Laplacian

The Laplacian command applies the Laplacian operator — the sum of second-order partial derivatives — to detect edges via zero-crossings. The output highlights regions of rapid intensity change.

When to use

The Laplacian is sensitive to fine detail and noise. Apply it after Gaussian Blur (the combined LoG — Laplacian of Gaussian — operator) for more robust edge and blob detection.

Parameters

Parameter	Description
Kernel size	Size of the Laplacian kernel (range 3–27)

Background

The Laplacian is defined as:

$$ \nabla^2 I = \frac{\partial^2 I}{\partial x^2} + \frac{\partial^2 I}{\partial y^2} $$

Zero-crossings in the output correspond to edges in the original image. Unlike gradient-based methods (Sobel, Canny), the Laplacian is isotropic — it responds equally to edges in all directions.