How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions? I am trying to understand the four 1D convolution operations involved in implementation of Laplacian of Gaussian(LoG). I have read this answer and I am also reading this pdf (See slide# 62 and 63). My current understanding is:

1) Pre-compute LoG and separate to 1D filters in x and y: gxx(x) and gyy(y).

2) Take Gaussian (g) and separate to: g(x) and g(y).

3) First apply g(y) and gyy(y) to the image. That makes two 1D convolutions.

4) Then apply g(x) to the result from gyy(y) and gxx(x) to the result from g(y). That adds two more 1D convolutions, making the total four.

Questions:

1) Is the above understanding correct?

2) How is this same as LoG?

3) Also, the diagram in slide #62 contradicts slide #63, in the pdf. Which one is correct? 

Edit:

It's actually slide#61 and slide#62. 

Edit2:

Please see the very last comment, posted Dec 19, 2018, on the first answer.
I think Chris Luengo's answer is perfect.
The trick is that you can calculate the 2nd derivative of the image (Using Finite Differences -> Convolution) and then blur it with Gaussian Filter.
Since both are seperable kernels you can do that by 4 1D convolutions.

If the input image is given by I


Calculate Ixx (The 2nd derivative on x direction) using convolution.
Filter Ixx with 1D Gaussian Kernel along the x direction.


Do the above for the y direction as well.
The LoG image is the sum of both.

To answer your questions:


See my explanation above. I think it matches your understanding.
This is the very definition (The Discrete) of the LoG.
I don't see the contradiction between #62 and #63.