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Phát hiện biên bằng toán tử Sobel

Toán tử Sobel Sx

Toán tử Sobel Sy

Mức tách ngưỡng

Threshold

Kích thước ảnh

M (số hàng)

N (số cột)

Ma trận ảnh xám

Gx₀₀ =

0	0	0
0	1	2
0	0	3

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (0×-2) + (1×0) + (2×2) + (0×-1) + (0×0) + (3×1) = 7

Gx₀₁ =

0	0	0
1	2	3
0	3	12

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (1×-2) + (2×0) + (3×2) + (0×-1) + (3×0) + (12×1) = 16

Gx₀₂ =

0	0	0
2	3	4
3	12	3

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (2×-2) + (3×0) + (4×2) + (3×-1) + (12×0) + (3×1) = 4

Gx₀₃ =

0	0	0
3	4	5
12	3	4

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (3×-2) + (4×0) + (5×2) + (12×-1) + (3×0) + (4×1) = -4

Gx₀₄ =

0	0	0
4	5	6
3	4	2

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (4×-2) + (5×0) + (6×2) + (3×-1) + (4×0) + (2×1) = 3

Gx₀₅ =

0	0	0
5	6	7
4	2	1

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (5×-2) + (6×0) + (7×2) + (4×-1) + (2×0) + (1×1) = 1

Gx₀₆ =

0	0	0
6	7	0
2	1	0

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (0×1) + (6×-2) + (7×0) + (0×2) + (2×-1) + (1×0) + (0×1) = -14

Gx₁₀ =

0	1	2
0	0	3
0	4	1

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (1×0) + (2×1) + (0×-2) + (0×0) + (3×2) + (0×-1) + (4×0) + (1×1) = 9

Gx₁₁ =

1	2	3
0	3	12
4	1	2

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (2×0) + (3×1) + (0×-2) + (3×0) + (12×2) + (4×-1) + (1×0) + (2×1) = 24

Gx₁₂ =

2	3	4
3	12	3
1	2	1

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (3×0) + (4×1) + (3×-2) + (12×0) + (3×2) + (1×-1) + (2×0) + (1×1) = 2

Gx₁₃ =

3	4	5
12	3	4
2	1	3

-1	0	1
-2	0	2
-1	0	1

= (3×-1) + (4×0) + (5×1) + (12×-2) + (3×0) + (4×2) + (2×-1) + (1×0) + (3×1) = -13

Gx₁₄ =

4	5	6
3	4	2
1	3	5

-1	0	1
-2	0	2
-1	0	1

= (4×-1) + (5×0) + (6×1) + (3×-2) + (4×0) + (2×2) + (1×-1) + (3×0) + (5×1) = 4

Gx₁₅ =

5	6	7
4	2	1
3	5	4

-1	0	1
-2	0	2
-1	0	1

= (5×-1) + (6×0) + (7×1) + (4×-2) + (2×0) + (1×2) + (3×-1) + (5×0) + (4×1) = -3

Gx₁₆ =

6	7	0
2	1	0
5	4	0

-1	0	1
-2	0	2
-1	0	1

= (6×-1) + (7×0) + (0×1) + (2×-2) + (1×0) + (0×2) + (5×-1) + (4×0) + (0×1) = -15

Gx₂₀ =

0	0	3
0	4	1
0	2	9

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (0×0) + (3×1) + (0×-2) + (4×0) + (1×2) + (0×-1) + (2×0) + (9×1) = 14

Gx₂₁ =

0	3	12
4	1	2
2	9	0

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (3×0) + (12×1) + (4×-2) + (1×0) + (2×2) + (2×-1) + (9×0) + (0×1) = 6

Gx₂₂ =

3	12	3
1	2	1
9	0	2

-1	0	1
-2	0	2
-1	0	1

= (3×-1) + (12×0) + (3×1) + (1×-2) + (2×0) + (1×2) + (9×-1) + (0×0) + (2×1) = -7

Gx₂₃ =

12	3	4
2	1	3
0	2	1

-1	0	1
-2	0	2
-1	0	1

= (12×-1) + (3×0) + (4×1) + (2×-2) + (1×0) + (3×2) + (0×-1) + (2×0) + (1×1) = -5

Gx₂₄ =

3	4	2
1	3	5
2	1	15

-1	0	1
-2	0	2
-1	0	1

= (3×-1) + (4×0) + (2×1) + (1×-2) + (3×0) + (5×2) + (2×-1) + (1×0) + (15×1) = 20

Gx₂₅ =

4	2	1
3	5	4
1	15	2

-1	0	1
-2	0	2
-1	0	1

= (4×-1) + (2×0) + (1×1) + (3×-2) + (5×0) + (4×2) + (1×-1) + (15×0) + (2×1) = 0

Gx₂₆ =

2	1	0
5	4	0
15	2	0

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (1×0) + (0×1) + (5×-2) + (4×0) + (0×2) + (15×-1) + (2×0) + (0×1) = -27

