# 1st and 2nd Gaussian derivatives for edge detection

I have a project about edge detection, I made research on internet about filters and read many articles but there is an article talked about using Sobel and Gaussian derivatives then it mentioned "edge" and "ridge" detection successively. I found the equation for 1st and 2nd Gaussian derivatives ($$3\times 3$$ and $$\sigma= 0.8$$) and applied the before mentioned method but I noticed blurred image with slightly enhanced edges. I still don't get the idea nor the exact role of using different Gaussian derivatives together for better edge detection, and how can I enhance curvilinear structure detection to get cleaner edges. If someone can break it down it would be appreciated.

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 "size" of the filter (support and shape factor of the function, here $$3\times 3$$ and $$\sigma= 0.8$$) for you.