2D Convolution

Perform 2D convolution between an input image and a kernel:

$$\text{C}[i,j] = \sum_{k=0}^{K_h-1}\sum_{l=0}^{K_w-1} \text{A}[i+k,j+l] \cdot \text{B}[k,l]$$

The convolution operation slides the 2D kernel over the input image, computing the sum of element-wise multiplications at each position. Zero padding is used at the boundaries.

Input:

• Matrix $\text{A}$ of size $\text{H} \times \text{W}$ (input image)
• Matrix $\text{B}$ of size $K_h \times K_w$ (convolution kernel)
• Both $K_h$ and $K_w$ are odd and smaller than $H$ and $W$ respectively

Output:

• Matrix $\text{C}$ of size $\text{H} \times \text{W}$ (convolved image)

Notes:

• All matrices $\text{A}$, $\text{B}$, and $\text{C}$ are stored in row-major order
• Use zero padding at the boundaries where the kernel extends beyond the input image
• The kernel is centered at each position, with $(K_h-1)/2$ rows and $(K_w-1)/2$ columns on each side