 6th column. Define k consecutive erosions of A as: AkB = ( …(AB)B) …)B) (9.5-13) Sk(A) = (AkB) − (AkB)B (9.5-12) Let K = max{k | (AkB) } (9.5-14) Then the skeleton can be found as: (c) 2003-2006 by Yu Hen Hu

  27. Pruning (c) 2003-2006 by Yu Hen Hu

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