1. DIGITAL IMAGE PROCESSING Instructors: Dr J. Shanbehzadeh Shanbehzadeh@gmail.com M.Yekke Zare M.Yekke Zare ( J.Shanbehzadeh M.Yekke Zare )

2. Point, Line and Edge Detection Thresholding Region-Based Segmentation Segmentation Using Morphological watersheds The Use of Motion in Segmentation Image Smoothing Using Frequency Domain Filters Fundamentals 10.6 10.510.4 10.3 10.2 10.5 10.410.3 10.210.1 Road map of chapter 10 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.YekkeZare )

3. Thresholding ( J.Shanbehzadeh M.Yekke Zare )

4. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Foundation 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )

5. 5 Thresholding image with dark background and a light object image with dark background and two light objects Foundation 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

6. 6 Thresholding a point (x,y) belongs to to an object class if T 1 < f(x,y)  T 2 to another object class if f(x,y) > T 2 to background if f(x,y)  T 1 T depends on only f(x,y) : only on gray-level values  Global threshold both f(x,y) and p(x,y) : on gray-level values and its neighbors  Local threshold Foundation- Multilevel thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

7. 7 Thresholding f(x,y) = i(x,y) r(x,y) a). computer generated reflectance function b). histogram of reflectance function c). computer generated illumination function (poor) d). product of a). and c). e). histogram of product image easily use global thresholding object and background are separated difficult to segment Foundation- The Role of Illumination ( J.Shanbehzadeh M.Yekke Zare )

8. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Basic Global Thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )

9. 9 Thresholding Basic Global Thresholding based on visual inspection of histogram 1. Select an initial estimate for T. 2. Segment the image using T. This will produce two groups of pixels: G 1 consisting of all pixels with gray level values > T and G 2 consisting of pixels with gray level values  T 3. Compute the average gray level values  1 and  2 for the pixels in regions G 1 and G 2 4. Compute a new threshold value 5. T = 0.5 (  1 +  2 ) 6. Repeat steps 2 through 4 until the difference in T in successive iterations is smaller than a predefined parameter T o. 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

10. 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation 10 Thresholding Basic Global Thresholding- Example: Heuristic method note: the clear valley of the histogram and the effective of the segmentation between object and background T 0 = 0 3 iterations with result T = 125 ( J.Shanbehzadeh M.Yekke Zare )

11. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Optimum Global Thresholding Using Otsu’s Method 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )

12. 12 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method Assumptions –It does not depend on modeling the probability density functions. –It does assume a bimodal histogram distribution 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

13. 13 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method Segmentation is based on “region homogeneity”. Region homogeneity can be measured using variance (i.e., regions with high homogeneity will have low variance). Otsu’s method selects the threshold by minimizing the within-class variance. 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

14. 14 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method (cont’d) Mean andVariance Consider an image with L gray levels and its normalized histogram –P(i) is the normalized frequency of i. Assuming that we have set the threshold at T, the normalized fraction of pixels that will be classified as background and object will be: T background object 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

15. 15 Thresholding Optimum Global Thresholding Using Otsu’s Method The mean gray-level value of the background and the object pixels will be: The mean gray-level value over the whole image (“grand” mean) is: 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

16. 16  The variance of the background and the object pixels will be:  The variance of the whole image is: 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Thresholding Optimum Global Thresholding Using Otsu’s Method ( J.Shanbehzadeh M.Yekke Zare )

17. 17 Otsu’s Method (cont’d) Within-class and between-class variance  It can be shown that the variance of the whole image can be written as follows: within-class variance between-class variance should be minimized! should be maximized! Thresholding Optimum Global Thresholding Using Otsu’s Method 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

18. 18 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method (cont’d) Determining the threshold  Since the total variance does not depend on T, the T that minimizes will also maximize  Let us rewrite as follows:  Find the T value that maximizes where 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

19. 19 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method (cont’d) Determining the threshold Start from the beginning of the histogram and test each gray- level value for the possibility of being the threshold T that maximizes 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

20. 20 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method (cont’d)  Drawbacks of the Otsu’s method  The method assumes that the histogram of the image is bimodal (i.e., two classes).  The method breaks down when the two classes are very unequal (i.e., the classes have very different sizes) In this case, may have two maxima. The correct maximum is not necessary the global one.  The method does not work well with variable illumination. 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

21. 21 Thresholding Optimum Global Thresholding Using Otsu’s Method Otsu’s Method (cont’d) 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

22. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Using Image Smoothing to improve Global Thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )

23. 23 Thresholding Using Image Smoothing to improve Global Thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

24. ( J.Shanbehzadeh M.Gholizadeh ) Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Using Edges to improve Global thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding

25. 25 Thresholding Using Edges to improve Global thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

26. 26 Thresholding Using Edges to improve Global thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

27. 27 Thresholding Using Edges to improve Global thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

28. 28 Thresholding Using Edges to improve Global thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

29. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding Multiple Thresholds 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )

30. 30 Thresholding Multiple Thresholds Otsu’s method can be extended to a multiple multiple thresholding method thresholding method. Between-class variance can be reformulated as 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

31. 31 Thresholding Multiple Thresholds The K classes are separated by K-1 thresholds and these optimal thresholds can be solved by maximizing For example (two thresholds) 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

32. 32 Thresholding Multiple Thresholds The following relationships hold: The optimum thresholds can be found by : The image is then segmented by 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

33. 33 Thresholding Multiple Thresholds 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation ( J.Shanbehzadeh M.Yekke Zare )

34. Thresholding FoundationBasic Global ThresholdingOptimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global ThresholdingUsing Edges to improve Global thresholdingMultiple Thresholds Variable Thresholding 10.1- Fundamentals 10.2- Point, Line and Edge Detection 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds 10.6- The Use of Motion in Segmentation Multivariable Thresholding ( J.Shanbehzadeh M.Yekke Zare )