2D Convolution Operation

2D convolutions are the most common due to their application in images; they are an element-wise multiplication and summation. For example, for the convolution in the diagram below, we have:

$$\begin{array}{rl}(0\times 0)& +(0\times 1)+(1\times 2)\\ +(3\times 2)& +(1\times 2)+(2\times 0)\\ +(2\times 0)& +(0\times 1)+(0\times 2)=10\end{array}$$

Some terminology:

• Kernel: The small matrix sliding over the input data
• Stride: Number of pixels by which the kernel moves as it slides over the input data
• Padding: Extra pixels around the edges of the input data to allow the kernel to fit properly at the borders of the input.

A $3\times 3$ kernel applied to a $5\times 5$ input with a $1\times 1$ padding using $2\times 2$ strides.