Zero mean filters for edges at different orientations

Course Q&A Deep Learning Specialization Convolutional Neural Networks
1

In the first question of the quiz, a filter like the following is presented.

\begin{matrix} 1 & 1 & 2 \\ 1 & 2 & -1 \\ 2 & -1 &-1 \end{matrix}

But this is not zero mean, while the other analogous matrices mentioned in the lecture for other orientations are zero mean.

Would matrices like

\begin{matrix} 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & -1 \end{matrix}

or

\begin{matrix} 2 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 &-2 \end{matrix}

be adequate alternatives?

2

The filters do not need to have a zero mean.

3

The dataset should have a zero mean, but not the filters.

4

If they are zero mean, their response to constant images will be zero. Isn’t this is a nice property for edge detectors?

5

Not necessarily. In a learning system, you’re not going to specify the exact filter. The filters will be learned through training. If an edge detector helps to minimize the cost, then a filter that happens to detect edges will be learned.

Training includes both the weight values for the filter and a bias value that compensates for any offsets.

Also keep in mind that the filters used in the quiz are just simple examples, and aren’t completely implemented systems.

6

Thank you for your explanation!