Digital Image Processing Lecture 15: Morphological Algorithms

1. Digital Image ProcessingLecture 15: Morphological Algorithms Prof. Charlene Tsai

2. Before Lecture … • Solution to previous quiz: all erosions

3. Overview • Extracting image components that are useful in the representation and description of shape. • We’ll consider: • Boundary extraction • Region filling • Extraction of connected components • Skeletonization

4. Boundary Extraction • Denote the boundary of set A by • Step1: eroding A by the structuring element B • Step2: taking the difference between A and its erosion.

5. Another Illustration Using B as the structuring element, so boundary is 1 pixel thick.

6. Region Filling • A is a set containing a subset whose elements are 8-connected boundary points of a region. • Goal: fill the entire region with 1’s.

7. Region Filling (con’d) Final Terminate when Xk=Xk-1

8. Some Remarks • The dilation process would fill the entire area if left unchecked. • limits the result to inside the region of interest. • Conditional dilation • Applicable to any finite number of such subsets, assuming that a point inside each boundary is given.

9. Connected Components • Extraction of connected components in a binary image is central to many automated image analysis applications. • Let Y be a connected component in set A and p a point of Y.

10. Application of Connected Component

11. Skeletonization • We have seen some algorithms for skeletonization when discussing topology. • Review: skeleton of a binary object is a collection of lines and curves that describe the size and shape of the object. • Different algorithms and many possible different skeletons of the same object. • Here we use a combination erosion and opening operations

12. (con’d) Formulation: with where The big K is the last iterative step before A erodes to an empty set. k time

13. Skeletonization: Demo Final skeleton

14. Grayscale Morphology – Dilation (Advance) • General formulation: where f is the grayscale image and b is the structuring element. • In other words, the value of dilation at (x,y) is the maximum of the sum of f and b in the interval spanned by b.

15. Example 1 2 3 4 5 (x) 1 2 3 4 5 (y) -1 0 1 -1 0 1 b f What is ?

16. Effect of Dilation • Two effects: • If all values of the structuring element are positive, the output image tends to be brighter. • Dark details either are reduced or eliminated, depending on how their values and shapes relate to the structuring element.

17. Grayscale Morphology - Erosion 1 2 3 4 5 (x) 1 2 3 4 5 (y) -1 0 1 -1 0 1 b f What is ?

18. Demo

19. Opening & Closing Opening: Closing:

20. Demo original

21. Application: Granulometry • Definition: determining the size distribution of particles in an image • Useful when objects are overlapping and clustered. • Detection of individual particles are hard.

22. (con’d) • Opening operations with structuring elements of increasing size are performed on the original image. • Motivation: opening operations of a particular size have the most effect on regions containing particles of similar size. • Method: • For every structuring element, compute the difference btw the Im-1 and Im, where m is the index of the structuring element. • At the end, normalize the differences => a histogram of particle-size distribution

23. Demo