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?
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.