1. Chapter 10 – Image Segmentation
DIGITAL IMAGE PROCESSING
Chapter 10 – Image Segmentation
Instructor:
Harikanth Pasinibilli

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

3. Thresholding
(P. Harikanth)

4. Thresholding Foundation Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Foundation
Foundation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

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

6. Thresholding a point (x,y) belongs to T depends on
Foundation- Multilevel thresholding
a point (x,y) belongs to
to an object class if T1 < f(x,y)  T2
to another object class if f(x,y) > T2
to background if f(x,y)  T1
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
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

7. Thresholding f(x,y) = i(x,y) r(x,y)
Foundation-The Role of Illumination
easily use global thresholding
object and background are separated
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
difficult to segment
(P. Harikanth)

8. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Foundation
Basic Global Thresholding
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

9. Thresholding Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
based on visual inspection of histogram
Select an initial estimate for T.
Segment the image using T. This will produce two groups of pixels: G1 consisting of all pixels with gray level values > T and G2 consisting of pixels with gray level values  T
Compute the average gray level values 1 and 2 for the pixels in regions G1 and G2
Compute a new threshold value
T = 0.5 (1 + 2)
Repeat steps 2 through 4 until the difference in T in successive iterations is smaller than a predefined parameter To.
(P. Harikanth)

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
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
T0 = 0
3 iterations
with result T = 125
(P. Harikanth)

11. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

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

13. Thresholding Otsu’s Method
Optimum Global Thresholding Using Otsu’s Method
Otsu’s Method
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
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.
(P. Harikanth)

14. Thresholding Optimum Global Thresholding Using Otsu’s Method T
Otsu’s Method (cont’d) Mean andVariance
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
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
object
background
(P. Harikanth)

15. 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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
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:
(P. Harikanth)

16. 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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
The variance of the background and the object pixels will be:
The variance of the whole image is:
(P. Harikanth)

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

18. 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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
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
(P. Harikanth)

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

20. Thresholding Drawbacks of the Otsu’s method
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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
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.
(P. Harikanth)

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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

22. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Foundation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

24. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

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
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

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

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

29. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Multiple Thresholds
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)

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

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

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

33. Thresholding Multiple Thresholds 10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
(P. Harikanth)

34. Thresholding Foundation Basic Global Thresholding
10.1- Fundamentals
10.2- Point, Line and Edge Detection
10.3- Thresholding
10.4- Region-Based Segmentation
Segmentation Using Morphological watersheds
10.6- The Use of Motion in Segmentation
Basic Global Thresholding
Optimum Global Thresholding Using Otsu’s Method
Using Image Smoothing to improve Global Thresholding
Using Edges to improve Global thresholding
Multiple Thresholds
Variable Thresholding
Variable Thresholding
Multivariable Thresholding
(P. Harikanth)