Little Bits of Artificial Intelligence

A Laplacian pattern detector is a type of edge detection operator used in image processing and computer vision. It highlights regions of rapid intensity change — typically edges, corners, or fine details — using the second derivative of the image intensity.

What It Does:

• Detects edges and fine detail by identifying where the rate of change of gradients is highest.
• Unlike Sobel (which uses first derivatives), the Laplacian uses the second derivative — it’s sensitive to areas where brightness sharply changes.

Basic Idea:

• If you think of an image as a height map, the Laplacian operator finds ridges or pits — sharp bumps or holes in the image.
• In math terms:


where f is the image intensity function.

Common Laplacian Kernel (3×3 matrix):

[ 0 -1 0 ]
[-1 4 -1 ]
[ 0 -1 0 ]

Or, a slightly more inclusive one:

[-1 -1 -1]
[-1 8 -1]
[-1 -1 -1]

Use Case Example:

In edge detection pipelines, it’s often used after Gaussian blur to reduce noise (known as Laplacian of Gaussian (LoG)).

What is Laplacian of Gaussian (LoG)?

Purpose:

• Detect edges more accurately and cleanly than Laplacian alone by first smoothing the image with a Gaussian filter to reduce noise, and then applying the Laplacian to find edges.

Formula:

Where:

• G(x,y) = Gaussian kernel
• I(x,y) = input image
• ∗ = convolution
• ∇^2 = Laplacian operator