Gx₃₀ =

0	4	1
0	2	9
0	6	7

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (4×0) + (1×1) + (0×-2) + (2×0) + (9×2) + (0×-1) + (6×0) + (7×1) = 26

Gx₃₁ =

4	1	2
2	9	0
6	7	8

-1	0	1
-2	0	2
-1	0	1

= (4×-1) + (1×0) + (2×1) + (2×-2) + (9×0) + (0×2) + (6×-1) + (7×0) + (8×1) = -4

Gx₃₂ =

1	2	1
9	0	2
7	8	0

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (2×0) + (1×1) + (9×-2) + (0×0) + (2×2) + (7×-1) + (8×0) + (0×1) = -21

Gx₃₃ =

2	1	3
0	2	1
8	0	2

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (1×0) + (3×1) + (0×-2) + (2×0) + (1×2) + (8×-1) + (0×0) + (2×1) = -3

Gx₃₄ =

1	3	5
2	1	15
0	2	1

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (3×0) + (5×1) + (2×-2) + (1×0) + (15×2) + (0×-1) + (2×0) + (1×1) = 31

Gx₃₅ =

3	5	4
1	15	2
2	1	3

-1	0	1
-2	0	2
-1	0	1

= (3×-1) + (5×0) + (4×1) + (1×-2) + (15×0) + (2×2) + (2×-1) + (1×0) + (3×1) = 4

Gx₃₆ =

5	4	0
15	2	0
1	3	0

-1	0	1
-2	0	2
-1	0	1

= (5×-1) + (4×0) + (0×1) + (15×-2) + (2×0) + (0×2) + (1×-1) + (3×0) + (0×1) = -36

Gx₄₀ =

0	2	9
0	6	7
0	1	2

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (2×0) + (9×1) + (0×-2) + (6×0) + (7×2) + (0×-1) + (1×0) + (2×1) = 25

Gx₄₁ =

2	9	0
6	7	8
1	2	3

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (9×0) + (0×1) + (6×-2) + (7×0) + (8×2) + (1×-1) + (2×0) + (3×1) = 4

Gx₄₂ =

9	0	2
7	8	0
2	3	10

-1	0	1
-2	0	2
-1	0	1

= (9×-1) + (0×0) + (2×1) + (7×-2) + (8×0) + (0×2) + (2×-1) + (3×0) + (10×1) = -13

Gx₄₃ =

0	2	1
8	0	2
3	10	1

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (2×0) + (1×1) + (8×-2) + (0×0) + (2×2) + (3×-1) + (10×0) + (1×1) = -13

Gx₄₄ =

2	1	15
0	2	1
10	1	2

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (1×0) + (15×1) + (0×-2) + (2×0) + (1×2) + (10×-1) + (1×0) + (2×1) = 7

Gx₄₅ =

1	15	2
2	1	3
1	2	4

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (15×0) + (2×1) + (2×-2) + (1×0) + (3×2) + (1×-1) + (2×0) + (4×1) = 6

Gx₄₆ =

15	2	0
1	3	0
2	4	0

-1	0	1
-2	0	2
-1	0	1

= (15×-1) + (2×0) + (0×1) + (1×-2) + (3×0) + (0×2) + (2×-1) + (4×0) + (0×1) = -19

Gx₅₀ =

0	6	7
0	1	2
0	2	1

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (6×0) + (7×1) + (0×-2) + (1×0) + (2×2) + (0×-1) + (2×0) + (1×1) = 12

Gx₅₁ =

6	7	8
1	2	3
2	1	8

-1	0	1
-2	0	2
-1	0	1

= (6×-1) + (7×0) + (8×1) + (1×-2) + (2×0) + (3×2) + (2×-1) + (1×0) + (8×1) = 12

Gx₅₂ =

7	8	0
2	3	10
1	8	1

-1	0	1
-2	0	2
-1	0	1

= (7×-1) + (8×0) + (0×1) + (2×-2) + (3×0) + (10×2) + (1×-1) + (8×0) + (1×1) = 9

Gx₅₃ =

8	0	2
3	10	1
8	1	0

-1	0	1
-2	0	2
-1	0	1

= (8×-1) + (0×0) + (2×1) + (3×-2) + (10×0) + (1×2) + (8×-1) + (1×0) + (0×1) = -18

