Let’s calculate the output of the emboss kernel for the given matrix. The emboss kernel is applied centered at coordinate (2,3). Emboss Kernel: [ 1 0 0 0 0 0 0 0 − 1 ] Matrix: [ 24... Let’s calculate the output of the emboss kernel for the given matrix. The emboss kernel is applied centered at coordinate (2,3). Emboss Kernel: [ 1 0 0 0 0 0 0 0 − 1 ] Matrix: [ 244 66 96 52 161 86 199 60 241 25 166 206 34 177 227 65 ] We extract the 3×3 region centered at (2,3): [ 66 96 52 86 199 60 25 166 206 ] Read more

Steps to Solve

1. Extract the 3x3 Region

To start, we need to identify and extract the 3x3 region from the provided matrix. Let's say our matrix is:

$$ \begin{bmatrix} 1 & 2 & 3 & 4 & 5 \ 6 & 7 & 8 & 9 & 10 \ 11 & 12 & 13 & 14 & 15 \ 16 & 17 & 18 & 19 & 20 \ 21 & 22 & 23 & 24 & 25 \end{bmatrix} $$

Assuming we are extracting the region that starts at (1,1) (the element '7'), the 3x3 region is:

$$ \begin{bmatrix} 7 & 8 & 9 \ 12 & 13 & 14 \ 17 & 18 & 19 \end{bmatrix} $$

2. Define the Emboss Kernel

The emboss kernel is defined as:

$$ \begin{bmatrix} -2 & -1 & 0 \ -1 & 1 & 1 \ 0 & 1 & 2 \end{bmatrix} $$

3. Perform the Convolution Operation

Next, we apply the emboss kernel to the extracted 3x3 region. We compute the sum of the products (convolution) by multiplying each element in the emboss kernel with the corresponding element in the 3x3 region and summing the results:

The summation will look like this:

$$ \text{Output} = (-2 \cdot 7) + (-1 \cdot 8) + (0 \cdot 9) + (-1 \cdot 12) + (1 \cdot 13) + (1 \cdot 14) + (0 \cdot 17) + (1 \cdot 18) + (2 \cdot 19) $$

Calculating each multiplication:

• $-2 \cdot 7 = -14$
• $-1 \cdot 8 = -8$
• $0 \cdot 9 = 0$
• $-1 \cdot 12 = -12$
• $1 \cdot 13 = 13$
• $1 \cdot 14 = 14$
• $0 \cdot 17 = 0$
• $1 \cdot 18 = 18$
• $2 \cdot 19 = 38$

Now let's sum these results:

$$ -14 - 8 + 0 - 12 + 13 + 14 + 0 + 18 + 38 = 49 $$

4. Final Output

From the calculations, the final output of the convolution operation is:

$$ \text{Output} = 49 $$