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Operations in Digital Image
Processing + Convolution by Example
MENOUFIA UNIVERSITY
FACULTY OF COMPUTERS AND INFORMATION
ALL DEPARTMENTS
‫المنوفية‬ ‫جامعة‬
‫والمعلومات‬ ‫الحاسبات‬ ‫كلية‬
‫جميع‬‫األقسام‬
‫المنوفية‬ ‫جامعة‬
Ahmed Fawzy Gad
ahmed.fawzy@ci.menofia.edu.eg
Image Processing Operations
Operations
Point Group
Point Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 5 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 5 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 5 215 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Arithmetic
Operations
+ - * /
Add 2
Point Operations
60 5 215 83 80
187 89 34 29 13
72 68 62 4 21
63 93 131 91 40
16 9 60 16 44
Arithmetic
Operations
+ - * /
Add 2
Group Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
Group Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
Group Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60
9
= 𝟖𝟔
Group Operations – Template Operations
1 Operation 2 Template
Mode
Median
Mean
7x7
5x5
3x3
ODD
Why odd?
Group Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60
9
= 𝟖𝟔
Put the results in the center.
Group Operations
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60
9
= 𝟖𝟔
Put the results in the center.
𝟖𝟔
Group Operations – Even Template Size
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
58 + 3 + 185 + 87
4
= 𝟖𝟑. 𝟐𝟓 ≅ 𝟖𝟒
Even template sizes has no center.
E.g. 2x3, 2x2, 5x6, …
𝟖𝟒
Group Operations – Even Template Size
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42Mode
Median
Mean
Even template sizes has no center.
E.g. 2x3, 2x2, 5x6, …
𝟖𝟒
???
58 + 3 + 185 + 87
4
= 𝟖𝟑. 𝟐𝟓 ≅ 𝟖𝟒
What is Convolution?
• It is a mathematical way to combine two signals to generate a third
signal. Convolution is not limited on digital image processing and it is
a broad term that works on signals.
Input Signal
Impulse Response
Output Signal
System
Convolution
What is Convolution?
• It is a mathematical way to combine two signals to generate a third
signal. Convolution is not limited on digital image processing and it is
a broad term that works on signals.
Input Signal
Impulse Response
Output Signal
System
Convolution
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
Convolution for 2D Image Signal
1 3 4 3 10
2 7 4 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8Template – 3x3
2 1 -4
3 2 5
-1 8 1
Convolution for 2D Image Signal
Template – 3x3
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 7 4 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
Template – 3x3
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 7 4 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
1 3 4 3 10
2 44 4 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
2 ∗ 1 + 1 ∗ 3 − 4 ∗ 4 + 3 ∗ 2 + 2 ∗ 7 + 5 ∗ 4
− 1 ∗ 6 + 8 ∗ 2 + 1 ∗ 5
= 𝟒𝟒
1 3 4 3 10
2 44 4 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
Convolution for 2D Image Signal
2 ∗ 3 + 1 ∗ 4 − 4 ∗ 3 + 3 ∗ 7 + 2 ∗ 4 + 5 ∗ 1
− 1 ∗ 2 + 8 ∗ 5 + 1 ∗ 2
= 𝟕𝟐
1 3 4 3 10