Gx₅₄ =

0	2	1
10	1	2
1	0	1

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (2×0) + (1×1) + (10×-2) + (1×0) + (2×2) + (1×-1) + (0×0) + (1×1) = -15

Gx₅₅ =

2	1	3
1	2	4
0	1	2

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (1×0) + (3×1) + (1×-2) + (2×0) + (4×2) + (0×-1) + (1×0) + (2×1) = 9

Gx₅₆ =

1	3	0
2	4	0
1	2	0

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (3×0) + (0×1) + (2×-2) + (4×0) + (0×2) + (1×-1) + (2×0) + (0×1) = -6

Gx₆₀ =

0	1	2
0	2	1
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (0×-1) + (1×0) + (2×1) + (0×-2) + (2×0) + (1×2) + (0×-1) + (0×0) + (0×1) = 4

Gx₆₁ =

1	2	3
2	1	8
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (2×0) + (3×1) + (2×-2) + (1×0) + (8×2) + (0×-1) + (0×0) + (0×1) = 14

Gx₆₂ =

2	3	10
1	8	1
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (3×0) + (10×1) + (1×-2) + (8×0) + (1×2) + (0×-1) + (0×0) + (0×1) = 8

Gx₆₃ =

3	10	1
8	1	0
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (3×-1) + (10×0) + (1×1) + (8×-2) + (1×0) + (0×2) + (0×-1) + (0×0) + (0×1) = -18

Gx₆₄ =

10	1	2
1	0	1
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (10×-1) + (1×0) + (2×1) + (1×-2) + (0×0) + (1×2) + (0×-1) + (0×0) + (0×1) = -8

Gx₆₅ =

1	2	4
0	1	2
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (1×-1) + (2×0) + (4×1) + (0×-2) + (1×0) + (2×2) + (0×-1) + (0×0) + (0×1) = 7

Gx₆₆ =

2	4	0
1	2	0
0	0	0

-1	0	1
-2	0	2
-1	0	1

= (2×-1) + (4×0) + (0×1) + (1×-2) + (2×0) + (0×2) + (0×-1) + (0×0) + (0×1) = -4

Gx = I ⊗ Sx

Gy₀₀ =

0	0	0
0	1	2
0	0	3

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (0×0) + (1×0) + (2×0) + (0×-1) + (0×-2) + (3×-1) = -3

Gy₀₁ =

0	0	0
1	2	3
0	3	12

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (1×0) + (2×0) + (3×0) + (0×-1) + (3×-2) + (12×-1) = -18

Gy₀₂ =

0	0	0
2	3	4
3	12	3

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (2×0) + (3×0) + (4×0) + (3×-1) + (12×-2) + (3×-1) = -30

Gy₀₃ =

0	0	0
3	4	5
12	3	4

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (3×0) + (4×0) + (5×0) + (12×-1) + (3×-2) + (4×-1) = -22

Gy₀₄ =

0	0	0
4	5	6
3	4	2

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (4×0) + (5×0) + (6×0) + (3×-1) + (4×-2) + (2×-1) = -13

Gy₀₅ =

0	0	0
5	6	7
4	2	1

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (5×0) + (6×0) + (7×0) + (4×-1) + (2×-2) + (1×-1) = -9

Gy₀₆ =

0	0	0
6	7	0
2	1	0

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (0×1) + (6×0) + (7×0) + (0×0) + (2×-1) + (1×-2) + (0×-1) = -4

Gy₁₀ =

0	1	2
0	0	3
0	4	1

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (1×2) + (2×1) + (0×0) + (0×0) + (3×0) + (0×-1) + (4×-2) + (1×-1) = -5

Gy₁₁ =

1	2	3
0	3	12
4	1	2

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (2×2) + (3×1) + (0×0) + (3×0) + (12×0) + (4×-1) + (1×-2) + (2×-1) = 0

Gy₁₂ =

2	3	4
3	12	3
1	2	1

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (3×2) + (4×1) + (3×0) + (12×0) + (3×0) + (1×-1) + (2×-2) + (1×-1) = 6

