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DIGITAL IMAGE PROCESSING. Chapter 10 – Image Segmentation. Instructors: Dr J. Shanbehzadeh [email protected] 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. - PowerPoint PPT Presentation
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DIGITAL IMAGE PROCESSING
Instructors:
Dr J. [email protected]
M.Yekke Zare
Chapter 10 – Image Segmentation
( J.Shanbehzadeh M.Yekke Zare )
Point, Line and Edge DetectionThresholdingRegion-Based SegmentationSegmentation Using Morphological watershedsThe Use of Motion in SegmentationImage Smoothing Using Frequency Domain FiltersFundamentals
10.610.610.510.410.310.2 10.510.410.310.210.110.1
Road map of chapter 10
10.1- Fundamentals10.2- Point, Line and Edge Detection10.3- Thresholding10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds10.6- The Use of Motion in Segmentation
( J.Shanbehzadeh M.YekkeZare )
Thresholding
( J.Shanbehzadeh M.Yekke Zare )
Thresholding
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
Foundation10.1- 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
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
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
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
Thresholding
f(x,y) = i(x,y) r(x,y)a). computer generated
reflectance functionb). histogram of reflectance functionc). computer generated illumination function (poor)d). product of a). and c).e). histogram of product image
easily use global thresholdingobject and background are separated
difficult to segment
Foundation-The Role of Illumination
( J.Shanbehzadeh M.Yekke Zare )
Thresholding
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
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
ThresholdingBasic 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: G1 consisting of all pixels with gray level values > T and G2 consisting of pixels with gray level values T
3. Compute the average gray level values 1 and 2 for the pixels in regions G1 and G2
4. Compute a new threshold value5. 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 To.
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
ThresholdingBasic Global Thresholding-Example: Heuristic method
note: the clear valley of the histogram and the effective of the segmentation between object and background
T0 = 03 iterations with result T = 125
( J.Shanbehzadeh M.Yekke Zare )
Thresholding
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
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
ThresholdingOptimum 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
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
ThresholdingOptimum 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:
Tbackground 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
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
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
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
ThresholdingOptimum 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
ThresholdingOptimum 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
ThresholdingOptimum 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
ThresholdingOptimum 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 )
Thresholding
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
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
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 )
( J.Shanbehzadeh M.Gholizadeh )
Thresholding
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
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
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
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
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
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 )
Thresholding
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
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
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
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
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
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 )
Thresholding
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 ThresholdingVariable 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 )
