1. The document discusses image segmentation techniques including edge detection methods. It describes segmenting an image into homogeneous regions using edge detection to find discontinuities. 2. Several edge detection methods are described including Robert, Prewitt, Sobel detectors as well as the Canny edge detector. The Canny edge detector uses a multi-stage algorithm to detect edges including filtering, finding gradients, non-maximum suppression, and hysteresis thresholding. 3. The document provides examples of applying different edge detection techniques and algorithms including the steps in the Canny edge detection method.

1. IMAGE SEGMENTATION

2. Segmentation Based on Image Discontinuities
Partitioning Image into discrete & non-overlapping Regions
R1 R2
R4
Homogenous Regions : R1, R2, R3, R4
R3
1. Primitive Detectors : Robert, Prewitt, Sobel, Kirsch
2. Vision : Marr Hildreth Poggio : LOG
3. Robotics : Canny Edge Detector
4. Edge Linking : Hough Transform

3. Point Detector
7 7 7 7 7 7 7
7 10 7 7 7 7 7
7 7 7 7 7 7 7
7 7 7 7 7 7 7
7 7 7 7 4 7 7
7 7 7 7 7 7 7
7 7 7 7 7 7 7
-1 -1 -1
-1 8 -1
-1 -1 -1
0 0 0 0 0 0 0
0 24 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 -24 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
I
P
0 0 0 0 0 0 0
0 24 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 24 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0

4. Line Detector
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 3
1 1 1 1 1 1 3 1
1 1 1 1 1 3 1 1
3 3 3 3 3 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
0 0 0 0 0 0
0 0 0 0 0 0
6 6 6 1 0 0
12 12 12 6 2 2
6 6 6 4 2 0
0 0 0 0 0 0
-1 -1 -1
2 2 2
-1 -1 -1
-1 2 -1
-1 2 -1
-1 2 -1
-1 -1 2
-1 2 -1
2 -1 -1
2 -1 -1
-1 2 -1
-1 -1 2
I
H V
0 0 0 0 0 4
0 0 0 0 4 12
0 0 0 0 12 4
0 0 0 4 4 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

5. Line Detector
0 0 0 0 0 4
0 0 0 0 4 12
6 6 6 1 12 4
12 12 12 6 4 2
6 6 6 4 2 0
0 0 0 0 0 0
-1 -1 -1
2 2 2
-1 -1 -1
-1 2 -1
-1 2 -1
-1 2 -1
-1 -1 2
-1 2 -1
2 -1 -1
2 -1 -1
-1 2 -1
-1 -1 2
I
H V
L
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 3
1 1 1 1 1 1 3 1
1 1 1 1 1 3 1 1
3 3 3 3 3 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1

6. Edge Detectors
1 1 1 1 2 2 2
1 1 1 1 2 2 2
1 1 1 1 2 2 2
2 2 2 2 1 1 1
2 2 2 2 1 1 1
2 2 2 2 1 1 1
2 2 2 2 1 1 1
Class Work
Robert
1 0
0 -1
0 1
-1 0
Prewitt
-1 -1 -1
0 0 0
1 1 1
-1 0 1
-1 0 1
-1 0 1
Sobel
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1

7. Edge Detectors
1 2 2 2 2 2 2
1 1 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 2 2 2
1 1 1 2 2 2 2
1 1 2 2 2 2 2
1 2 2 2 2 2 2
Class Work
Robert
1 0
0 -1
0 1
-1 0
Prewitt
-1 -1 -1
0 0 0
1 1 1
-1 0 1
-1 0 1
-1 0 1
Sobel
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1

8. Canny Edge Detector
Characteristics:
1. Criterion 1 : Good Detection : Robustness to noise :The
optimum detector must minimize the probability of false
positive as well as false negative.
2. Criterion 2 : Good Localization : The edge must be as close as
possible to the true edges.
3. Criterion 3 : Strong Response Constraint : Not too many or too
few responses : The detector must return one point only for each
point.
Steps :
1. Smoothing with Gaussian Filter
2. Compute Derivative of filter image
3. Find magnitude & orientation of gradient
4. Apply Non Maxima Suppression
5. Apply Hysteresis Threshold