Gy₁₃ =

3	4	5
12	3	4
2	1	3

1	2	1
0	0	0
-1	-2	-1

= (3×1) + (4×2) + (5×1) + (12×0) + (3×0) + (4×0) + (2×-1) + (1×-2) + (3×-1) = 9

Gy₁₄ =

4	5	6
3	4	2
1	3	5

1	2	1
0	0	0
-1	-2	-1

= (4×1) + (5×2) + (6×1) + (3×0) + (4×0) + (2×0) + (1×-1) + (3×-2) + (5×-1) = 8

Gy₁₅ =

5	6	7
4	2	1
3	5	4

1	2	1
0	0	0
-1	-2	-1

= (5×1) + (6×2) + (7×1) + (4×0) + (2×0) + (1×0) + (3×-1) + (5×-2) + (4×-1) = 7

Gy₁₆ =

6	7	0
2	1	0
5	4	0

1	2	1
0	0	0
-1	-2	-1

= (6×1) + (7×2) + (0×1) + (2×0) + (1×0) + (0×0) + (5×-1) + (4×-2) + (0×-1) = 7

Gy₂₀ =

0	0	3
0	4	1
0	2	9

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (0×2) + (3×1) + (0×0) + (4×0) + (1×0) + (0×-1) + (2×-2) + (9×-1) = -10

Gy₂₁ =

0	3	12
4	1	2
2	9	0

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (3×2) + (12×1) + (4×0) + (1×0) + (2×0) + (2×-1) + (9×-2) + (0×-1) = -2

Gy₂₂ =

3	12	3
1	2	1
9	0	2

1	2	1
0	0	0
-1	-2	-1

= (3×1) + (12×2) + (3×1) + (1×0) + (2×0) + (1×0) + (9×-1) + (0×-2) + (2×-1) = 19

Gy₂₃ =

12	3	4
2	1	3
0	2	1

1	2	1
0	0	0
-1	-2	-1

= (12×1) + (3×2) + (4×1) + (2×0) + (1×0) + (3×0) + (0×-1) + (2×-2) + (1×-1) = 17

Gy₂₄ =

3	4	2
1	3	5
2	1	15

1	2	1
0	0	0
-1	-2	-1

= (3×1) + (4×2) + (2×1) + (1×0) + (3×0) + (5×0) + (2×-1) + (1×-2) + (15×-1) = -6

Gy₂₅ =

4	2	1
3	5	4
1	15	2

1	2	1
0	0	0
-1	-2	-1

= (4×1) + (2×2) + (1×1) + (3×0) + (5×0) + (4×0) + (1×-1) + (15×-2) + (2×-1) = -24

Gy₂₆ =

2	1	0
5	4	0
15	2	0

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (1×2) + (0×1) + (5×0) + (4×0) + (0×0) + (15×-1) + (2×-2) + (0×-1) = -15

Gy₃₀ =

0	4	1
0	2	9
0	6	7

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (4×2) + (1×1) + (0×0) + (2×0) + (9×0) + (0×-1) + (6×-2) + (7×-1) = -10

Gy₃₁ =

4	1	2
2	9	0
6	7	8

1	2	1
0	0	0
-1	-2	-1

= (4×1) + (1×2) + (2×1) + (2×0) + (9×0) + (0×0) + (6×-1) + (7×-2) + (8×-1) = -20

Gy₃₂ =

1	2	1
9	0	2
7	8	0

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (2×2) + (1×1) + (9×0) + (0×0) + (2×0) + (7×-1) + (8×-2) + (0×-1) = -17

Gy₃₃ =

2	1	3
0	2	1
8	0	2

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (1×2) + (3×1) + (0×0) + (2×0) + (1×0) + (8×-1) + (0×-2) + (2×-1) = -3

Gy₃₄ =

1	3	5
2	1	15
0	2	1

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (3×2) + (5×1) + (2×0) + (1×0) + (15×0) + (0×-1) + (2×-2) + (1×-1) = 7

Gy₃₅ =

3	5	4
1	15	2
2	1	3

1	2	1
0	0	0
-1	-2	-1

= (3×1) + (5×2) + (4×1) + (1×0) + (15×0) + (2×0) + (2×-1) + (1×-2) + (3×-1) = 10

Gy₃₆ =

5	4	0
15	2	0
1	3	0

1	2	1
0	0	0
-1	-2	-1

= (5×1) + (4×2) + (0×1) + (15×0) + (2×0) + (0×0) + (1×-1) + (3×-2) + (0×-1) = 6

Gy₄₀ =

0	2	9
0	6	7
0	1	2

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (2×2) + (9×1) + (0×0) + (6×0) + (7×0) + (0×-1) + (1×-2) + (2×-1) = 9

Gy₄₁ =

2	9	0
6	7	8
1	2	3

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (9×2) + (0×1) + (6×0) + (7×0) + (8×0) + (1×-1) + (2×-2) + (3×-1) = 12

