Laplacian second derivative

1. Is the Laplacian the second derivative?
2. What is the rule for Laplace second order derivative?
3. What does the Laplacian operator tell us?
4. What is the disadvantage of using a second order derivative filters for edge detection?

Is the Laplacian the second derivative?

The major difference between Laplacian and other operators like Prewitt, Sobel, Robinson and Kirsch is that these all are first order derivative masks but Laplacian is a second order derivative mask.

What is the rule for Laplace second order derivative?

2nd Derivative rule for the Laplace transformation) For anly differentiable function f [0, +oc) with piecewise continuous second derivative f" [0, +oo) such that f , f' aned f" satisfy (1) for some N 7 0 and K > 0, one has that Lf" (s) = sCfH(s) f' (0) sf(0) for every > 0.

What does the Laplacian operator tell us?

The Laplacian measures what you could call the « curvature » or stress of the field. It tells you how much the value of the field differs from its average value taken over the surrounding points.

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.