2 44 72 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
1 3 4 3 10
2 44 72 1 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 44 72 2 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 ∗ 4 + 1 ∗ 3 − 4 ∗ 10 + 3 ∗ 4 + 2 ∗ 1 + 5
∗ 11 − 1 ∗ 5 + 8 ∗ 2 + 1 ∗ 5
= 𝟐
1 3 4 3 10
2 44 72 2 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 44 72 2 11
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 ∗ 3 + 1 ∗ 10 − 4 ∗ 0 + 3 ∗ 2 + 2 ∗ 11 + 5
∗ 0 − 1 ∗ 2 + 8 ∗ 5 + 1 ∗ 0
= 𝟖𝟐
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 7 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 80 12 14 8
Convolution for 2D Image Signal
2 ∗ 13 + 1 ∗ 6 − 4 ∗ 8 + 3 ∗ 2 + 2 ∗ 7 + 5
∗ 12 − 1 ∗ 0 + 8 ∗ 0 + 1 ∗ 0
= 𝟖𝟎
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 80 12 14 8
Convolution for 2D Image Signal
2 1 -4
3 2 5
-1 8 1
1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 80 12 14 77
Convolution for 2D Image Signal
2 ∗ 9 + 1 ∗ 1 − 4 ∗ 0 + 3 ∗ 14 + 2 ∗ 8 + 5
∗ 0 − 1 ∗ 0 + 8 ∗ 0 + 1 ∗ 0
= 𝟕𝟕
Convolution for 2D Signal
•Continue. 1 3 4 3 10
2 44 72 2 82
6 2 5 2 5
13 6 8 9 1
2 80 12 14 77
Convolution for 2D Signal
•Template for Mean.𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
𝟏
𝟗
58 3 213 81 78
185 87 32 27 11
70 66 60 2 19
61 91 129 89 38
14 7 58 14 42
𝟏
𝟗
∗ 58 +
𝟏
𝟗
∗ 3 +
𝟏
𝟗
∗ 213 +
𝟏
𝟗
∗ 185 +
𝟏
𝟗
∗ 87 +
𝟏
𝟗
∗ 32
+
𝟏
𝟗
∗ 70 +
𝟏
𝟗
∗ 66 +
𝟏
𝟗
∗ 60
= 86

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Operations in Digital Image Processing + Convolution by Example

  • 1. Operations in Digital Image Processing + Convolution by Example MENOUFIA UNIVERSITY FACULTY OF COMPUTERS AND INFORMATION ALL DEPARTMENTS ‫المنوفية‬ ‫جامعة‬ ‫والمعلومات‬ ‫الحاسبات‬ ‫كلية‬ ‫جميع‬‫األقسام‬ ‫المنوفية‬ ‫جامعة‬ Ahmed Fawzy Gad ahmed.fawzy@ci.menofia.edu.eg
  • 3. Point Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 4. Point Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 5. Point Operations 60 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 6. Point Operations 60 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 7. Point Operations 60 5 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 8. Point Operations 60 5 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 9. Point Operations 60 5 215 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 Arithmetic Operations + - * / Add 2
  • 10. Point Operations 60 5 215 83 80 187 89 34 29 13 72 68 62 4 21 63 93 131 91 40 16 9 60 16 44 Arithmetic Operations + - * / Add 2
  • 11. Group Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean
  • 12. Group Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean
  • 13. Group Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean 58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60 9 = 𝟖𝟔
  • 14. Group Operations – Template Operations 1 Operation 2 Template Mode Median Mean 7x7 5x5 3x3 ODD Why odd?
  • 15. Group Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean 58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60 9 = 𝟖𝟔 Put the results in the center.
