Kernel to calculate second order partial derivative of digital image

1. What is the second derivative of an image?
2. Which method is the best way to compute the derivative of an image?

What is the second derivative of an image?

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.

Which method is the best way to compute the derivative of an image?

Image derivatives can be computed by using small convolution filters of size 2 × 2 or 3 × 3, such as the Laplacian, Sobel, Roberts and Prewitt operators. However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives and Gabor filters.