A \(4\times4\) image \(f\) is convolved with the separable kernel \(h=h_1 h_2^T\), where \(h_1=[1,2,1]\) and \(h_2=[1,2,1]\). What is the output value at the central position if the window of \(f\) is all ones, without normalization?
The 2D kernel has a sum equal to the product of the 1D sums, which is 4 times 4, that is 16. A kernel summing to 12 would correspond to a bad factorization.
2D convolution is the operation that combines an image \(f(x,y)\) with a kernel \(h(x,y)\) by sliding the kernel and summing products at each position.