Image Processing: what is the correct form of the Laplacian Filter

[Master1022]

Homework Statement

What is the correct form of the Laplacian filter in image processing?

Relevant Equations

Laplacian

Hi,

I just have a quick question regarding image processing. What is the correct form of the Laplacian for image processing?

I have seen different versions online and don't understand which one is meant to be the conventional one. I know that:
$$\nabla^2 f(x, y) = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}$$

Type 1:
$$\begin{pmatrix} 2 & -1 & 2 \\ -1 & -4 & -1 \\ 2 & -1 & 2 \\ \end{pmatrix}$$

I believe this is derived by forming matrices for the second derivative in the x and y-directions separately and then combining those matrices. This one does that across all the 3 rows/columns.

Type 2:
$$\begin{pmatrix} 0 & -1 & 0 \\ -1 & -4 & -1 \\ 0 & -1 & 0 \\ \end{pmatrix}$$

This one is derived by doing the same as above, but only populating the central row/column.

Any help would be greatly appreciated.

 

[LightHero]

The correct form of the Laplacian for image processing is Type 2: \begin{pmatrix} 0 & -1 & 0 \\ -1 & -4 & -1 \\ 0 & -1 & 0 \\ \end{pmatrix} This is the most commonly used form of the Laplacian and is derived by forming matrices for the second derivative in the x and y-directions separately and then combining those matrices, but only populating the central row/column. This version is often referred to as the "central difference" or "centered difference" approach.