This convolutional filters look similar to the results of the derivative of the Gaussian filter with respect to x and y.
The way you can think about them is that if you were to look at a 1d vector, from the perspective of a pixel in the 1d vector, to find the difference between your left neighbor and your right neighbor, you would just do your left neighbor minus your right neighbor or vice versa. This is equivalent to 1 * left neighbor + (-1) * right neighbor + 0 * your own value. This is essentially why you have it of the form [-1, 0, 1]. Then it becomes a matter of if it's vertical or horizontal. The way I've described it is more with left neighbor and right neighbor, which is horizontal. You can also view it as the neighbor above and below you. Then, the reason why there is a 2 for the row that the pixel is centered in from a 2D perspective is that you want to emphasize more for the row of the exact pixel, more than the difference above and below the pixel.
This convolutional filters look similar to the results of the derivative of the Gaussian filter with respect to x and y.
The way you can think about them is that if you were to look at a 1d vector, from the perspective of a pixel in the 1d vector, to find the difference between your left neighbor and your right neighbor, you would just do your left neighbor minus your right neighbor or vice versa. This is equivalent to 1 * left neighbor + (-1) * right neighbor + 0 * your own value. This is essentially why you have it of the form [-1, 0, 1]. Then it becomes a matter of if it's vertical or horizontal. The way I've described it is more with left neighbor and right neighbor, which is horizontal. You can also view it as the neighbor above and below you. Then, the reason why there is a 2 for the row that the pixel is centered in from a 2D perspective is that you want to emphasize more for the row of the exact pixel, more than the difference above and below the pixel.