Calculating a convolution of an Image with C++: Image Processing

In convolution, the calculation performed at a pixel is a weighted sum of grey levels from a neighbourhood surrounding a pixel. Grey levels taken from the neighbourhood are weighted by coefficients that come from a matrix or convolution kernel. The kernel's dimensions define the size of the neighbourhood in which calculation take place. The most common dimension is 3x3. I am using this size of matrix in this article. During convolution, we take each kernel coefficient in turn and multiply it by a value from the neighbourhood of the image lying under the kernel. We apply the kernel to the image in such a way that the value at the top-left corner of the kernel is multiplied by the value at bottom-right corner of the neighbourhood. This can be expressed by following mathematical expression for kernel of size mxn.