I've been diving into smoothing kernels and I came up with a lot of questions that I haven't been able to find in the internet. If you can I'd appreciate the help :)
(Capitals and bold were used for formatting)
QUESTION 1
It is my understanding that if we do:
Image $\rightarrow$ Gaussian Smoothing kernel on X $\rightarrow$ Gaussian Derivative Kernel on Y = Image Derivative along Y for Edge Detection
Image $\rightarrow$ Gaussian Derivative Kernel on X $\rightarrow$ Gaussian Smoothing kernel on Y = Image Derivative along X for Edge Detection
What happens if we do this?
Image $\rightarrow$ Gaussian Derivative Kernel on X $\rightarrow$ Gaussian Derivative Kernel on Y = ???
Does it make sense?
What is the correct way to visualize both derivatives? Is it the magnitude?
$$||\nabla f|| = \sqrt{{\left(\frac{\partial Image}{\partial x}\right)}^2+{\left(\frac{\partial Image}{\partial y}\right)}^2}$$
QUESTION 2
On the other hand, I was looking at the Prewitt and Sobel operators and I realized that both:
- Do Smoothing on one axis
- And the Derivative on the other
Is it a better strategy to do smoothing on both axis and then just apply a derivative on the axis of interest? It feels a bit like duplication (like the derivative is also smoothing)
QUESTION 3
What is the practical difference between the 1st and 2nd Derivative for edge detection?
QUESTION 4 Is the "Gaussian 2nd Derivative" what is called "Laplacian of Gaussian"? Any specific reason? I feel like everyone calls it Laplacian for short
Thanks for the help and sorry for the huge amount of questions! :)