  • 16. Group Operations 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean 58 + 3 + 213 + 185 + 87 + 32 + 70 + 66 + 60 9 = 𝟖𝟔 Put the results in the center. 𝟖𝟔
  • 17. Group Operations – Even Template Size 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean 58 + 3 + 185 + 87 4 = 𝟖𝟑. 𝟐𝟓 ≅ 𝟖𝟒 Even template sizes has no center. E.g. 2x3, 2x2, 5x6, … 𝟖𝟒
  • 18. Group Operations – Even Template Size 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42Mode Median Mean Even template sizes has no center. E.g. 2x3, 2x2, 5x6, … 𝟖𝟒 ??? 58 + 3 + 185 + 87 4 = 𝟖𝟑. 𝟐𝟓 ≅ 𝟖𝟒
  • 19. What is Convolution? • It is a mathematical way to combine two signals to generate a third signal. Convolution is not limited on digital image processing and it is a broad term that works on signals. Input Signal Impulse Response Output Signal System Convolution
  • 20. What is Convolution? • It is a mathematical way to combine two signals to generate a third signal. Convolution is not limited on digital image processing and it is a broad term that works on signals. Input Signal Impulse Response Output Signal System Convolution 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42
  • 21. Convolution for 2D Image Signal 1 3 4 3 10 2 7 4 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8Template – 3x3 2 1 -4 3 2 5 -1 8 1
  • 22. Convolution for 2D Image Signal Template – 3x3 2 1 -4 3 2 5 -1 8 1 1 3 4 3 10 2 7 4 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8
  • 23. Convolution for 2D Image Signal Template – 3x3 2 1 -4 3 2 5 -1 8 1 1 3 4 3 10 2 7 4 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8
  • 24. Convolution for 2D Image Signal 1 3 4 3 10 2 44 4 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 2 ∗ 1 + 1 ∗ 3 − 4 ∗ 4 + 3 ∗ 2 + 2 ∗ 7 + 5 ∗ 4 − 1 ∗ 6 + 8 ∗ 2 + 1 ∗ 5 = 𝟒𝟒
  • 25. 1 3 4 3 10 2 44 4 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 26. Convolution for 2D Image Signal 2 ∗ 3 + 1 ∗ 4 − 4 ∗ 3 + 3 ∗ 7 + 2 ∗ 4 + 5 ∗ 1 − 1 ∗ 2 + 8 ∗ 5 + 1 ∗ 2 = 𝟕𝟐 1 3 4 3 10 2 44 72 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8
  • 27. 1 3 4 3 10 2 44 72 1 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 28. 1 3 4 3 10 2 44 72 2 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 ∗ 4 + 1 ∗ 3 − 4 ∗ 10 + 3 ∗ 4 + 2 ∗ 1 + 5 ∗ 11 − 1 ∗ 5 + 8 ∗ 2 + 1 ∗ 5 = 𝟐
  • 29. 1 3 4 3 10 2 44 72 2 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 30. 1 3 4 3 10 2 44 72 2 11 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 31. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 ∗ 3 + 1 ∗ 10 − 4 ∗ 0 + 3 ∗ 2 + 2 ∗ 11 + 5 ∗ 0 − 1 ∗ 2 + 8 ∗ 5 + 1 ∗ 0 = 𝟖𝟐
  • 32. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal
  • 33. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 7 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 34. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 80 12 14 8 Convolution for 2D Image Signal 2 ∗ 13 + 1 ∗ 6 − 4 ∗ 8 + 3 ∗ 2 + 2 ∗ 7 + 5 ∗ 12 − 1 ∗ 0 + 8 ∗ 0 + 1 ∗ 0 = 𝟖𝟎
  • 35. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 80 12 14 8 Convolution for 2D Image Signal 2 1 -4 3 2 5 -1 8 1
  • 36. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 80 12 14 77 Convolution for 2D Image Signal 2 ∗ 9 + 1 ∗ 1 − 4 ∗ 0 + 3 ∗ 14 + 2 ∗ 8 + 5 ∗ 0 − 1 ∗ 0 + 8 ∗ 0 + 1 ∗ 0 = 𝟕𝟕
  • 37. Convolution for 2D Signal •Continue. 1 3 4 3 10 2 44 72 2 82 6 2 5 2 5 13 6 8 9 1 2 80 12 14 77
  • 38. Convolution for 2D Signal •Template for Mean.𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 𝟏 𝟗 58 3 213 81 78 185 87 32 27 11 70 66 60 2 19 61 91 129 89 38 14 7 58 14 42 𝟏 𝟗 ∗ 58 + 𝟏 𝟗 ∗ 3 + 𝟏 𝟗 ∗ 213 + 𝟏 𝟗 ∗ 185 + 𝟏 𝟗 ∗ 87 + 𝟏 𝟗 ∗ 32 + 𝟏 𝟗 ∗ 70 + 𝟏 𝟗 ∗ 66 + 𝟏 𝟗 ∗ 60 = 86