Does this mean that to (approximately) produce a Laplacian pyramid, instead of the Gaussian filter > compute residual > subsample algorithm, we can replace it with Laplacian filter > subsample?

I assume that this method is faster, but also produces some (possibly negligible) info loss because it is an approximation?

@Samleo Unfortunately, I don't believe this would be faster. The reason is the following:

Although you can directly produce the Laplacian image in a single operation, you still need to produce a corresponding blurry image before downsampling. So in both cases, I expect that you need to do 1 blurring operation, 1 addition/subtraction operation between images, and 1 downsampling operation for every level of your pyramid.

I was thinking that the Laplacian filter would replace the (Gaussian + subtraction to get the residual) component, hence reducing one operation? But maybe I am wrong

Your definitely right that the Laplacian filter would replace the Gaussian + subtraction operation, and this step would be more efficient if the goal were to only generate this one image. But to create the next level of the Laplacian image, you still need to compute the Gaussian-filtered image.

As a result, the two approaches would be either Gaussian filter > compute Laplacian image from residual > subsample, or Laplacian filter > compute Gaussian image from residual > subsample.

Ah ok that makes sense now, thank you!