9. Canny Edge Detector
1. Smoothing with Gaussian Filter
Image I(r,c)
DiscreteApproximation of Gaussian Kernels
source :wikipedia
1 2 1
2 4 2
1 2 1
1 4 7 4 1
4 16 26 16 4
7 26 41 26 7
4 16 26 16 4
1 4 7 4 1
0 0 1 2 1 0 0
0 3 13 22 13 3 0
1 13 59 97 59 13 1
2 22 97 150 87 22 2
1 13 59 97 59 13 1
0 3 13 22 13 3 0
0 0 1 2 1 0 0

10. 2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
Canny Edge Detector
2. Compute Derivative of Filter Image
Sobel
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
I
-3 -1 0 0 0
-3 -1 -1 0 0
-1 -3 -4 -4 -4
0 -1 -3 -4 -4
0 0 0 0 0
3 1 0 0 0
3 3 1 0 0
1 3 2 0 0
0 1 1 0 0
0 0 0 0 0

11. 2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
Canny Edge Detector
3. Compute magnitude & Orientation of Gradient
Sobel
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
I
-3 -1 0 0 0
-3 -1 -1 0 0
-1 -3 -4 -4 -4
0 -1 -3 -4 -4
0 0 0 0 0
3 1 0 0 0
3 3 1 0 0
1 3 2 0 0
0 1 1 0 0
0 0 0 0 0
4.2 1.4 0 0 0
4.2 3.2 1.4 0 0
1.4 4.2 4.5 4 4
0 1.4 3.2 4 4
0 0 0 0 0
Gradient Magnitude

12. 2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
I
Canny Edge Detector
3. Compute magnitude & Orientation of Gradient
Sobel
-3 -1 0 0 0
-3 -3 -1 0 0
-1 -3 -4 -4 -4
0 -1 -3 -4 -4
0 0 0 0 0
3 1 0 0 0
3 3 1 0 0
1 3 2 0 0
0 1 1 0 0
0 0 0 0 0
D D D
D D
D
D D D D D
Gradient Orientation

13. Canny Edge Detector
4.Apply Non Maxima Suppression
Exploring Pixels for
NonMaxima Suppression
D D D
D D
D
D D D D D
Gradient Orientation
D D D
D D
D
D D D D D
Colour Coded Orientation

14. 4.2 1.4 0 0 0
4.2 3.2 1.4 0 0
1.4 4.2 4.5 4 4
0 1.4 3.2 4 4
0 0 0 0 0
Gradient Magnitude
Canny Edge Detector
4.Apply Non Maxima Suppression
Gradient Magnitude with
D D D
D D
D
D D D D D
Colour Coded Orientation
Exploring Pixels for
NonMaxima Suppression
4.3 1.4 0 0 0
4.1 3.3 1.5 0 0
1.3 4.3 4.4 4.1 4.0
0 1.5 3.3 4.0 3.9
0 0 0 0 0
4.3 0 0 0 0
4.1 3.3 0 0 0
0 4.3 4.4 4.1 4.0
0 0 0 0 0
0 0 0 0 0
Additive Noise : Dithering
Gradient Magnitude after
NonMaxima Suppression

15. Canny Edge Detector
4.Apply Non Maxima Suppression
2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
I Gradient Magnitude Gradient Magnitude after
Non Maxima Suppression
4.3 1.4 0 0 0
4.1 3.3 1.5 0 0
1.3 4.3 4.4 4.1 4.0
0 1.5 3.3 4.0 3.9
0 0 0 0 0
4.3 0 0 0 0
4.1 3.3 0 0 0
0 4.3 4.4 4.1 4.0
0 0 0 0 0
0 0 0 0 0

