Laplacian of a Gaussian (LoG) is just another linear filter which is a combination of Gaussian followed by the Laplacian filter on an image. Since the 2nd derivative is very sensitive to noise, it is always a good idea to remove noise by smoothing the image before applying the Laplacian to ensure that noise is not aggravated. Because of the associative property of convolution, it can be thought of as taking the 2nd derivative (Laplacian) of the Gaussian filter and then applying the resulting (combined) filter onto the image, hence the name LoG. It can be efficiently approximated using the difference of two Gaussians (DoG) with different scales (variances), as shown in the following diagram:
The following code block ...
