1st and 2nd Gaussian derivatives for edge detection
An edge remains a concept that is a bit complicated to define, as it may involve a certain level of interpretation. For a pixel-wise point of view, I consider that a potential edge breaks down into three main features: it is singular (non-continuous, non-differentiable) across one direction, and more regular (smooth) in the other direction, at a certain scale.
The singular part can be enhanced by the derivative part of the 2D filter; a first derivative should be extremal at the singularity, a second derivative could be zero. The regular part can be strengthened by the smoothing aspect the filter. Both should be combined at a certain scale, driven by the &quot;size&quot; of the filter (support and shape factor of the function, here $3\times 3$ and $\sigma= 0.8$) for you.
The proper choice of efficient sets of filters to detect edges and contours requires to carefully adapt to the nature of your image (resolution, etc.) and the type of noise it suffers.