16. Canny Edge Detector 40 50 60
60 80 70 60
10 55 90
80 100 70
40 70
80 40 60
60 20 40 50
0.4 0.5 0.6
0.6 0.8 0.7 0.6
0.1 0.5 0.9
0.8 1.0 0.7
0.4 0.7
0.8 0.4 0.6
0.6 0.2 0.4 0.5
5.Apply Hysteresis Thresholding
Gradient
Image
Normalised
Gradient
Image
pixel
source : cv-tricks.com
0.4 0.5 0.6
0.6 0.8 0.7 0.6
0.1 0.5 0.9
0.8 1.0 0.7
0.4 0.7
0.8 0.4 0.6
0.6 0.2 0.4 0.5
After Double Thresholding No Edges
Strong Weak
0.4 0.5 0.6
0.6 0.8 0.7 0.6
0.5 0.9
0.8 1.0 0.7
0.4 0.7
0.8 0.4 0.6
0.6 0.4 0.5
0.4 0.5 0.6
0.6 0.8 0.7 0.6
0.5 0.9
0.8 1.0 0.7
0.4 0.7
0.8 0.4 0.6
0.6 0.4 0.5
After Hysteresis Thresholding

17. Canny Edge Detector
5.Apply Hysteresis Thresholding
Algorithm :
4. For all Valid Pixels, Mark a 8-Neighbour Connected
Weak Pixel as Valid
Continue 4. till at least one weak pixel turns valid
5. The remaining weak pixels are invalid
40 50 60
60 80 70 60
10 55 90
80 100 70
40 70
80 40 60
60 20 40 50
Edge Map
Gradient Image

18. Canny Edge Detector
Sobel
2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 2 2 2
1 1 1 1 1 1 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
I
-4 -3 -1 0 0
-3 -4 -3 -1 0
0 -1 -3 -4 -3
0 0 -1 -3 -4
0 0 0 0 -1
2 1 1 0 0
1 2 3 1 0
0 1 3 2 1
0 0 1 1 2
0 0 0 0 1
Class Work
Will Require
Calculator

19. Canny Edge Detector
2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 2 2 2
1 1 1 1 1 1 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
-4 -3 -1 0 0
-3 -4 -3 -1 0
0 -1 -3 -4 -3
0 0 -1 -3 -4
0 0 0 0 -1
2 1 1 0 0
1 2 3 1 0
0 1 3 2 1
0 0 1 1 2
0 0 0 0 1
I
Class Work Find Edge Magnitude & Edge Orientation for Image I. Apply
Non Maxima Suppression.
4.5 3.2 1.4 0 0
3.2 4.5 4.2 1.4 0
0 1.4 4.2 4.5 3.2
0 0 1.4 3.2 4.5
0 0 0 0 1.4
Class Work Solution
D D
D
D
D D
D D D D
Magnitude Orientation

20. Canny Edge Detector
2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 2 2 2
1 1 1 1 1 1 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
I
Class Work Solution
4.5 3.2 1.4 0 0
3.2 4.5 4.2 1.4 0
0 1.4 4.2 4.5 3.2
0 0 1.4 3.2 4.5
0 0 0 0 1.4
D D
D
D
D D
D D D D
Edge Magnitude Edge Orientation
Apply Non Maxima Suppression.
D D
D
D
D D
D D D D
Colour Coded Edge Orientation

21. Canny Edge Detector Class Work Solution
2 2 2 2 2 2 2
1 2 2 2 2 2 2
1 1 1 2 2 2 2
1 1 1 1 2 2 2
1 1 1 1 1 1 2
1 1 1 1 1 1 1
1 1 1 1 1 1 1
4.5 3.2 1.4 0 0
3.2 4.5 4.2 1.4 0
0 1.4 4.2 4.5 3.2
0 0 1.4 3.2 4.5
0 0 0 0 1.4
D D
D
D
D D
D D D D
I Edge Magnitude Edge Orientation
D D
D
D
D D
D D D D
4.5 0 0 0 0
0 4.5 4.2 0 0
0 0 4.2 4.5 0
0 0 0 0 4.5
0 0 0 0 1.4
Colour Coded Edge Orientation
Edge Magnitude after Non Maxima Suppression

