# Why is second-order Gaussian called Laplacian Gaussian?

We usually use Laplacian of Gaussian as the filter for edge detection or blob detection. But the filter itself is essentially a second order Gaussian. So why do we call it Laplacian of Gaussian? Is there some other meanings behind it?

• HINT: A second order of what operation on a Gaussian? – A_A Feb 28 '18 at 11:41

## 2 Answers

Applying a Gaussian filter is a linear operation, also taking any type of derivative (finite difference) like Laplacian are also linear operations. Now considering the order of applying these operations doesn't matter (a property of convolution), you could combine them in many different ways, e.g. take Laplacian at first then take Gaussian or Gaussian first and Laplacian next, also you could apply Gausian on Laplacian or Laplacian on Gaussian and find a LoG Kernel, then apply the obtained Kernel on image once, which is more efficient in number of computations.

• More efficient in number of operations, but also much more precise. With the LoG you compute the exact Laplacian of the blurred image, rather than a finite difference approximation of the Laplacian. – Cris Luengo May 29 '18 at 18:15

I think it's calles LoG because as you wrote you take the second derivation of the gaussian filter.

A laplace operation is a derivation in 2 (or more) dimensions . In 2 dimensions it's what you do when creating the kernel. You derive the Gausskernel with the laplacian operation.

For more details on the laplacian operator see laplace operator wolfram alpha.