Are the following sequence of operations the same -
- Down-sampling filtering followed by gradient filtering with kernel [-1 0 1]
- Gradient filtering with kernel [-1 0 1] followed by down-sampling
Could you point me to some math which can answer this question.
Intuitively, I am thinking that these operations are the same. That is because down-sampling can be loosely modeled as low-pass filtering and since convolution is associative, I guess they should produce similar results. But I am not able to quantitatively prove this to be a fact.