22. Canny Edge Detector
0.2 0.6
0.3 0.8
0.4
0.5
0.6
0.4 0.7
0.4 0.8
Fig a
Class Work

23. Representation & Description
R1 R2
R3
R4
Result of Segmentation
External Characteristics :
Primal Focus is Shape Characteristics
Representation : Boundary
Description as Features –
Length, Orientation of st lines,
No of concavities
Internal Characteristics :Pixel
Primal Focus is Colour, Texture
Representation: Pixel
Description as Features :
Histogram, Covariance, Co-occurrence
Ideally Features to be Translation,
Rotation & Scale Invariant

24. Boundary Following
Moore Boundary Tracking Algorithm
No L T CT O/B Boundary
Points
1 (1,1) O (1,1) F
2 (1,0) B
3 (0,0) B
4 (0,1) B
5 (0,2) B
6 (0,2) (1,2) O (1,2) S
7 (0,2) B
8 (0,3) B
9 (0,3) (1,3) O (1,3)
10 (0,3) B
11 (0,4) B
12 (1,4) B
13 (2,4) B
14 (2,4) (2,3) O (2.3)
15 (2,4) B
16 (3.4) B
17 (3,4) (3,3) O (3,3)
18 (3.4) B
19 (4,4) B
20 (4.3) B
0 1 2 3 4
0
1
2
3
4
No L T CT O/B Boundary
Points
21 (4,2) B
22 (3.2) B
23 (3,2) (2,2) O (2,2)
24 (3,2) B
25 (3,1) B
25 (2,1) B
26 (2.1) (1,1) O (1,1) =F
28 (2,1) B
29 (2,0) B
30 (1,0) B
31 (0,0) B
32 (0,1) B
33 (0,2) B
34 (1,2) O (1,2)=S
35 T
Current Traversal CT
Last Traversal LT
Object/Background Point O/
Termination T

25. R
Boundary Following
Determine the Traversal Table & Boundary Points for a
Region R in Fig a by Moore Boundary Tracking Algorithm
No L T CT O/B Boundary
Points
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0 1 2 3
0
1
2
3
Fig a
ClassWork

26. ClassWork Solution Boundary Following
No L T CT O/B Boundary
Points
1 (1,0) (1.1) O (1,1) F
2 (1,0) B
3 (0,0) B
4 (0,1) B
5 (0,2) B
6 (0,2) (1,2) O (1,2) S
7 (0,2) B
8 (0,3) B
9 (1,3) B
10 (2,3) B
11 (2,3) (2,2) O (2,2)
12 (2,3) B
13 (3.3) B
14 (3,2) B
15 (3.1) B
16 (3,1) (2,1) O (2,1)
17 (3,1) B
18 (3,0) B
19 (2,0) B
20 (1,0) B
0 1 2 3
0
1
2
3
Fig a
No L T CT O/B Boundary
Points
21 (1,0) (1,1) O (1,1) = F
22 (1,0) B
23 (0,0) B
24 (0,1) B
25 (0,2) B
25 (0,2) (1,2) O (1,2) =S
26 T
Determine the Traversal Table & Boundary Points for a
Region R in Fig a by Moore Boundary Tracking Algorithm

27. Freeman Chain Code
0
1
2
3
4
5
6
7
P1
P2
Code :
P1: 07575443121
P2: 12107575443
First Difference :
Circular First Difference:
Shape No:
Order :
7626707617
77626707617
07617776267
11
Find Minima
77626707617
77762670761
17776267076
61777626707
76177762670
07617776267
70761777626
67076177762
26707617776
62670761777
76267076177

28. 0
1
3
4
5
Class Work
2
6
7
Freeman Chain Code
P P
Find Chain Code, Difference Code, Shape No & Order for Fig a & b.
Fig a Fig b

29. 1
3
4 0
5
Class Work Solution
2
6
7
Freeman Chain Code
P P
Code : 0642
First Difference : 666
Circular First Difference: 6666
Shape No: 6666
Order : 4
7531
666
6666
6666

30. Thank You