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DIGITAL IMAGE PROCESSING

DIGITAL IMAGE PROCESSING. Chapter 10 – Image Segmentation. Instructors: Dr J. Shanbehzadeh Shanbehzadeh@gmail.com M.Yekke Zare. Road map of chapter 10. 10.5. 10.3. 10.3. 10.4. 10.1. 10.1. 10.2. 10.2. 10.4. 10.5. 10.6. 10.6. Point, Line and Edge Detection. Thresholding.

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DIGITAL IMAGE PROCESSING

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  1. DIGITAL IMAGE PROCESSING Chapter 10 – Image Segmentation Instructors: Dr J. Shanbehzadeh Shanbehzadeh@gmail.com M.YekkeZare ( J.ShanbehzadehM.YekkeZare )

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

  3. Thresholding ( J.ShanbehzadehM.YekkeZare )

  4. Foundation • Foundation • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

  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 • 10.5 - Segmentation Using Morphological watersheds • 10.6- The Use of Motion in Segmentation ( J.ShanbehzadehM.YekkeZare )

  6. Thresholding 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 • 10.5 - Segmentation Using Morphological watersheds • 10.6- The Use of Motion in Segmentation ( J.ShanbehzadehM.YekkeZare )

  7. Thresholding 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 ( J.ShanbehzadehM.YekkeZare )

  8. Foundation Basic Global Thresholding • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

  9. 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 • 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. ( J.ShanbehzadehM.YekkeZare )

  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 • 10.5 - Segmentation Using Morphological watersheds • 10.6- The Use of Motion in Segmentation T0 = 0 3 iterations with result T = 125 ( J.ShanbehzadehM.YekkeZare )

  11. Foundation Optimum Global Thresholding Using Otsu’s Method • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

  12. Thresholding 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 • 10.5 - 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 ( J.ShanbehzadehM.YekkeZare )

  13. Thresholding 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 • 10.5 - 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. ( J.ShanbehzadehM.YekkeZare )

  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: • 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 T object background ( J.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  16. Thresholding Optimum Global Thresholding Using Otsu’s Method • 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 ( J.ShanbehzadehM.YekkeZare )

  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 • 10.5 - 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 ( J.ShanbehzadehM.YekkeZare )

  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 • 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 where ( J.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  20. 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 • 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. ( J.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  22. Foundation Using Image Smoothing to improve Global Thresholding • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  24. Foundation Using Edges to improve Global thresholding • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.Shanbehzadeh M.Gholizadeh )

  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.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  29. Foundation Multiple Thresholds • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

  30. Thresholding Multiple Thresholds • Otsu’s method can be extended to a • multiple multiplethresholding method thresholdingmethod. • 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.ShanbehzadehM.YekkeZare )

  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 • 10.5 - Segmentation Using Morphological watersheds • 10.6- The Use of Motion in Segmentation For example (two thresholds) ( J.ShanbehzadehM.YekkeZare )

  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 • 10.5 - 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 ( J.ShanbehzadehM.YekkeZare )

  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.ShanbehzadehM.YekkeZare )

  34. Foundation • Variable Thresholding • Multivariable Thresholding Thresholding • Basic Global Thresholding Optimum Global Thresholding Using Otsu’s Method Using Image Smoothing to improve Global Thresholding Using Edges to improve Global thresholding • 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 ( J.ShanbehzadehM.YekkeZare )

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