Morphological Image Processing

1. Morphological Image Processing Md. Rokanujjaman Assistant Professor Dept of Computer Science and Engineering Rajshahi University

2. What are Morphological Operations? Morphological operations come from the word “morphing” in Biology which means “changing a shape”. Morphing Image morphological operations are used to manipulate object shapes such as thinning, thickening, and filling. Binary morphological operations are derived from set operations.

3. Basic Set Operations Concept of a set in binary image morphology: Each set may represent one object. Each pixel (x,y) has its status: belong to a set or not belong to a set.

4. Translation and Reflection Operations Translation Reflection B A z = (z1,z2) (A)z

5. Logical Operations* *For binary images only

6. Structuring Element The two most common structuring elements (given a Cartesian grid) are the 4-connected and 8-connected sets, N4 and N8. They are illustrated in Figure . Figure: The standard structuring elements N4 and N8.

7. Binary Images For a binary image, white pixels are normally taken to represent foreground regions, while black pixels denote background. (Note that in some implementations this convention is reversed, and so it is very important to set up input images with the correct polarity for the implementation being used). Then the set of coordinates corresponding to that image is simply the set of two-dimensional Euclidean coordinates of all the foreground pixels in the image, with an origin normally taken in one of the corners so that all coordinates have positive elements.

8. Fundamental Morphological Operations Erosion and dilation work (at least conceptually) by translating the structuring element to various points in the input image, and examining the intersection between the translated kernel coordinates and the input image coordinates. For instance, in the case of erosion, the output coordinate set consists of just those points to which the origin of the structuring element can be translated, while the element still remains entirely `within' the input image. Virtually all other mathematical morphology operators can be defined in terms of combinations of erosion and dilation along with set operators such as intersection and union. Some of the more important are opening, closing and skeletonization.

9. Fitting and Hitting When we place a structuring element in a binary image, each of its pixels is associated with the corresponding pixel of the neighborhood under the structuring element. In this sense, a morphological operation resembles a “binary correlation”. The operation is logical rather than arithmetic in nature. The structuring element is said to fit the image if, for each of its pixels that is set to 1 , the corresponding image pixel is also 1. The structuring element is said to hit, an image if for any of its pixels that is set to 1, the corresponding image pixel is also 1.

10. Dilation Operations Or The dilation A by B is the set of all displacements z, such that reflection of B and A overlap by at least one element. = Empty set Dilate means “extend” A = Object to be dilated B = Structuring element

11. Dilation Operations (cont.) Reflection Structuring Element (B) Intersect pixel Center pixel Original image (A)

12. Dilation Operations (cont.) Result of Dilation Boundary of the “center pixels” where intersects A

13. Example: Application of Dilation “Repair” broken characters

14. Erosion Operation Or, The erosion of A by B is the set of all points z such that B translated by z is contained in A Erosion means “trim” A = Object to be eroded B = Structuring element

15. Erosion Operations (cont.) Structuring Element (B) Original image (A) Intersect pixel Center pixel

16. Erosion Operations (cont.) Result of Erosion Boundary of the “center pixels” where B is inside A

17. Example: Application of Dilation and Erosion Remove small objects such as noise

18. Duality Between Dilation and Erosion where c = complement Proof:

19. Opening Operation The process of erosion followed by dilation is called opening. It has the effect of eliminating small and thin objects, breaking the objects at thin points and smoothing the boundaries/contours of the objects. = Combination of all parts of A that can completely contain B Opening eliminates narrow and small details and corners.

20. Example of Opening

21. Closing Operation The process of dilation followed by erosion is called closing. It has the effect of filling small and thin holes, connecting nearby objects and smoothing the boundaries/contours of the objects. Closing fills narrow gaps and notches

22. Example of Closing

23. Example: Application of Morphological Operations Finger print enhancement

24. Hit-or-Miss Transformation * Hit-or-miss transform can be used for shape detection/ Template matching. where X = shape to be detected W = window that can contain X

25. Hit-or-Miss Transformation (cont.) *

26. Boundary Extraction The boundaries/edges of a region/shape can be extracted by first applying erosion on A by B and subtracting the eroded A from A. Original image Boundary

27. Region Filling Region filling can be performed by using the following definition. Given a symmetric structuring element B, one of the non-boundary pixels (X) is consecutively diluted and its intersection with the complement of A is taken as follows: Terminates when Xk= Xk-1 where X0 = seed pixel p Original image Results of region filling

28. Extraction of Connected Components Terminates when Xk= Xk-1 where X0 = seed pixel p

29. Convex Hull * Convex hull has no concave part. Convex hull Algorithm: where

30. Example: Convex Hull

31. Thinning * *

32. Example: Thinning Make an object thinner.

33. Thickening * * . . . . . Make an object thicker

34. Skeletons Dot lines are skeletons of this structure

35. Skeletons (cont.) with where k times and

36. Skeletons

37. Thank You