Gy₄₂ =

9	0	2
7	8	0
2	3	10

1	2	1
0	0	0
-1	-2	-1

= (9×1) + (0×2) + (2×1) + (7×0) + (8×0) + (0×0) + (2×-1) + (3×-2) + (10×-1) = -7

Gy₄₃ =

0	2	1
8	0	2
3	10	1

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (2×2) + (1×1) + (8×0) + (0×0) + (2×0) + (3×-1) + (10×-2) + (1×-1) = -19

Gy₄₄ =

2	1	15
0	2	1
10	1	2

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (1×2) + (15×1) + (0×0) + (2×0) + (1×0) + (10×-1) + (1×-2) + (2×-1) = 5

Gy₄₅ =

1	15	2
2	1	3
1	2	4

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (15×2) + (2×1) + (2×0) + (1×0) + (3×0) + (1×-1) + (2×-2) + (4×-1) = 24

Gy₄₆ =

15	2	0
1	3	0
2	4	0

1	2	1
0	0	0
-1	-2	-1

= (15×1) + (2×2) + (0×1) + (1×0) + (3×0) + (0×0) + (2×-1) + (4×-2) + (0×-1) = 9

Gy₅₀ =

0	6	7
0	1	2
0	2	1

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (6×2) + (7×1) + (0×0) + (1×0) + (2×0) + (0×-1) + (2×-2) + (1×-1) = 14

Gy₅₁ =

6	7	8
1	2	3
2	1	8

1	2	1
0	0	0
-1	-2	-1

= (6×1) + (7×2) + (8×1) + (1×0) + (2×0) + (3×0) + (2×-1) + (1×-2) + (8×-1) = 16

Gy₅₂ =

7	8	0
2	3	10
1	8	1

1	2	1
0	0	0
-1	-2	-1

= (7×1) + (8×2) + (0×1) + (2×0) + (3×0) + (10×0) + (1×-1) + (8×-2) + (1×-1) = 5

Gy₅₃ =

8	0	2
3	10	1
8	1	0

1	2	1
0	0	0
-1	-2	-1

= (8×1) + (0×2) + (2×1) + (3×0) + (10×0) + (1×0) + (8×-1) + (1×-2) + (0×-1) = 0

Gy₅₄ =

0	2	1
10	1	2
1	0	1

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (2×2) + (1×1) + (10×0) + (1×0) + (2×0) + (1×-1) + (0×-2) + (1×-1) = 3

Gy₅₅ =

2	1	3
1	2	4
0	1	2

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (1×2) + (3×1) + (1×0) + (2×0) + (4×0) + (0×-1) + (1×-2) + (2×-1) = 3

Gy₅₆ =

1	3	0
2	4	0
1	2	0

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (3×2) + (0×1) + (2×0) + (4×0) + (0×0) + (1×-1) + (2×-2) + (0×-1) = 2

Gy₆₀ =

0	1	2
0	2	1
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (0×1) + (1×2) + (2×1) + (0×0) + (2×0) + (1×0) + (0×-1) + (0×-2) + (0×-1) = 4

Gy₆₁ =

1	2	3
2	1	8
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (2×2) + (3×1) + (2×0) + (1×0) + (8×0) + (0×-1) + (0×-2) + (0×-1) = 8

Gy₆₂ =

2	3	10
1	8	1
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (3×2) + (10×1) + (1×0) + (8×0) + (1×0) + (0×-1) + (0×-2) + (0×-1) = 18

Gy₆₃ =

3	10	1
8	1	0
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (3×1) + (10×2) + (1×1) + (8×0) + (1×0) + (0×0) + (0×-1) + (0×-2) + (0×-1) = 24

Gy₆₄ =

10	1	2
1	0	1
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (10×1) + (1×2) + (2×1) + (1×0) + (0×0) + (1×0) + (0×-1) + (0×-2) + (0×-1) = 14

Gy₆₅ =

1	2	4
0	1	2
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (1×1) + (2×2) + (4×1) + (0×0) + (1×0) + (2×0) + (0×-1) + (0×-2) + (0×-1) = 9

Gy₆₆ =

2	4	0
1	2	0
0	0	0

1	2	1
0	0	0
-1	-2	-1

= (2×1) + (4×2) + (0×1) + (1×0) + (2×0) + (0×0) + (0×-1) + (0×-2) + (0×-1) = 10

Phát hiện biên bằng toán tử Sobel

Gx = I ⊗ Sx

Gy = I ⊗ Sy

G = |Gx| + |Gy|

Tách ngưỡng 15