Principle:Kornia Kornia Gradient Edge Detection
| Knowledge Sources | |
|---|---|
| Domains | Vision Image_Processing Filters |
| Last Updated | 2026-02-09 15:00 GMT |
Overview
Technique of detecting edges by computing first-order spatial gradient magnitudes using discrete derivative filters.
Description
Gradient-based edge detection computes the rate of intensity change using discrete approximations of the first spatial derivative. The Sobel operator convolves the image with two 3x3 kernels to approximate horizontal and vertical gradients, then combines them into a magnitude map. Edges appear as high-magnitude regions.
Unlike Canny, Sobel produces continuous gradient magnitudes rather than binary edges, making it suitable for applications that need gradient strength information. The Laplacian operator uses second-order derivatives to detect zero-crossings at edges. Both are simpler and faster than Canny but produce thicker, less clean edges.
Usage
Use Sobel for gradient magnitude computation when you need continuous edge strength (not binary). Use Laplacian for second-order edge detection. Both are building blocks for more complex algorithms.
Theoretical Basis
Sobel kernels approximate horizontal and vertical image gradients:
Gradient magnitude combines horizontal and vertical components:
The Laplacian kernel (3x3) approximates the second spatial derivative:
The Laplacian detects edges at zero-crossings of the second derivative, where the intensity transitions from increasing to decreasing or vice versa.
Sobel pseudocode:
gx = convolve(image, G_x)
gy = convolve(image, G_y)
magnitude = sqrt(gx^2 + gy^2)
Laplacian pseudocode:
edges = convolve(image, L)
edge_pixels = zero_crossings(edges)