Page 262 - Ai Book - 10

Solved Examples

Let us compute the convolution of an input matrix and kernel matrix.
1 2 1 1 –2 1
1 2 3 11 15 13

–1 0 –2 –2 0 –1
4 5 6 17 18 12

1 –2 1 1 2 1
7 8 9 11 –23 –23

Input Image Kernel Image Flipped Kernel Convolution Output

The individual steps are as follow:

1 –2 1 1 –2 1 1 –2 1

–2 0 –1 –2 0 –1 –2 0 –1
1 2 3 1 2 3 1 2 3

1 2 1 1 2 1 1 2 1
4 5 6 4 5 6 4 5 6

7 8 9 7 8 9 7 8 9

0–2+8+5 = 11 –2+0–3+4+10+6 = 15 –4+0+5+12 = 13

1 –2 1 1 –2 1 1 –2 1
1 2 3 1 2 3 1 2 3

–2 0 –1 –2 0 –1 –2 0 –1
4 5 6 4 5 6 4 5 6

1 2 1 1 2 1 1 2 1
7 8 9 7 8 9 7 8 9

0–2+8+5 = 11 1–7+3–8+0–6+16+9 = 18 2–6–10+0+8+18 = 12

1 2 3 1 2 3 1 2 3

1 –2 1 1 –2 1 1 –2 1
4 5 6 4 5 6 4 5 6

–2 0 –1 –2 0 –1 –2 0 –1
7 8 9 7 8 9 7 8 9

1 2 1 1 2 1 1 2 1

–8+5+0–8 = – 11 4–10+6–14+0–9 = – 23 5–12–16+0 = – 23

136
136