Are 2nd Order Edge Detectors More Susceptible to Noise?

Second order filters are always more sensitive to noise (e.g. laplacian filter), and the same and better results can be obtained when a first order (e.g. sobel filter).

1. What is the disadvantage of using a second order derivative filters for edge detection?
2. Which second order operator is most sensitive to noise in edge filtering?
3. Why are second order edge detectors better at finding edges than first order detectors?
4. Why the second derivative is useful for edge detection?

What is the disadvantage of using a second order derivative filters for edge detection?

However there are disadvantages to the use of second order derivatives. (We should note that first derivative operators exaggerate the effects of noise.) Second derivatives will exaggerated noise twice as much. No directional information about the edge is given.

Which second order operator is most sensitive to noise in edge filtering?

Laplacian is an isotropic operator, also it is cheaper to implement than the gradient (one mask only). It does not provide information about edge direction and it is more sensitive to noise (diff erentiates twice).

Why are second order edge detectors better at finding edges than first order detectors?

Generally 2nd derivative is more sensitive to noise than 1st derivative. The 2nd derivative is usually accompanied by zero crossing detection, so it works better when grey level transitions are smooth.

Why the second derivative is useful for edge detection?

The 2nd derivative of an image where the image highlights regions of rapid intensity change and is therefore often used for edge detection zero crossing edge detectors.