1. Digital Image Processing In The Name Of God Digital Image Processing Lecture8: Image Segmentation M. Ghelich Oghli By: M. Ghelich Oghli E-mail: m.g31_mesu@yahoo.com Fall 2012

2. Image Segmentation Description: Subdividing image into its constituent regions or objects There is not any absolute theory of image segmentation. Rather, there are a collection of methods that have received some degree of popularity.

3. Detection of Discontinuity Point Detection

4. Detection of Discontinuity Line Detection

5. Example of Line Detection

6. Detection of Discontinuity Edge Detection: detection of discontinuity in image Edge Model

7. Edge Detection using first order derivatives using second order derivatives

8. Noise effect in Edge Detection Result: noise filtering is required especially in second order derivatives

9. Gradient operators

10. Edge Detection (first order derivatives)

11. Edge Detection (Second order derivatives) Laplacian Laplacian of Gaussian (LoG)

12. Edge Detection (LoG)

13. Image Segmentation 1.Hard segmentation A pixel belongs to object or background

14. Image Segmentation 2. Soft (Fuzzy) segmentation First classSecond classThird class

15. Image Segmentation Image Segmentation methods Pixel based methods Region based methods Clustering segmentation methods Boundary detection Texture segmentation

16. Image Segmentation Pixel based methods  Conceptually, the simplest approach we can take for segmentation.  But, it is not the best method.  The most sensible example of this category: Thresholding

17. Foundation:

18. Thresholding In A: light objects in dark background To extract the objects: –Select a T that separates the objects from the background –i.e. any (x,y) for which f(x,y)>T is an object point. A thresholded image: (objects) (background)

19. Thresholding In B: a more general case of this approach (multilevel thresholding) So: (x,y) belongs: –To one object class if T 1 <f(x,y)≤T 2 –To the other if f(x,y)>T 2 –To the background if f(x,y)≤T 1

20. Global Thresholding

21. Multi level Thresholding

22. Adaptive Thresholding Advantage: Alleviates the illumination problem Method: Divides the original image to subimages and applies threshold to each subimage individually

23. Adaptive Thresholding

24. Image Segmentation Region based methods  Region based methods doesn’t include one of the most important disadvantage of pixel-based techniques and it is ignoring pixel relationships and connectivity.  An object consists of not independent and not isolated pixels.  A robust segmentation method should consider this fact.

25. Region Growing  In this method neighboring pixels of similar amplitude are grouped together to form a segmented region.  Image segmentation partitions the set X into the subsets R(i), i=1,…,N having the following properties X = i=1,..N U R(i) R(i) ∩ R(j) = 0 for i ≠ j P(R(i)) = TRUE for i = 1,2,…,N P(R(i) U R(j)) = FALSE for i ≠ j

26. Region Growing by Pixel Aggregation A simple approach to image segmentation is to start from some pixels (seeds) representing distinct image regions and to grow them, until they cover the entire image For region growing we need a rule describing a growth mechanism and a rule checking the homogeneity of the regions after each growth step

27. Region Growing by Pixel Aggregation The growth mechanism – at each stage k and for each region Ri(k), i = 1,…,N, we check if there are unclassified pixels in the 8-neighbourhood of each pixel of the region border Before assigning such a pixel x to a region Ri(k),we check if the region homogeneity: P(Ri(k) U {x}) = TRUE, is valid

28.  Gray Space map  Compute the seed gray level (V) and look for pixels have the same gray level and over lap the seed  Then define a set of gray levels from “V- D” to “V+D” Region Growing by Pixel Aggregation Ghelich Oghli, M., Fallahi, A., Pooyan, M. Automatic Region Growing Method using GSmap and Spatial Information on Ultrasound Images. In: 18th Iranian Conference on Electrical Engineering, May 11-13, pp. 35-38 (2010)  At each iteration we increase the difference D by 1

29. Region Growing by Pixel Aggregation Ghelich Oghli, M., Fallahi, A., Pooyan, M. Automatic Region Growing Method using GSmap and Spatial Information on Ultrasound Images. In: 18th Iranian Conference on Electrical Engineering, May 11-13, pp. 35-38 (2010)

30. Image Segmentation Clustering segmentation methods  Subdividing data's into classes based on some criteria's.

31. K-Means Clustering 1.Set ic (iteration count) to 1 2.Choose randomly a set of K means m 1 (1), …, m K (1) (Center of Classes). 3.For each pixel compute D(x i, m k (ic)), k=1,…K and assign x i to the cluster C j with nearest mean. 4.Increment ic by 1, update the means to get m 1 (ic),…,m K (ic). 5.Repeat steps 3 and 4 until C k (ic) = C k (ic+1) for all k.

32. K-Means Clustering In some applications (Specially medical application) because of effect of other slices, absolutely assigning a pixel to a class is not logically true. So, we should classify data's by a fuzziness view. And we should use: Fuzzy C-Means (FCM) algorithm

33. Fuzzy C-Means (FCM) A membership function exists for each class at every pixel location  0; if the pixel does not belong to the class  1; if the pixel belongs, with absolute certainty, to the class  0-1; degree of belonging a pixel to a class  at any pixel location the sum of the membership functions of all the classes must be 1  The fuzzy membership function reflects the similarity between the data value at that pixel and the value of the class centroid.

34. Fuzzy C-Means (FCM)

36. Boundary Detection or Curve Fitting It is possible to segment an image into regions of common attribute by detecting the boundary of each region for which there is a significant change in attribute across the boundary. Methodology Initial guess Iteratively deforming curves according to the minimization of internal and external energy functional and controls the smoothness of the curve.

37. Boundary Detection or Curve Fitting

38. Drawback (Speckle Noise) Example

39. Deformable models –Parametric Deformable models (Snake) –Geometric Deformable models (Level set) Boundary Detection or Curve Fitting

40. Levelset This figure illustrates several important ideas about the level set method. A bounded region Boundary=zero level set Graph of a level set function Changing (Evolving) in Region… Moving X-Y plane through …